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BEGIN:VEVENT
SUMMARY:Yoshinori Gongyo (The University of Tokyo)
DTSTART:20200423T160000Z
DTEND:20200423T170000Z
DTSTAMP:20260404T111216Z
UID:ZAG/1
DESCRIPTION:Title: On a generalized Batyrev's cone conjecture\nby Yoshinori Gongyo (Th
e University of Tokyo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\
nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Hacon (The University of Utah)
DTSTART:20200428T160000Z
DTEND:20200428T170000Z
DTSTAMP:20260404T111216Z
UID:ZAG/2
DESCRIPTION:Title: Recent progress in the MMP for 3-folds and 4-folds in char p>0\nby
Christopher Hacon (The University of Utah) as part of ZAG (Zoom Algebraic
Geometry) seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arnaud Beauville (Université de Nice)
DTSTART:20200430T150000Z
DTEND:20200430T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/3
DESCRIPTION:Title: Vector bundles on Fano threefolds and K3 surfaces\nby Arnaud Beauvi
lle (Université de Nice) as part of ZAG (Zoom Algebraic Geometry) seminar
\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chen Jiang (Shanghai Center for Mathematical Sciences\, Fudan Univ
ersity)
DTSTART:20200505T150000Z
DTEND:20200505T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/4
DESCRIPTION:Title: Minimal log discrepancies of 3-dimensional non-canonical singularities<
/a>\nby Chen Jiang (Shanghai Center for Mathematical Sciences\, Fudan Univ
ersity) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nCa
nonical and terminal singularities\, introduced by Reid\, appear naturally
in minimal model program and play important roles in the birational class
ification of higher dimensional algebraic varieties. Such singularities ar
e well-understood in dimension 3\, while the property of non-canonical sin
gularities is still mysterious. We investigate the difference between cano
nical and non-canonical singularities via minimal log discrepancies (MLD).
We show that there is a gap between MLD of 3-dimensional non-canonical si
ngularities and that of 3-dimensional canonical singularities\, which is p
redicted by a conjecture of Shokurov. This result on local singularities h
as applications to global geometry of Calabi–Yau 3-folds. We show that t
he set of all non-canonical klt Calabi–Yau 3-folds are bounded modulo fl
ops\, and the global indices of all klt Calabi–Yau 3-folds are bounded f
rom above.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Grushevsky (Stony Brook University)
DTSTART:20200507T180000Z
DTEND:20200507T190000Z
DTSTAMP:20260404T111216Z
UID:ZAG/5
DESCRIPTION:Title: Geometry of moduli of cubic threefolds\nby Samuel Grushevsky (Stony
Brook University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nA
bstract\nThe moduli space of cubic threefolds can be thought of as a GIT q
uotient of the projective space of all cubic polynomials\, studied via the
period map to a ball quotient\, or via the intermediate Jacobians. We des
cribe the relations between various compactifications of the moduli space
of cubic threefolds that arise in these ways\, and compute their cohomolog
y. Based on joint works with S. Casalaina-Martin\, K. Hulek\, R. Laza.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kristin De Vleming (University of California\, San Diego)
DTSTART:20200512T160000Z
DTEND:20200512T170000Z
DTSTAMP:20260404T111216Z
UID:ZAG/6
DESCRIPTION:Title: Wall crossing for K-moduli spaces of plane curves\nby Kristin De Vl
eming (University of California\, San Diego) as part of ZAG (Zoom Algebrai
c Geometry) seminar\n\n\nAbstract\nThis talk will focus on compactificatio
ns of the moduli space of smooth plane curves of degree d at least 4. We
will regard a plane curve as a log Fano pair (P2\, aC)\, where a is a rati
onal number\, and study the compactifications arising from K stability for
these pairs and log Fano pairs in general. We establish a wall crossing
framework to study these spaces as a varies and show that\, when a is smal
l\, the moduli space coming from K stability is isomorphic to the GIT modu
li space. We describe all wall crossings for degree 4\, 5\, and 6 plane c
urves and discuss the picture for general Q-Gorenstein smoothable log Fano
pairs. This is joint work with Kenneth Ascher and Yuchen Liu.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Christian Ottem (University of Oslo)
DTSTART:20200514T153000Z
DTEND:20200514T163000Z
DTSTAMP:20260404T111216Z
UID:ZAG/7
DESCRIPTION:Title: Tropical degenerations and stable rationality\nby John Christian Ot
tem (University of Oslo) as part of ZAG (Zoom Algebraic Geometry) seminar\
n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mircea Mustață (University of Michigan)
DTSTART:20200519T170000Z
DTEND:20200519T180000Z
DTSTAMP:20260404T111216Z
UID:ZAG/11
DESCRIPTION:Title: Minimal exponent and Hodge filtrations\nby Mircea Mustață (Unive
rsity of Michigan) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nA
bstract\nI will discuss an invariant of singularities\, Saito's minimal ex
ponent\, and its connections with various other invariants of singularitie
s. The minimal exponent is a refinement of the log canonical threshold tha
t can be used to also measure rational hypersurface singularities. This i
s based on joint work with Mihnea Popa.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zsolt Patakfalvi (École polytechnique fédérale de Lausanne)
DTSTART:20200526T170000Z
DTEND:20200526T180000Z
DTSTAMP:20260404T111216Z
UID:ZAG/12
DESCRIPTION:Title: On the Beauville-Bogomolov decomposition in positive characteristic\nby Zsolt Patakfalvi (École polytechnique fédérale de Lausanne) as pa
rt of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAbstract: I wi
ll present a joint with Maciej Zdanowicz towards a positive characteristic
version of the Beauville-Bogomolov decomposition. Over the complex number
s this decomposition was shown using differential geometry methods in the
70's and in the 80's. It concerns varieties with trivial canonical bundle\
, which we call K-trivial here. The main statement over the complex number
is that smooth projective K-trivial varieties admit an etale cover which
splits as a product of three types of varieties: abelian\, Calabi-Yau and
symplectic. I will present a similar statement in positive characteristic
for (weakly) ordinary K-trivial varieties\, the proof of which uses purely
positive characteristic methods.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xavier Roulleau (University of Aix-Marseille)
DTSTART:20200521T110000Z
DTEND:20200521T120000Z
DTSTAMP:20260404T111216Z
UID:ZAG/13
DESCRIPTION:Title: On the geometric models of K3 surfaces with finite automorphism group
and Picard number larger than two\nby Xavier Roulleau (University of A
ix-Marseille) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstra
ct\nVinberg and Nikulin classified K3 surfaces which have finite automorph
ism group and Picard number 4 and 3\,5\,..\,19 respectively. That classifi
cation is lattice theoretic\, according to the Neron-Severi group of these
surfaces\; there are 118 such lattices. In this talk I will discuss on th
e geometric construction of these surfaces (by double coverings or complet
e intersections) and describe their (finite) set of (-2)-curves\, which gi
ves the ample cone. Most of the moduli spaces of these K3 surfaces are uni
rational. A part of this talk is based on a joint work with Michela Arteba
ni and Claudia Correa Diesler.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Kuznetsova (Higher School of Economics)
DTSTART:20200528T140000Z
DTEND:20200528T150000Z
DTSTAMP:20260404T111216Z
UID:ZAG/18
DESCRIPTION:Title: Sextic double solids\nby Alexandra Kuznetsova (Higher School of Ec
onomics) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nA
bstract: One of the first examples of unirational non-rational threefold w
as provided by Artin and Mumford and it was a double cover of P^3 branched
in a nodal quartic surface\, so called quartic double solid.\nThen Endras
s studied this class of varieties and showed that the example by Artin and
Mumford gives a unique family of non-rational nodal quartic double solids
. I am going to tell about the next interesting class of threefolds --- no
dal sextic double solids. I will describe 4 families of them such that any
non-rational variety of this type lies in one of those families and expla
in the proof.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Schreieder (Leibniz University)
DTSTART:20200602T110000Z
DTEND:20200602T120000Z
DTSTAMP:20260404T111216Z
UID:ZAG/19
DESCRIPTION:Title: Equality in the Bogomolov-Miyaoka-Yau inequality in the non-general ty
pe case\nby Stefan Schreieder (Leibniz University) as part of ZAG (Zoo
m Algebraic Geometry) seminar\n\n\nAbstract\nWe classify all good minimal
models of dimension n and with vanishing Chern number $c_1^{n-2}c_2(X)=0$\
, which corresponds to equality in the Bogomolov-Miyaoka—Yau inequality
in the non-general type case. Here the most interesting case is that of Ko
daira dimension n-1\, where any minimal model is known to be good. Our res
ult solves completely a problem a Kollar. In dimension three\, our approac
h together with previous work of Grassi and Kollar also leads to a complet
e solution of a conjecture of Kollar\, asserting that on a minimal threefo
ld\, c_1c_2 is either zero or universally bounded away from zero. Joint wo
rk with Feng Hao.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Caucher Birkar (University of Cambridge)
DTSTART:20200604T130000Z
DTEND:20200604T140000Z
DTSTAMP:20260404T111216Z
UID:ZAG/20
DESCRIPTION:Title: Geometry of polarised varieties\nby Caucher Birkar (University of
Cambridge) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\
nI will talk about projective varieties polarised by ample divisors (or mo
re generally nef and big divisors) in particular from a birational geometr
y point of view\, and present some recent results in this direction.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Prokhorov (Moscow State University)
DTSTART:20200609T153000Z
DTEND:20200609T163000Z
DTSTAMP:20260404T111216Z
UID:ZAG/21
DESCRIPTION:Title: General elephants for 3-fold extremal contractions\nby Yuri Prokho
rov (Moscow State University) as part of ZAG (Zoom Algebraic Geometry) sem
inar\n\n\nAbstract\nI will discuss effective results on the classification
of extremal contractions in the 3-dimensional MMP. In particular\, I will
present some recent result based on joint work with Shigefumi Mori on the
existence of general elephants.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Zharkov (Kansas State University)
DTSTART:20200611T140000Z
DTEND:20200611T150000Z
DTSTAMP:20260404T111216Z
UID:ZAG/22
DESCRIPTION:Title: Topological SYZ fibrations with discriminant in codimension 2\nby
Ilya Zharkov (Kansas State University) as part of ZAG (Zoom Algebraic Geom
etry) seminar\n\n\nAbstract\nTo date only for K3 surfaces (trivial) and th
e quintic threefold (due to M. Gross) the discriminant can be made to be i
n codimension two. I will outline the source of the problem and how to res
olve it in much more general situations using phase and over-tropical pair
s-of-pants. Joint project with Helge Ruddat.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolaos Tziolas (University of Cyprus)
DTSTART:20200616T153000Z
DTEND:20200616T163000Z
DTSTAMP:20260404T111216Z
UID:ZAG/23
DESCRIPTION:Title: Vector fields on canonically polarized surfaces\nby Nikolaos Tziol
as (University of Cyprus) as part of ZAG (Zoom Algebraic Geometry) seminar
\n\n\nAbstract\nIn this talk I will present some results about the geomet
ry of canonically polarized surfaces defined over a field of positive char
acteristic which have a nontrivial global vector field\, equivalently non
reduced automorphism scheme\, and the implications that the existence of s
uch surfaces has in the moduli problem of canonically polarized surfaces.\
n
LOCATION:https://stable.researchseminars.org/talk/ZAG/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claire Voisin (Collège de France)
DTSTART:20200618T140000Z
DTEND:20200618T150000Z
DTSTAMP:20260404T111216Z
UID:ZAG/24
DESCRIPTION:Title: Triangle varieties and surface decomposition of hyper-Kahler manifolds
\nby Claire Voisin (Collège de France) as part of ZAG (Zoom Algebraic
Geometry) seminar\n\n\nAbstract\nIn recent years\, new constructions of c
omplete families of polarized hyper-Kahler manifolds have been found start
ing from Fano geometry. These hyper-Kahler manifolds also appear as genera
l deformations of Hilbert schemes of K3 surfaces or O'Grady manifolds. I w
ill introduce the notion of surface decomposition for a variety X with a n
ontrivial Hodge structure on degree 2 cohomology. I will show that this no
tion is restrictive topologically\, as it implies Beauville-Fujiki type re
lations. I will also show the existence of such a surface decomposition f
or the general hyper-Kahler manifolds mentioned above. This has interes
ting consequences on Beauville's conjecture on the Chow ring of hyper-Kahl
er manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Polishchuk (University of Oregon)
DTSTART:20200623T170000Z
DTEND:20200623T180000Z
DTSTAMP:20260404T111216Z
UID:ZAG/25
DESCRIPTION:Title: Hyperelliptic limits of quadrics through canonical curves and the supe
r-Schottky locus\nby Alexander Polishchuk (University of Oregon) as pa
rt of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will describe
joint works with Eric Rains and with Giovanni Felder and David Kazhdan. T
he first part will be about a classical topic of quadrics through canonica
lly embedded curves. We study limiting quadrics as canonical curves approa
ch a hyperelliptic limit. There is a surprizingly simple description of al
l such limits. I will also discuss the connection to ribbon curves (which
are thickenings of rational normal curves) and to the blow up of the modul
i space of curves at the hyperelliptic locus. In the second part I will ta
lk about the super-period map for supercurves and the calculation of its i
nfinitesimal variation. This variation is given by a natural Massey produc
t that can be defined for any curve with a theta-characteristic. Combining
this with the result of part 1 we get some information about the super-Sc
hottky locus.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Mumford (Harvard University and Brown University)
DTSTART:20200625T150000Z
DTEND:20200625T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/26
DESCRIPTION:Title: A moduli space in the differential geometry world\nby David Mumfor
d (Harvard University and Brown University) as part of ZAG (Zoom Algebraic
Geometry) seminar\n\n\nAbstract\nThe space of simple closed smooth plane
curves is an infinite dimensional manifold and supports a great diversity
of Riemannian metrics. They have very diverse curvature properties and eve
n include universal Teichmuller space. I want to talk in particular about
a recent example: modeling 2D waves in water (aka gravity waves) that some
believe explains so-called rogue waves.\nAfter the talk\, we plan to have
Q&A session at 16:00 GMT. If you have a question for Prof. Mumford\, let
Ivan Cheltsov know in advance (by e-mail).\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Izzet Coskun (University of Illinois at Chicago)
DTSTART:20200630T150000Z
DTEND:20200630T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/27
DESCRIPTION:Title: The stabilization of the cohomology of moduli spaces of sheaves on sur
faces\nby Izzet Coskun (University of Illinois at Chicago) as part of
ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nThe Betti numbers of
the Hilbert scheme of points on a smooth\, irreducible projective surface
have been computed by Gottsche. These numbers stabilize as the number of p
oints tends to infinity. In contrast\, the Betti numbers of moduli spaces
of semistable sheaves on a surface are not known in general. In joint work
with Matthew Woolf\, we conjecture these also stabilize and that the stab
le numbers do not depend on the rank. We verify the conjecture for large c
lasses of surfaces. I will discuss our conjecture and provide the evidence
for it.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Susanna Zimmermann (Université Angers)
DTSTART:20200702T100000Z
DTEND:20200702T110000Z
DTSTAMP:20260404T111216Z
UID:ZAG/28
DESCRIPTION:Title: Finite quotients of Cremona groups\nby Susanna Zimmermann (Univers
ité Angers) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstrac
t\nThe Cremona group is the group of birational self-maps of the projectiv
e space\, and it is very very big. While in dimension 2 over algebraically
closed fields there are no finite quotients of this group\, there are man
y such quotients over non-closed fields and in higher dimension. I will di
scuss why this is and how these quotients come up.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ziquan Zhuang (MIT)
DTSTART:20200707T170000Z
DTEND:20200707T180000Z
DTSTAMP:20260404T111216Z
UID:ZAG/29
DESCRIPTION:Title: K-stability of Fano varieties via admissible flags\nby Ziquan Zhua
ng (MIT) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI
'll present a general approach to prove the K-stability of explicit Fano v
arieties. Among the applications\, we confirm the existence of K\\"ahler-E
instein metrics on all smooth Fano hypersurfaces of Fano index two\, calcu
late the stability thresholds of some Fano varieties and provide a counter
example to the Higher Rank Finite Generation conjecture. Based on joint wo
rk with Hamid Ahmadinezhad.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harold Blum (University of Utah)
DTSTART:20200709T150000Z
DTEND:20200709T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/30
DESCRIPTION:Title: On properness of K-moduli spaces and destabilizations of Fano varietie
s\nby Harold Blum (University of Utah) as part of ZAG (Zoom Algebraic
Geometry) seminar\n\n\nAbstract\nK-stability is an algebraic notion that d
etects when a smooth Fano variety admits a Kahler-Einstein metric. Recentl
y\, there has been significant progress on constructing moduli spaces of K
-polystable Fano varieties using algebraic methods. One of the remaining o
pen problems is to show that these moduli spaces are proper. In this talk\
, I will discuss work with Daniel Halpern-Leistner\, Yuchen Liu\, and Chen
yang Xu\, in which we reduce the properness of such K-moduli spaces to the
existence of certain optimal destabilization of Fano varieties.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hélène Esnault (Freie Universität Berlin)
DTSTART:20200714T140000Z
DTEND:20200714T150000Z
DTSTAMP:20260404T111216Z
UID:ZAG/31
DESCRIPTION:Title: Density of arithmetic representations\nby Hélène Esnault (Freie
Universität Berlin) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\
nAbstract\nThe lecture surveys recent work with Moritz Kerz. The motivati
on is the conjecture that the Hard-Lefschetz (HL) property holds on smoot
h projective varieties defined over algebraically closed char. $p>0$ fiel
ds for cohomology with values in semi-simple $\\ell$-adic local systems $
V$. We know it is true if $V$ comes from geometry (Deligne\, Beilinson-Ber
nstein-Deligne-Gabber) by Deligne’s theory of weights. In absence of wei
ghts\, we proved it if $V$ has rank $1$ and reduced the whole HL conjectur
e to a density conjecture on arithmetic semi-simple $\\ell$-adic systems o
n $P^1$ minus $3$ closed points\, which we can prove in rank $2$.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Schuett (Leibniz Universität Hannover)
DTSTART:20200716T153000Z
DTEND:20200716T163000Z
DTSTAMP:20260404T111216Z
UID:ZAG/32
DESCRIPTION:Title: Rational curves on Enriques surfaces\, but only few\nby Matthias S
chuett (Leibniz Universität Hannover) as part of ZAG (Zoom Algebraic Geom
etry) seminar\n\n\nAbstract\nRational curves play a fundamental role for t
he structure of an Enriques surface. I will first review the general theor
y before focussing on the case of low degree rational curves. To this end\
, I will discuss joint work with S. Rams (Krakow) which develops an explic
it sharp bound on the number of rational curves of given degree relative t
o the degree of the surface. The proof builds on a general argument in par
allel to the case of K3 surfaces which allows us to extend bounds of Miyao
ka and Degtyarev.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jihun Park (POSTECH)
DTSTART:20200721T110000Z
DTEND:20200721T120000Z
DTSTAMP:20260404T111216Z
UID:ZAG/33
DESCRIPTION:Title: Cayley octads\, plane quartic curves\, Del Pezzo surfaces of degree 2
and double Veronese cones\nby Jihun Park (POSTECH) as part of ZAG (Zoo
m Algebraic Geometry) seminar\n\n\nAbstract\nA net of quadrics in the 3-di
mensional projective space whose singular members are parametrized by a sm
ooth plane quartic curve has exactly eight distinct base points\, called a
regular Cayley octad. It is a classical result that there is a one-to-o
ne correspondence between isomorphism classes of regular Cayley octads and
isomorphism classes of smooth plane quartic curves equipped with even the
ta-characteristics. We can also easily observe a one-to-one correspondenc
e between isomorphism classes of smooth plane quartic curves and isomorphi
sm classes of smooth Del Pezzo surfaces of degree 2. In this talk\, we set
up a one-to-one correspondence between isomorphism classes of smooth plan
e quartic curves and isomorphism classes of double Veronese cones with 28-
singular points. Also\, we explain how the 36 even theta characteristics o
f a given smooth quartic curve appear in the corresponding double Veronese
cone. This is a joint work with Hamid Ahmadinezhad\, Ivan Cheltsov and Co
nstantin Shramov.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruadhai Dervan (University of Cambridge)
DTSTART:20200723T150000Z
DTEND:20200723T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/34
DESCRIPTION:Title: Stability of fibrations\nby Ruadhai Dervan (University of Cambridg
e) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nThe not
ion of K-stability of a polarised variety has been heavily studied in rece
nt years\, due to its link both with moduli theory (one should be able to
form moduli spaces of K-stable varieties) and to Kahler geometry (K-stabil
ity should be equivalent to the existence of a constant scalar curvature K
ahler metric on the variety). This story has been particularly successful
for Fano varieties. I will describe a notion of stability for polarised fi
brations\, which generalises K-stability of polarised varieties when the b
ase of the fibration is a point\, and slope stability of a vector bundle w
hen the variety is the projectivisation of a vector bundle. I will specula
te that one should be able to form moduli spaces of stable fibrations\, mu
ch as one can form moduli spaces of slope stable vector bundles over a fix
ed base. The main result\, however\, will be a description of the link wit
h certain canonical metrics on fibrations. This is joint work with Lars Se
ktnan.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Pierre Demailly (Université Grenoble Alpes)
DTSTART:20200728T153000Z
DTEND:20200728T163000Z
DTSTAMP:20260404T111216Z
UID:ZAG/35
DESCRIPTION:Title: Hermitian-Yang-Mills approach to the conjecture of Griffiths on the po
sitivity of ample vector bundles\nby Jean-Pierre Demailly (Université
Grenoble Alpes) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbs
tract\nGiven a vector bundle of arbitrary rank with ample determinant line
bundle on a projective manifold\, we propose a new elliptic system of dif
ferential equations of Hermitian-Yang-Mills type for the curvature tensor.
The system is designed so that solutions provide Hermitian metrics with p
ositive curvature in the sense of Griffiths - and even in the stronger dua
l Nakano sense. As a consequence\, if an existence result could be obtaine
d for every ample vector bundle\, the Griffiths conjecture on the equival
ence between ampleness and positivity of vector bundles would be settled.
We also discuss a new concept of volume for vector bundles.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ziwen Zhu (University of Utah)
DTSTART:20200730T150000Z
DTEND:20200730T163000Z
DTSTAMP:20260404T111216Z
UID:ZAG/36
DESCRIPTION:Title: Equivariant K-stability under finite group action\nby Ziwen Zhu (U
niversity of Utah) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nA
bstract\nEquivariant K-stability is defined via equivariant test configura
tions. By definition it is weaker than the usual K-stability and for varie
ties with large symmetry\, it is often easier to check equivariant K-stabi
lity. For reductive group action\, it is conjectured that equivariant K-po
lystability implies K-polystability. In this talk\, I will discuss recent
results about equivariant K-stability and present a proof of the conjectur
e for finite group action. The talk is based on joint work with Yuchen Liu
.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamid Ahmadinezhad (Loughborough University)
DTSTART:20200804T140000Z
DTEND:20200804T150000Z
DTSTAMP:20260404T111216Z
UID:ZAG/37
DESCRIPTION:Title: Birational geometry of Fano 3-fold hypersurfaces of higher index\n
by Hamid Ahmadinezhad (Loughborough University) as part of ZAG (Zoom Algeb
raic Geometry) seminar\n\n\nAbstract\nI will speak about an approach to bi
rational classification of Fano 3-folds\, post MMP. As a part of this gene
ral guideline\, I will highlight some recent results about birational geom
etry of Fano hypersurfaces of higher index. The latter is a joint work wit
h Ivan Cheltsov and Jihun Park.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marina Logares (Universidad Complutense de Madrid)
DTSTART:20200806T150000Z
DTEND:20200806T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/38
DESCRIPTION:Title: Poisson and symplectic geometry of the moduli spaces of Higgs bundles<
/a>\nby Marina Logares (Universidad Complutense de Madrid) as part of ZAG
(Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will talk about some na
tural Poisson and symplectic properties of the moduli spaces of Higgs bund
les when some extra structure\, such as a framing\, is added. This is an o
verview of various past and ongoing work with I. Biswas\, J. Martens\, A.
Peón-Nieto and S. Szabó. I will not assume any previous knowledge on the
subject.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Lazarsfeld (Stony Brook University)
DTSTART:20200811T170000Z
DTEND:20200811T180000Z
DTSTAMP:20260404T111216Z
UID:ZAG/39
DESCRIPTION:Title: Cayley-Bacharach theorems and multiplier ideals\nby Robert Lazarsf
eld (Stony Brook University) as part of ZAG (Zoom Algebraic Geometry) semi
nar\n\n\nAbstract\nCayley-Bacharach theorems originate in the classical st
atement if two plane curves of degrees c and d meet in cd points\, then
any curve of degree (c + d - 3) passing through all but one of these point
s must also pass through the remaining one. Following work of Griffiths an
d Harris in the 1970s\, one now sees this as a special case of a general r
esult about zero-loci of sections of a vector bundle. I will explain how b
ringing multiplier ideals into the picture leads (for free) to a variant t
hat allows for excess vanishing. This is joint work with Lawrence Ein.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuchen Liu (Yale University)
DTSTART:20200813T150000Z
DTEND:20200813T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/40
DESCRIPTION:Title: On K-stability of cubic hypersurfaces\nby Yuchen Liu (Yale Univers
ity) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nK-sta
bility of Fano varieties is an algebro-geometric stability condition chara
cterizing the existence of K\\"ahler-Einstein metrics. Recent progress on
K-stability suggests that it provides a good moduli theory for Fano variet
ies. In this talk\, I will explain how K-moduli spaces can help us prove K
-stability of smooth cubic hypersurfaces in dimension at most 4\, using a
local-to-global volume comparison result. Part of this talk is based on jo
int work with Chenyang Xu.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Corti (Imperial College London)
DTSTART:20200818T170000Z
DTEND:20200818T180000Z
DTSTAMP:20260404T111216Z
UID:ZAG/41
DESCRIPTION:Title: Smoothing Gorenstein toric affine 3-folds\nby Alessio Corti (Impe
rial College London) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\
nAbstract\nI will state a conjecture on the smoothing components of the de
formation space\, and discuss one or more of the following topics: possibl
e strategies for proving it\, applications to the Fanosearch program\, glo
bal and higher dimensional analogs. The talk is based on a recent collabor
ation with Andrea Petracci and Matej Filip.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Pagani (University of Liverpool)
DTSTART:20200820T150000Z
DTEND:20200820T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/42
DESCRIPTION:Title: Classifying fine compactified universal Jacobians\nby Nicola Pagan
i (University of Liverpool) as part of ZAG (Zoom Algebraic Geometry) semin
ar\n\n\nAbstract\nWe introduce the notion of a fine compactified Jacobian
of a nodal curve\, as an arbitrary compact open subspace of the moduli spa
ce of rank-1 torsion-free simple sheaves. We show that fine compactified J
acobians correspond to a certain combinatorial datum\, which is obtained b
y only keeping track\, for all sheaves\, of (1) the locus where it fails t
o be locally free\, and (2) its multidegree. This notion generalizes to fl
at families of curves\, and so does its combinatorial counterpart. When th
e family is the universal family over the moduli space of curves\, we have
the following results: (a) in the absence of marked points\, we can fully
classify these combinatorial data and deduce that the only fine compactif
ied universal Jacobians are the classical ones (which were constructed by
Pandharipande and Simpson in the nineties) and (b) in the presence of mark
ed points there are exotic (and new) examples that cannot be obtained as c
ompactified universal Jacobians associated to a polarization. This is a jo
int work in progress with Jesse Kass.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Boehning (University of Warwick)
DTSTART:20200825T170000Z
DTEND:20200825T180000Z
DTSTAMP:20260404T111216Z
UID:ZAG/43
DESCRIPTION:Title: Rigid\, not infinitesimally rigid surfaces of general type with ample
canonical bundle\nby Christian Boehning (University of Warwick) as par
t of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn the talk I wi
ll report on work in progress\, joint with Roberto Pignatelli and Hans-Chr
istian von Bothmer\, that concerns the construction of surfaces of general
type with ample canonical bundle and Kuranishi space (and possibly also G
ieseker moduli space) a non-reduced point. The main tools are configuratio
ns of lines and their incidence schemes as well as the theory of abelian c
overs due to Pardini and others.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Berman (Chalmers University of Technology)
DTSTART:20200827T100000Z
DTEND:20200827T110000Z
DTSTAMP:20260404T111216Z
UID:ZAG/44
DESCRIPTION:Title: Kahler-Einstein metrics\, Archimedean Zeta functions and phase transit
ions\nby Robert Berman (Chalmers University of Technology) as part of
ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nWhile the existence o
f a unique Kahler-Einstein metrics on a canonically polarized manifold X w
as established already in the seventies there are very few explicit formul
as available (even in the case of complex curves!). In this talk I will gi
ve a non-technical introduction to a probabilistic approach to Kahler-Eins
tein metrics\, which\, in particular\, yields canonical approximations of
the Kahler-Einstein metric on X. The approximating metrics in question are
expressed as explicit period integrals and the conjectural extension to t
he case of a Fano variety leads to some intriguing connections with Zeta f
unctions and the theory of phase transitions in statistical mechanics.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jarod Alper (University of Washington)
DTSTART:20200903T170000Z
DTEND:20200903T180000Z
DTSTAMP:20260404T111216Z
UID:ZAG/46
DESCRIPTION:Title: Advances in moduli theory\nby Jarod Alper (University of Washingto
n) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nWe will
survey how recent advances in moduli theory allow for a new technique to
construct projective moduli spaces of objects with potentially non-finite
automorphism groups such as sheaves\, complexes or Fano varieties. We wi
ll primarily explore this technique through the lens of the moduli space o
f vector bundles over a smooth curve where the definitions and concepts ar
e most readily internalized. Time permitting\, we will discuss applicatio
ns to Bridgeland stability and perhaps how this construction technique\, w
hich works now only in characteristic zero\, can be generalized to positiv
e characteristic.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Höring (Université Côte d'Azur)
DTSTART:20200908T100000Z
DTEND:20200908T110000Z
DTSTAMP:20260404T111216Z
UID:ZAG/47
DESCRIPTION:Title: Fano manifolds such that the tangent bundle is (not) big\nby Andre
as Höring (Université Côte d'Azur) as part of ZAG (Zoom Algebraic Geome
try) seminar\n\n\nAbstract\nLet X be a Fano manifold. While the properties
of the anticanonical divisor -KX and its multiples have been studied by m
any authors\, the positivity of the tangent bundle TX is much more elusive
. We give a complete characterisation of the pseudoeffectivity of TX for d
el Pezzo surfaces\, hypersurfaces in the projective space and del Pezzo th
reefolds. This is joint work with Jie Liu and Feng Shao.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joaquín Moraga (Princeton University)
DTSTART:20200910T150000Z
DTEND:20200910T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/48
DESCRIPTION:Title: Topology and geometry of Kawamata log terminal singularities\nby J
oaquín Moraga (Princeton University) as part of ZAG (Zoom Algebraic Geome
try) seminar\n\n\nAbstract\nIn this talk\, we will discuss the topology of
Kawamata log terminal singularities. We show that from the perspective of
the fundamental group klt singularities are close to quotient singulariti
es. For instance\, the regional fundamental group of a klt singularity of
dimension n contains a normal abelian subgroup of rank at most n and index
at most c(n). Then\, we proceed to study geometric implications of the to
pology of klt singularities. We give a characterization theorem in the cas
e that the abelian part of the fundamental group is large of full rank.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Rana (Lawrence University)
DTSTART:20200915T150000Z
DTEND:20200915T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/49
DESCRIPTION:Title: Singularities and divisors in the moduli space of surfaces\nby Jul
ie Rana (Lawrence University) as part of ZAG (Zoom Algebraic Geometry) sem
inar\n\n\nAbstract\nThe KSBA moduli space of stable surfaces (surfaces wit
h slc singularities and ample canonical class) is a natural compactificati
on of Gieseker's moduli space of surfaces of general type. In contrast wit
h the moduli space of curves\, very little is known about the birational g
eometry of KSBA moduli spaces\; indeed\, there are very few examples of di
visors in KSBA moduli spaces. I will give an example of a divisor in the m
oduli space of quintic surfaces corresponding to surfaces with cyclic quot
ient singularities. I also discuss joint work with Giancarlo Urz\\'ua wher
e we give bounds that help to narrow the search.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthony Varilly-Alvarado (Rice University)
DTSTART:20200527T150000Z
DTEND:20200527T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/50
DESCRIPTION:Title: Rational curves on K3 surfaces\nby Anthony Varilly-Alvarado (Rice
University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Louis Colliot-Thelene (Université Paris-Sud)
DTSTART:20200922T140000Z
DTEND:20200922T150000Z
DTSTAMP:20260404T111216Z
UID:ZAG/51
DESCRIPTION:Title: Zero-cycles on del Pezzo surfaces\nby Jean-Louis Colliot-Thelene (
Université Paris-Sud) as part of ZAG (Zoom Algebraic Geometry) seminar\n\
n\nAbstract\nLet k be an arbitary field of characteristic zero and X be a
smooth\, projective\, geometrically rational surface. Birational classific
ation of such surfaces (over k) is due to Enriques\, Manin\, Iskovskikh\,
Mori. We are interested in zero-cycles on such surfaces. In 1974\, Daniel
Coray showed that on a smooth cubic surface X with a closed point of degr
ee prime to 3 there exists a closed point of degree 1\, 4 or 10. Whether 4
and 10 may be omitted is still an open question. We first show how a comb
ination of generisation\, specialisation\, Bertini theorems and "large" f
ields avoids considerations of special cases in Coray's argument. For smoo
th cubic surfaces X with a rational point\, we show that any zero-cycle of
degree at least 10 is rationally equivalent to an effective cycle. We est
ablish analogues of these results for del Pezzo surfaces X of degree 2 and
of degree 1. This completes the proof that for any geometrically rational
surface X with a rational point\, there exists an integer N which depend
s only on the geometry of the surface\, such that any zero-cycle of degre
e at least N is rationally equivalent to an effective zero-cycle. For smoo
th cubic surfaces X without a rational point\, we relate the question whet
her there exists a degree 3 point which is not on a line to the question w
hether rational points are dense on a del Pezzo surface of degree 1.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Thompson (Loughborough University)
DTSTART:20200924T150000Z
DTEND:20200924T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/52
DESCRIPTION:Title: Mirror symmetry for fibrations and degenerations\nby Alan Thompson
(Loughborough University) as part of ZAG (Zoom Algebraic Geometry) semina
r\n\n\nAbstract\nIn a 2004 paper\, Tyurin briefly hinted at a novel relati
onship between Calabi-Yau mirror symmetry and the Fano-LG correspondence.
More specifically\, if one can degenerate a Calabi-Yau manifold to a pair
of (quasi-)Fanos\, then one expects to be able to express the mirror Calab
i-Yau in terms of the corresponding Landau-Ginzburg models. Some details o
f this correspondence were worked out by C. F. Doran\, A. Harder\, and I i
n a 2017 paper\, but much remains mysterious. In this talk I will describe
recent attempts to better understand this picture\, and how it hints at a
broader mirror symmetric correspondence between degeneration and fibratio
n structures. As an example of this correspondence\, I will discuss the qu
estion of finding mirrors to certain exact sequences which describe the Ho
dge theory of degenerations. The material in this talk is joint work in pr
ogress with C. F. Doran.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Zarhin (Penn State University)
DTSTART:20200929T140000Z
DTEND:20200929T150000Z
DTSTAMP:20260404T111216Z
UID:ZAG/53
DESCRIPTION:Title: Jordan properties of automorphism groups of algebraic varieties and co
mplex manifolds\nby Yuri Zarhin (Penn State University) as part of ZAG
(Zoom Algebraic Geometry) seminar\n\n\nAbstract\nA classical theorem of J
ordan asserts that each finite subgroup of the complex general linear grou
p GL(n) is "almost commutative": it contains a commutative normal subgrou
p with index bounded by an universal constant that depends only on n. We d
iscuss an analogue of this property for the groups of birational (and bire
gular) automorphisms of complex algebraic varieties and the groups of bim
eromorphic automorphisms of compact complex manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Burt Totaro (UCLA)
DTSTART:20201001T160000Z
DTEND:20201001T170000Z
DTSTAMP:20260404T111216Z
UID:ZAG/54
DESCRIPTION:Title: The Hilbert scheme of points on affine space\nby Burt Totaro (UCLA
) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will d
iscuss the Hilbert scheme of d points in affine n-space\, with some exampl
es. This space has many irreducible components for n at least 3 and has be
en poorly understood. For n greater than d\, we determine the homotopy typ
e of the Hilbert scheme in a range of dimensions. Many questions remain. (
Joint with Marc Hoyois\, Joachim Jelisiejew\, Denis Nardin\, Maria Yakerso
n.)\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (MIT)
DTSTART:20201006T160000Z
DTEND:20201006T170000Z
DTSTAMP:20260404T111216Z
UID:ZAG/55
DESCRIPTION:Title: Cohomology of the moduli of Higgs bundles and the Hausel-Thaddeus conj
ecture\nby Junliang Shen (MIT) as part of ZAG (Zoom Algebraic Geometry
) seminar\n\n\nAbstract\nWe describe the cohomological structure of the mo
duli space of stable SL_n Higgs bundles on a curve following the topologic
al mirror symmetry conjecture of Hausel-Thaddeus. For the approach\, we es
tablish a connection between:\n(a) the moduli space of twisted Higgs bundl
es by an effective divisor of degree greater than 2g-2\, and\n(b) the modu
li space of K_C-Higgs bundles\,\nusing vanishing cycle functors. This allo
ws us to apply Ngo's support theorem\, which has a simpler form in the cas
e (a) (by Ngo\, Chaudouard-Laumon\, de Cataldo)\, to the case of (b) which
concerns hyper-Kähler geometries. In particular\, this gives a new proof
of the Hausel-Thaddeus conjecture proven previously by Gröchenig-Wyss-Zi
egler via p-adic integrations. Based on joint work with Davesh Maulik.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Logvinenko (Cardiff University)
DTSTART:20201008T153000Z
DTEND:20201008T163000Z
DTSTAMP:20260404T111216Z
UID:ZAG/56
DESCRIPTION:Title: Skein-triangulated representations of generalised braids\nby Timot
hy Logvinenko (Cardiff University) as part of ZAG (Zoom Algebraic Geometry
) seminar\n\n\nAbstract\nOrdinary braid group Br_n is a well-known algebra
ic structure which encodes configurations of n non-touching strands (“br
aids”) up to continious transformations (“isotopies”). A classical r
esult of Khovanov and Thomas states that there is a natural categorical ac
tion of Br_n on the derived category of the cotangent bundle of the variet
y of complete flags in C^n.\nIn this talk\, I will introduce a new structu
re: the category GBr_n of generalised braids. These are the braids whose s
trands are allowed to touch in a certain way. They have multiple endpoint
configurations and can be non-invertible\, thus forming a category rather
than a group. In the context of triangulated categories\, it is natural to
impose certain relations which result in the notion of a skein-triangulat
ed representation of GBr_n.\nA decade-old conjecture states that there a s
kein-triangulated action of GBr_n on the cotangent bundles of the varietie
s of full and partial flags in C^n. We prove this conjecture for n = 3. We
also show that any categorical action of Br_n can be lifted to a skein-tr
iangulated action of GBr_n\, which behaves like a categorical nil Hecke al
gebra. This is a joint work with Rina Anno and Lorenzo De Biase.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana-Maria Castravet (Université de Versailles St-Quentin-en-Yveli
nes)
DTSTART:20201013T140000Z
DTEND:20201013T150000Z
DTSTAMP:20260404T111216Z
UID:ZAG/57
DESCRIPTION:Title: Blown-up toric surfaces with non-polyhedral effective cone\nby Ana
-Maria Castravet (Université de Versailles St-Quentin-en-Yvelines) as par
t of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will report on
recent joint work with Antonio Laface\, Jenia Tevelev and Luca Ugaglia.\n
We construct examples of projective toric surfaces whose blow-up at a gene
ral point has a\nnon-polyhedral pseudoeffective cone\, both in characteris
tic 0 and in prime characteristic.\nAs a consequence\, we prove that the p
seudo-effective cone of the Grothendieck-Knudsen moduli space of stable\,
n-pointed\, rational stable curves\, is not polyhedral if\nn>=10 in chara
cteristic 0 and in positive characteristic for an infinite set of primes o
f positive density.\nIn particular\, these moduli spaces are not Mori drea
m spaces even in positive characteristic.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandra Di Rocco (KTH)
DTSTART:20201015T140000Z
DTEND:20201015T150000Z
DTSTAMP:20260404T111216Z
UID:ZAG/58
DESCRIPTION:Title: Algebraic Geometry of Data\nby Sandra Di Rocco (KTH) as part of ZA
G (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIt is often convenient
to visualise algebraic varieties (and hence systems of polynomial equation
s) by sampling. The key challenge is to have the right distribution and d
ensity in order to recover the shape\, i.e the topology of the variety. Bo
ttlenecks are pairs of points on the variety joined by a line which is nor
mal to the variety at both points. These points play a special role in det
ermining the appropriate density of a point-sample. Under suitable generic
ity assumptions the number of bottlenecks of an affine variety is finite a
nd we call it the bottleneck degree. We show that it is determined by (cla
ssical) invariants of the variety\, i.e. polar classes. The talk is based
on joint work with D. Eklund and M. Weinstein.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gergely Berczi (Aarhus University)
DTSTART:20201020T150000Z
DTEND:20201020T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/59
DESCRIPTION:Title: Non-reductive group actions and hyperbolicity\nby Gergely Berczi (
Aarhus University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nA
bstract\nNon-reductive reparametrisation group actions play central role i
n hyperbolicity questions. Using recently developed intersection theory on
non-reductive geometric invariant theory-type quotients and following the
strategy of Demailly\, Siu et al\, last year we completed a proof of the
Green-Griffiths-Lang and Kobayashi hyperbolicity conjectures for generic h
ypersurfaces of polynomial degree. We explain elements of the proof. Joint
work with F. Kirwan.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Mumford (Harvard University and Brown University)
DTSTART:20200625T160000Z
DTEND:20200625T170000Z
DTSTAMP:20260404T111216Z
UID:ZAG/60
DESCRIPTION:Title: Q&A with legendary geometers: David Mumford\nby David Mumford (Har
vard University and Brown University) as part of ZAG (Zoom Algebraic Geome
try) seminar\n\n\nAbstract\nQ&A with David Mumford (please\, no algebraic
geometry questions). If you want to ask a question you should e-mail it in
advance to i.cheltsov@ed.ac.uk\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Liedtke (Technical University of Munich)
DTSTART:20200917T150000Z
DTEND:20200917T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/61
DESCRIPTION:Title: Rational curves on K3 surfaces\nby Christian Liedtke (Technical Un
iversity of Munich) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n
Abstract\nWe prove that every complex projective K3 surface contains infin
itely rational curves\, which confirms a folklore conjecture on K3 surface
s. This was previously known for elliptic K3 surfaces (Bogomolov-Tschinkel
)\, for very general K3 surfaces (Chen)\, as well as for K3 surfaces of od
d Picard rank (Bogomolov-Hassett-Tschinkel\, Li-Liedtke). We finish this c
onjecture by introducing two new techniques: “regeneration” (a sort of
converse to degeneration) and the “marked point trick” (a technique f
or controlled degenerations)\, which allows to treat the missing cases. Th
is is joint work with Xi Chen and Frank Gounelas.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Borisov (Binghamton University)
DTSTART:20201022T150000Z
DTEND:20201022T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/62
DESCRIPTION:Title: Projective geometry approach to Jacobian Conjecture\nby Alexander
Borisov (Binghamton University) as part of ZAG (Zoom Algebraic Geometry) s
eminar\n\n\nAbstract\nacobian Conjecture is one of the oldest unsolved pro
blems in Algebraic Geometry\, going back to a 1939 paper by Keller. It is
infamous for the large number of incorrect proofs that have been proposed
over the years. In fact\, it is quite possible that the conjecture is fals
e\, especially in higher dimensions. For the past 10-15 years I have been
making slow but steady progress in understanding this enigma in dimension
two\, using classical methods of algebraic geometry of projective surfaces
and some inspiration from the Minimal Model Program. I will explain my ap
proach and where it has led me\, and will also discuss some related conjec
tures.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Greb (University of Duisburg-Essen)
DTSTART:20201027T160000Z
DTEND:20201027T170000Z
DTSTAMP:20260404T111216Z
UID:ZAG/63
DESCRIPTION:Title: Projective flatness over klt spaces and uniformisation of varieties wi
th nef anti-canonical divisor\nby Daniel Greb (University of Duisburg-
Essen) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI w
ill discuss a criterion for the projectivisation of a reflexive sheaf on a
klt space to be induced by a projective representation of the fundamental
group of the smooth locus. This criterion is then applied to give a chara
cterisation of finite quotients of projective spaces and Abelian varieties
by Q-Chern class (in)equalities and a suitable stability condition. This
stability condition is formulated in terms of a naturally defined extensio
n of the tangent sheaf by the structure sheaf. I will further examine case
s in which this stability condition is satisfied\, comparing it to K-semis
tability and related notions. This is joint work with Stefan Kebekus and T
homas Peternell.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junyan Cao (Université Côte d'Azur)
DTSTART:20201029T140000Z
DTEND:20201029T150000Z
DTSTAMP:20260404T111216Z
UID:ZAG/64
DESCRIPTION:Title: On the Ohsawa-Takegoshi extension theorem\nby Junyan Cao (Universi
té Côte d'Azur) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAb
stract\nAbstract: Since it was established\, the Ohsawa-Takegoshi extensio
n theorem turned out to be a fundamental tool in complex geometry. We esta
blish a new extension result for twisted canonical forms defined on a hype
rsurface with simple normal crossings of a projective manifold with a cont
rol on its L^2 norme. It is a joint work with Mihai Paun.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bianca Viray (University of Washington)
DTSTART:20201103T170000Z
DTEND:20201103T180000Z
DTSTAMP:20260404T111216Z
UID:ZAG/65
DESCRIPTION:Title: On quadratic points on intersections of two quadrics\nby Bianca Vi
ray (University of Washington) as part of ZAG (Zoom Algebraic Geometry) se
minar\n\n\nAbstract\nSpringer's theorem and the Amer-Brumer theorem togeth
er imply that intersections of two quadrics have a rational point if and o
nly if they have a 0-cycle of degree 1. In this talk\, we consider whethe
r this statement can be strengthened in the case when there is no rational
point\, namely when 1) the least degree of a 0-cycle can be 2\, and 2) wh
en this occurs\, whether there is an effective 0-cycle of degree 2. We re
port on results in this direction\, paying particular attention to the cas
e of local and global fields. This is joint work with Brendan Creutz.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristiano Spotti (Aarhus University)
DTSTART:20201105T130000Z
DTEND:20201105T140000Z
DTSTAMP:20260404T111216Z
UID:ZAG/66
DESCRIPTION:Title: Geometric aspects of Kaehler-Einstein metrics on klt pairs\nby Cri
stiano Spotti (Aarhus University) as part of ZAG (Zoom Algebraic Geometry)
seminar\n\n\nAbstract\nIn this talk I will discuss about the existence an
d geometric properties (e.g.\, tangent cones asymptotics\, metric degenera
tions\, etc...) of conical Kähler-Einstein metrics on klt pairs.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksandr Pukhlikov (University of Liverpool)
DTSTART:20201110T150000Z
DTEND:20201110T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/67
DESCRIPTION:Title: Rationally connected rational double covers of primitive Fano varietie
s\nby Aleksandr Pukhlikov (University of Liverpool) as part of ZAG (Zo
om Algebraic Geometry) seminar\n\n\nAbstract\nWe show that for a Zariski g
eneral hypersurface $V$ of degree $M+1$ in ${\\mathbb P}^{M+1}$ for $M\\ge
qslant 5$ there are no Galois rational covers $X\\dashrightarrow V$ with a
n abelian Galois group\, where $X$ is a rationally connected variety. In p
articular\, there are no rational maps $X\\dashrightarrow V$ of degree 2 w
ith $X$ rationally connected. This fact is true for many other families of
primitive Fano varieties as well and motivates a conjecture on absolute r
igidity of primitive Fano varieties.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jürgen Hausen (University of Tübingen)
DTSTART:20201112T160000Z
DTEND:20201112T170000Z
DTSTAMP:20260404T111216Z
UID:ZAG/68
DESCRIPTION:Title: Automorphisms of k*-surfaces\nby Jürgen Hausen (University
of Tübingen) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstra
ct\nAfter recalling the necessary background on k*-surfaces\, we give a co
mplete description of the automorhpism group of a non-toric rational norma
l projective k*-surface in terms of isotropy group orders and self interse
ction numbers of suitable invariant curves. We also discuss the basic ingr
edients and ideas of the proof.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michela Artebani (Universidad de Concepcion)
DTSTART:20201117T150000Z
DTEND:20201117T160000Z
DTSTAMP:20260404T111216Z
UID:ZAG/69
DESCRIPTION:Title: Cox rings of K3 surfaces\nby Michela Artebani (Universidad de Conc
epcion) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nGi
ven a normal complex projective variety X with finitely generated divisor
class group\, its Cox ring R(X) is the Cl(X)-graded algebra whose homogene
ous pieces are Riemann-Roch spaces of divisors of X. This object is partic
ularly interesting when it is finitely generated\, since in such case X ca
n be obtained as a GIT quotient of an open subset of Spec R(X) by the acti
on of a quasi-torus [1]. Finding a presentation or even a minimal generati
ng set for R(X) is in general a difficult problem\, already in the case of
surfaces. In this talk\, after an introduction to the subject\, we will c
oncentrate on complex projective K3 surfaces\, which are known to have fin
itely generated Cox ring exactly when their automorphism group is finite [
2]. We show that the Cox ring can be generated by homogeneous elements who
se degrees are either classes of (-2)-curves\, sums of at most three eleme
nts in the Hilbert basis of the nef cone\, or classes of divisors of the f
orm 2(E+E')\, where E\,E' are elliptic curves with E.E'=2. As an applicati
on\, we compute Cox rings of Mori dream K3 surfaces of Picard number 3 and
4. This is joint work with C. Correa Deisler\, A. Laface and X. Roulleau
[3\,4].\n\nReferences.\n[1] I. Arzhantsev\, U. Derenthal\, J. Hausen\, and
A. Laface\, Cox rings\, Cambridge Studies in Advanced Mathematics\, vol.
144\, Cambridge University Press\, Cambridge\, 2015.\n[2] M. Artebani\, J.
Hausen\, and A. Laface\, On Cox rings of K3 surfaces\, Compos. Math. 146
(2010)\, no. 4\, 964–998. arXiv:0901.0369\n[3] M. Artebani\, C. Correa D
eisler\, and A. Laface\, Cox rings of K3 surfaces of Picard number three\,
J. Algebra 565C (2021)\, 598–626. arXiv:1909.01267\n[4] M. Artebani\, C
. Correa Deisler\, and X. Roulleau\, Mori dream K3 surfaces of Picard numb
er four: projective models and Cox rings. arXiv:2011.00475.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yukari Ito (Kavli IPMU)
DTSTART:20201119T100000Z
DTEND:20201119T110000Z
DTSTAMP:20260404T111216Z
UID:ZAG/70
DESCRIPTION:Title: The McKay correspondence\nby Yukari Ito (Kavli IPMU) as part of ZA
G (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nThe original McKay corr
espondence was observed by John McKay as a correspondence between a finite
subgroup G of SL(2\,C) and simple Lie algebra in representation theory an
d developed as a correspondence between the group G and the minimal resolu
tion of the quotient singularity C^2/G in algebraic geometry. In this talk
\, I will introduce the McKay correspondence in dimension three and show r
ecent progress and open problems.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kazushi Ueda (University of Tokyo)
DTSTART:20201124T100000Z
DTEND:20201124T110000Z
DTSTAMP:20260404T111216Z
UID:ZAG/71
DESCRIPTION:Title: Noncommutative del Pezzo surfaces\nby Kazushi Ueda (University of
Tokyo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAbs
tract: We introduce the notion of noncommutative del Pezzo surfaces\, and
show that a collection of 12-d general vector bundles of certain ranks and
degrees on an elliptic curve produces a noncommutative del Pezzo surface
of degree d. We also define the moduli stack of marked noncommutative del
Pezzo surfaces\, and show that it contains the configuration space of 9-d
points in general position on the projective plane as a locally closed sub
stack. This is a joint work in progress with Tarig Abdelgadir and Shinnosu
ke Okawa.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuji Odaka (Kyoto University)
DTSTART:20201126T100000Z
DTEND:20201126T110000Z
DTSTAMP:20260404T111216Z
UID:ZAG/72
DESCRIPTION:Title: On compactifying moduli and degenerations of K-trivial varieties\n
by Yuji Odaka (Kyoto University) as part of ZAG (Zoom Algebraic Geometry)
seminar\n\n\nAbstract\nSome background review: the KSBA moduli of varietie
s of ample canonical classes is interpreted via K-stability resp.\, KE met
rics (O’10\, resp.\, Berman-Guenancia’13). A recent trend since 2012 i
s to establish its Fano analogue\, and study their K-stability itself\, wh
ich still continues to be developed by more and more contributors wonderfu
lly. Luckily\, in both cases\, K-polystable / KE varieties (should) form p
rojective (compact) moduli schemes.\nHowever\, nevertheless of general K-m
oduli expectation\, such existence of projective moduli of K-polystable/cs
cK (polarized) varieties is NOT true “at the boundary”\, even for clas
sical K-trivial / Calabi-Yau cases. Indeed\, as a general theory\, no “c
anonical” algebro-geometric compactification theory of moduli of polariz
ed CY vars seems established. E.g. An idea pursued and fairly developed is
to attach ample extra divisors on the CY vars (to pass to “K:ample”-l
ike situations) and take their “log KSBA” compactifications\, but diff
erent choice of the extra divisors can lead to different log KSBA compacti
fications.\nIn our talk\, based on our several recent papers (partially j.
w.w. Yoshiki Oshima)\, we discuss the possibilities of still getting “ca
nonical (geometric) compactifications” of the moduli of polarized K-tri
vial / CY varieties and corresponding "canonical limits"\, especially giv
ing more explicit conjectures in hyperKahler / K3 case\, with certain conf
irmations. This involves not only classical AG but also DG of collapsing C
Y metrics\, symmetric space theory (Lie\, Cartan\, .. Satake..)\, non-arch
imedean/tropical geometry\, and some mirror symmetric phenomena. Examples
and pictures will be used for the illustration.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takuzo Okada (Saga University)
DTSTART:20201201T100000Z
DTEND:20201201T110000Z
DTSTAMP:20260404T111216Z
UID:ZAG/73
DESCRIPTION:Title: K-stability of birationally superrigid Fano 3-fold weighted hypersurfa
ces\nby Takuzo Okada (Saga University) as part of ZAG (Zoom Algebraic
Geometry) seminar\n\n\nAbstract\nFor Fano varieties\, birational superrigi
dity and K-stability are completely different notions. On the other hand\,
they are both related to mildness of singularities of (pluri-)anticanonic
al divisors/systems. In fact\, it is conjectured that a birational superri
gid Fano variety is K-stable. In my talk I will explain recent results tha
t give a positive answer to the conjecture for Fano 3-fold weighted hypers
urfaces. This is a joint work with In-Kyun Kim and Joonyeong Won.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hulya Arguz (Versailles Saint-Quentin-en-Yvelines University)
DTSTART:20201203T130000Z
DTEND:20201203T140000Z
DTSTAMP:20260404T111216Z
UID:ZAG/74
DESCRIPTION:Title: Enumerating punctured log Gromov-Witten invariants from wall-crossing<
/a>\nby Hulya Arguz (Versailles Saint-Quentin-en-Yvelines University) as p
art of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nPunctured log
Gromov—Witten invariants of Abramovich—Chen--Gross—Siebert are obtai
ned by counting of stable maps with prescribed tangency conditions (which
are allowed to be negative) relative to a not necessarily smooth divisor.
In this talk we describe an algorithmic method to compute punctured log Gr
omov-Witten invariants of log Calabi-Yau varieties\, which are obtained by
blowing-up of toric varieties along hypersurfaces on the toric boundary.
For this we use tropical geometry and wall-crossing computations. This is
joint work with Mark Gross (arxiv:2007.08347).\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keiji Oguiso (University of Tokyo)
DTSTART:20201208T110000Z
DTEND:20201208T120000Z
DTSTAMP:20260404T111216Z
UID:ZAG/75
DESCRIPTION:Title: Smooth projective rational varieties with non-finitely generated discr
ete automorphism group\nby Keiji Oguiso (University of Tokyo) as part
of ZAG (Zoom Algebraic Geometry) seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artan Sheshmani (Harvard University Center for Mathematical scienc
es and Applications)
DTSTART:20201210T150000Z
DTEND:20201210T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/76
DESCRIPTION:Title: DT invariants from Gerstenhaber-BV structures\, and degeneration techn
ique\nby Artan Sheshmani (Harvard University Center for Mathematical s
ciences and Applications) as part of ZAG (Zoom Algebraic Geometry) seminar
\n\n\nAbstract\nWe discuss Donaldson-Thomas (DT) invariants of torsion she
aves with 2 dimensional support on a smooth projective surface in an ambie
nt non-compact Calabi Yau fourfold given by the total space of a rank 2 bu
ndle on the surface. We prove that in certain cases\, when the rank 2 bund
le is chosen appropriately\, the universal truncated Atiyah class of these
codimension 2 sheaves reduces to one\, defined over the moduli space of s
uch sheaves realized as torsion codimension 1 sheaves in a noncompact divi
sor (threefold) embedded in the ambient fourfold. Such reduction property
of universal Atiyah class enables us to relate our fourfold DT theory to a
reduced DT theory of a threefold and subsequently then to the moduli spac
es of sheaves on the base surface. We finally make predictions about modul
arity of such fourfold invariants when the base surface is an elliptic K3.
There are connections between these invariants and birational properties
of the base surface which we will discuss if time permits.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sho Tanimoto (Kumamoto University)
DTSTART:20201215T110000Z
DTEND:20201215T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/77
DESCRIPTION:Title: Rational curves on Fano threefolds\nby Sho Tanimoto (Kumamoto Univ
ersity) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nMo
ri proved that a smooth Fano variety contains a lots of rational curves us
ing famous Bend and Break technique. Thus it is natural to study the space
of rational curves on a smooth Fano variety. Lines and conics on Fano thr
eefolds are well studied\, and one may ask what one can say about higher d
egree rational curves. Recently we established Movable Bend and Break for
Fano threefolds claiming that any free curve of high degree breaks into th
e union of two free curves. A proof is intricate\, and it relies on many p
roperties of three dimensional MMP such as Mori’s classification of divi
sorial contractions on smooth projective threefolds. In this talk I would
like to explain some aspects of our proof of Movable Bend and Break as wel
l as an application to Batyrev’s conjecture predicting a polynomial grow
th of the number of components of bounded degree for the moduli space of r
ational curves. If time permits\, then I also explain a relation of our st
udy to Geometric Manin’s conjecture which is an inspiration of our study
. This is joint work with Roya Beheshti\, Brian Lehmann\, and Eric Riedl.\
n
LOCATION:https://stable.researchseminars.org/talk/ZAG/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Harder (Lehigh University)
DTSTART:20201217T160000Z
DTEND:20201217T170000Z
DTSTAMP:20260404T111217Z
UID:ZAG/78
DESCRIPTION:Title: Log symplectic pairs and mixed Hodge structures\nby Andrew Harder
(Lehigh University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n
Abstract\nA log symplectic pair is a pair (X\,Y) consisting of a smooth pr
ojective variety X and a divisor Y in X so that there is a non-degenerate
log 2-form on X with poles along Y. I will discuss the relationship betwee
n log symplectic pairs and degenerations of hyperkaehler varieties\, and h
ow this naturally leads to a class of log symplectic pairs called log symp
lectic pairs of "pure weight". I will talk about common properties of coho
mology rings of log symplectic pairs of pure weight and type III degenerat
ions of hyperkaehler varieties\, in particular\, the fact that both have t
he curious hard Lefschetz' (CHL) property discovered by Hausel and Rodrigu
ez-Villegas. Finally I will discuss partial results towards proving that i
n both of these cases\, the CHL property is a consequence of P=W type resu
lts. Part of this is based on work with Li\, Shen\, and Yin.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Han-Bom Moon (Fordham University)
DTSTART:20201222T150000Z
DTEND:20201222T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/79
DESCRIPTION:Title: Point configurations\, phylogenetic trees\, and dissimilarity vectors<
/a>\nby Han-Bom Moon (Fordham University) as part of ZAG (Zoom Algebraic G
eometry) seminar\n\n\nAbstract\nIn 2004 Pachter and Speyer introduced the
dissimilarity maps for phylogenetic trees and asked two important question
s about their relationship with tropical Grassmannian. Multiple authors an
swered affirmatively the first of these questions\, showing that dissimila
rity vectors lie on the tropical Grassmannian\, but the second question\,
whether the set of dissimilarity vectors forms a tropical subvariety\, rem
ained opened. In this talk\, we present a weighted variant of the dissimil
arity map and show that weighted dissimilarity vectors form a tropical sub
variety of the tropical Grassmannian in exactly the way that Pachter-Speye
r envisioned. This tropical variety has a geometric interpretation in term
s of point configurations on rational normal curves. This is joint work wi
th Alessio Caminata\, Noah Giansiracusa\, and Luca Schaffler.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hokuto Uehara (Tokyo Metropolitan University)
DTSTART:20201224T100000Z
DTEND:20201224T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/80
DESCRIPTION:Title: Exceptional collections on the Hilzebruch surface of degree 2\nby
Hokuto Uehara (Tokyo Metropolitan University) as part of ZAG (Zoom Algebra
ic Geometry) seminar\n\n\nAbstract\nThe purpose of my talk is to clarify t
he structure of exceptional collections of the derived category of coheren
t sheaves on the Hirzebruch surface of degree 2 (a special weak del Pezzo
surface)\, to the extent it is understood by Orlov and Kuleshov for del Pe
zzo surfaces.\n (1) First\, we prove that for any exceptional object in it
\, one can find an autoequivalence which sends it to an exceptional vector
bundle.\nThis result was conjectured by Shinnosuke Okawa and the speaker
in 2015.\n (2) Refining the method of the proof of the above result\, and
based on a deformation argument\, we prove that the braid group on 4 stran
ds acts transitively (up to shifts) on the set of exceptional collections
of length 4. This is a special case of an old conjecture by Bondal and Pol
ishchuk.\n (3) We also prove that any exceptional collection can be extend
ed to a full exceptional collection.\nMy talk is based on a joint work wit
h Shinnosuke Okawa (Osaka) and Akira Ishii (Nagoya).\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingjun Han (Johns Hopkins University)
DTSTART:20201229T150000Z
DTEND:20201229T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/81
DESCRIPTION:Title: The ACC for local volumes and boundedness of singularities\nby Jin
gjun Han (Johns Hopkins University) as part of ZAG (Zoom Algebraic Geometr
y) seminar\n\n\nAbstract\nKawamata log terminal (klt) singularities form a
n important class of singularities due to its fundamental roles in MMP\, K
\\”ahler-Einstein geometry\, and K-stability. Recently\, Chi Li introduc
ed a new invariant called the local volume of a klt singularity which enco
des lots of interesting geometric and topological information. A folklore
conjecture predicts that local volumes satisfy the ascending chain conditi
on (ACC) when the coefficients of the boundary divisors belong to a DCC se
t. In this talk\, we will show the ACC conjecture for local volumes holds
when the ambient variety is fixed. We will also explore the relation betwe
en log canonical thresholds\, local volumes\, and delta-plt blow-ups. This
is based on ongoing joint work with Yuchen Liu and Lu Qi.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiromichi Takagi (Gakushuin University)
DTSTART:20210107T100000Z
DTEND:20210107T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/84
DESCRIPTION:Title: Key varieties for prime Q-Fano threefolds of codimension 4\nby Hir
omichi Takagi (Gakushuin University) as part of ZAG (Zoom Algebraic Geomet
ry) seminar\n\n\nAbstract\nI talk about my construction of key varieties f
or prime Q-Fano threefolds of codimension 4 related with (P^2)^2-fibration
s.I discuss their relations with the cluster variety constructed by Coughl
an and Ducat.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patricio Gallardo (UC Riverside)
DTSTART:20210112T180000Z
DTEND:20210112T190000Z
DTSTAMP:20260404T111217Z
UID:ZAG/85
DESCRIPTION:Title: Compactifications of the moduli space of cubic surfaces\nby Patric
io Gallardo (UC Riverside) as part of ZAG (Zoom Algebraic Geometry) semina
r\n\n\nAbstract\nWe discuss the interplay between geometric and Hodge theo
retical compactifications for the moduli space of cubic surfaces. In parti
cular\, we prove that Naruki's compactification is toroidal and has a modu
lar interpretation in terms of stable pairs. This last is joint work with
Matt Kerr and Luca Schaffler. If time allows\, we will describe open que
stions and ongoing generalizations of such a relationship to the case of p
airs involving cubic surfaces and their anticanonical divisors.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiromu Tanaka (University of Tokyo)
DTSTART:20210114T100000Z
DTEND:20210114T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/86
DESCRIPTION:Title: On Mori fibre spaces in positive characteristic\nby Hiromu Tanaka
(University of Tokyo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n
\nAbstract\nThe minimal model program conjecture predicts that any algebra
ic variety is birational to either a minimal model or a Mori fibre space.\
nIn this talk\, we first summarise some results on Mori fibre spaces in po
sitive characteristic.\nWe also discuss some open problems related to this
topic.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shihoko Ishii (University of Tokyo)
DTSTART:20210119T090000Z
DTEND:20210119T100000Z
DTSTAMP:20260404T111217Z
UID:ZAG/87
DESCRIPTION:Title: Uniform bound of the number of weighted blow-ups to compute the minima
l log discrepancy for smooth 3-folds\nby Shihoko Ishii (University of
Tokyo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn
the talk I will show that the minimal log discrepancy of every pair consis
ting of a smooth 3-fold and a "general" real ideal is computed by the divi
sor obtained by at most two weighted blow ups.\n\nOur proof suggests the
following conjecture:\n\nEvery pair consisting of a smooth N-fold and a ``
general” real ideal is computed by a divisor obtained by at most N-1 wei
ghted blow ups.\n\nThis is regarded as a weighted blow up version of Musta
ta-Nakamura’s conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osamu Fujino (Osaka University)
DTSTART:20210121T100000Z
DTEND:20210121T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/88
DESCRIPTION:Title: On extremal contractions of log canonical pairs\nby Osamu Fujino (
Osaka University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAb
stract\nThe cone and contraction theorem holds for projective log canonica
l pairs. Let us consider an extremal contraction morphism of a log canonic
al pair. We prove that every irreducible component of the exceptional locu
s is uniruled. This result was first proved by Yujiro Kawamata for kawamat
a log terminal pairs. His proof uses a relative Kawamata--Viehweg vanishin
g theorem for projective bimeromorphic morphisms of complex analytic space
s and does not work for log canonical pairs. Our approach is based on the
theory of quasi-log schemes and can be applied to more general settings. W
e need a semipositivity theorem coming from the theory of variations of mi
xed Hodge structure. We note that we do not use the minimal model program.
\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frances Kirwan (University of Oxford)
DTSTART:20210126T140000Z
DTEND:20210126T150000Z
DTSTAMP:20260404T111217Z
UID:ZAG/89
DESCRIPTION:Title: Moduli of unstable objects in algebraic geometry\nby Frances Kirwa
n (University of Oxford) as part of ZAG (Zoom Algebraic Geometry) seminar\
n\n\nAbstract\nThe construction of the moduli spaces of stable curves of f
ixed genus is one of the classical applications of Mumford's geometric inv
ariant theory (GIT)\, developed in the 1960s\; many other moduli spaces of
'stable' objects can be constructed using GIT\, as well as in other ways.
The aim of this talk is to explain how recent methods from a version of G
IT for non-reductive group actions can help us to use suitable 'stability
conditions' to stratify moduli stacks into locally closed strata such that
not only the open 'stable' strata but also the 'unstable' strata have coa
rse moduli spaces. In the case of moduli stacks of bundles over a nonsingu
lar projective curve\, these stratifications refine the stratification by
Harder-Narasimhan type. The talk is based on joint work with Gergely Bercz
i\, Vicky Hoskins and Joshua Jackson.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabrizio Catanese (University of Bayreuth)
DTSTART:20210128T140000Z
DTEND:20210128T150000Z
DTSTAMP:20260404T111217Z
UID:ZAG/90
DESCRIPTION:Title: Varieties of nodal surfaces\, Coding theory\, and cubic discriminants<
/a>\nby Fabrizio Catanese (University of Bayreuth) as part of ZAG (Zoom Al
gebraic Geometry) seminar\n\n\nAbstract\nNodal Hypersurfaces Y in project
ive space are those whose singularities have nondegenerate Hessian. \nBas
ic numerical invariants are the dimension n and the degree d of the hype
rsurface Y\, and the number \\nu of singular points. \nIf you fix those i
ntegers (n\, d\,\\nu) these hypersurfaces are parametrized by the so-call
ed Nodal Severi varieties F(n\, d\, \\nu). \nThe first basic questions co
ncerning them are: \n1) for which triples is F(n\, d\, \\nu) nonempty ? \
n2) When is it irreducible ? \n\nAlready intriguing is the situation for s
urfaces\, indeed for n=2 the answer to 1) is known for d <= 6\, also the m
aximal number of nodes \\mu (d) that a nodal surface in 3-space of degree
d can have is known only for d <= 6.\n\nThe known maximizing nodal surfa
ces (those with \\mu(d) nodes) are: the Cayley cubic\, the Kummer quartic
surfaces\, the Togliatti quintics\, the Barth sextic.\n\nAn important chap
ter in Coding theory is the theory of binary linear codes\, vector subspac
es of a vector space (Z/2)^n.\n\nI will recall basic notions and methods
of coding theory (e.g. the McWilliams identities) and describe some codes
related to quadratic forms. \n\nNodal surfaces are related to coding theo
ry via the first homology of their smooth part: it is a binary code K\, w
hich was used by Beauville to show that\, for d=5 \, \\mu(d) = 31. Coding
theory was also crucial in order to prove that \\mu(6) < = 65. \n\nOur ma
in results concern the cases d = 4\,5\,6 (d=2\,3 being elementary). \n\nTH
M 1. For d=4 the components of F(4\, \\nu) and their incidence correspond
ence are determined by their extended codes K’\, which are all the shor
tenings of the first Reed Muller code.\n\nWe extend this result to nodal K
3 surfaces of all degrees\, this sheds light on the case d=5.\n\nTHM 2.
For d=5 the codes K occurring are classified\, up to a possible exceptio
n. F(5\, \\nu) is irreducible for \\nu = 31\, and for \\nu = 29\,30\,31 th
ese surfaces are discriminants of the projection of a cubic hypersurface
in 5-space. \n\nTHM 3. For d=6 and \\nu = 65 the codes K\, K’ are uni
quely determined\, and can be described explicitly via the Doro-Hall grap
h\, attached to the group \\SigmaL(2\, 25)\, and the geometry of the Barth
sextic. Every 65 nodal sextic occurs as discriminant of the projection o
f a cubic hypersurface in 6-space with < = 33 nodes.\n\n\nIrreducibilit
y for d=6\, and 65 nodes\, is related to the geometry of nodal cubic hype
rsurfaces in n-space\, and of the linear subspaces contained in them.\n\nW
e pose the question whether\, in the case of even dimension n\, the cubic
hypersurface with maximal number of singularities is\nprojectively equiva
lent to the Segre cubic s_1=s_3=0 (which is locally rigid).\n\nFor theorem
2 I benefited of the cooperation of Sandro Verra\, for theorem 3 of Yon
ghwa Cho\, Michael Kiermaier\, Sascha Kurz and the Linux Cluster of the U
niversitaet Bayreuth\, while Davide Frapporti and Stephen Coughlan coope
rated for the geometry of nodal cubic hypersurfaces.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Donaldson (Imperial College London and Simons Center for Geo
metry and Physics)
DTSTART:20210202T150000Z
DTEND:20210202T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/91
DESCRIPTION:Title: Enumerative geometry\, Fredholm analysis and moduli spaces of surfaces
of general type\nby Simon Donaldson (Imperial College London and Simo
ns Center for Geometry and Physics) as part of ZAG (Zoom Algebraic Geometr
y) seminar\n\n\nAbstract\nIn the first part of the talk we will review som
e background in deformation theory\, comparing the points of view from al
gebraic geometric and differential geometry/global analysis. We will revie
w in outline some known established examples in which a "virtual fundament
al class" of a moduli space can be defined. In the second part of the talk
we will explore the possibility that these ideas can be applied to moduli
spaces of surfaces of general type using the KSBA compactification. We wi
ll make some standard observations about these moduli spaces\, whose dimen
sion often differs from the virtual dimension. We will illustrate the disc
ussion by a calculation in the case of sextic surfaces with a particular f
inite symmetry group.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shinnosuke Okawa (Osaka University)
DTSTART:20210204T110000Z
DTEND:20210204T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/92
DESCRIPTION:Title: Moduli space of semiorthogonal decompositions\nby Shinnosuke Okawa
(Osaka University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n
Abstract\nSemiorthogonal decomposition (SOD) of triangulated categories is
quite interesting and of fundamental importance for various reasons. For
example\, SOD of the derived category of coherent sheaves is closely relat
ed to the geometry of varieties\, such as the minimal model program (MMP)
among others. It is therefore desirable to understand the general properti
es of SODs\, partly so as to classify SODs of as many triangulated categor
ies as possible. The purpose of this talk is to explain certain moduli spa
ces of SODs which we introduced. To a smooth projective morphism of excell
ent schemes f: X \\to B\, we associate an algebraic space over B which cla
ssifies the SODs of the derived categories of the fibers of f. We will dis
cuss properties and various aspects of this moduli space including applica
tions\, comparison to MMP\, and open problems.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrica Floris (Université de Poitiers)
DTSTART:20210209T110000Z
DTEND:20210209T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/93
DESCRIPTION:Title: Connected algebraic groups acting on Fano fibrations over $\\mathbb P^
1$\nby Enrica Floris (Université de Poitiers) as part of ZAG (Zoom Al
gebraic Geometry) seminar\n\n\nAbstract\nLet G be a connected algebraic gr
oup and X a variety endowed with a regular action of G and a Mori fibre sp
ace X/P1 whose fibre is a Fano variety of Picard rank at least 2. In this
talk I will explain why there is a proper horizontal subvariety of X which
is invariant under the action of G\, alongside with some applications of
this result to the classification of connected algebraic subgroups of the
Cremona group in dimension 4. This is a joint work with Jeremy Blanc.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasso de Fernex (University of Utah)
DTSTART:20210211T180000Z
DTEND:20210211T190000Z
DTSTAMP:20260404T111217Z
UID:ZAG/94
DESCRIPTION:Title: Motivic integration on Berkovic spaces\nby Tomasso de Fernex (Univ
ersity of Utah) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbst
ract\nThe purpose of the talk is to offer a new perspective on motivic int
egration. Working over a field with trivial norm\, I will introduce a moti
vic measure on the Berkovich analytification of an algebraic variety and d
efine integration in this setting. The construction is geometric with a si
milar spirit as Kontsevich’s original definition\, and leads to the form
ulation of a functorial theory which mirrors\, in this aspect\, the functo
riality of Cluckers and Loeser's approach via constructible motivic functi
ons. The approach does not rely on model theory but rather on geometric pr
operties such as resolution of singularities and the weak factorization th
eorem. The talk is based on joint work with Chung Ching Lau.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusuke Nakamura (University of Tokyo)
DTSTART:20210216T110000Z
DTEND:20210216T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/95
DESCRIPTION:Title: Inversion of adjunction for quotient singularities\nby Yusuke Naka
mura (University of Tokyo) as part of ZAG (Zoom Algebraic Geometry) semina
r\n\n\nAbstract\nThe minimal log discrepancy is an invariant of singularit
ies defined in birational geometry\, and it is related to the conjecture o
f termination of flips. In this talk\, we will discuss the minimal log dis
crepancies of quotient singularities. I will show that the PIA (precise in
version of adjunction) conjecture holds for quotient singularities. The ma
in tool of this talk involves the theory of the arc space of a quotient si
ngularity established by Denef and Loeser. This is joint work with Kohsuke
Shibata.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frediani Paola (Università di Pavia)
DTSTART:20210218T140000Z
DTEND:20210218T150000Z
DTSTAMP:20260404T111217Z
UID:ZAG/96
DESCRIPTION:Title: A canonical Hodge theoretic projective structure on compact Riemann su
rfaces\nby Frediani Paola (Università di Pavia) as part of ZAG (Zoom
Algebraic Geometry) seminar\n\n\nAbstract\nIn this talk we will show the e
xistence of a canonical projective structure on every compact Riemann surf
ace\, coming from Hodge theory. We will show that it differs from the cano
nical projective structure produced by the uniformisation theorem. In fact
the (0\,1)- component of the differential of the corresponding sections o
f the moduli space of projective structures over the moduli space of curve
s are different. The one corresponding to the projective structure coming
from uniformisation was computed by Zograf and Takhtadzhyan as the Weil-Pe
tersson Kaehler form on the moduli space of curves. Ours is the pullback v
ia the Torelli map of a nonzero constant scalar multiple of the Siegel fo
rm on the moduli space of principally polarised abelian varieties. These a
re results obtained in collaboration with I. Biswas\, E. Colombo and G.P.
Pirola.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shing-Tung Yau (Harvard University)
DTSTART:20210223T153000Z
DTEND:20210223T163000Z
DTSTAMP:20260404T111217Z
UID:ZAG/97
DESCRIPTION:Title: Geometry of Conifold Transitions\nby Shing-Tung Yau (Harvard Unive
rsity) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nCon
ifold transitions were introduced by Clemens\, Reid and Friedman to connec
t Calabi-Yau threefolds with different topologies. However\, this operatio
n may produce a complex manifold with trivial canonical bundle which is no
n-Kahler. I will discuss this transition from the point of view of metrics
and differential geometry\, and propose a non-Kahler analog of Calabi-Yau
metrics which originates in heterotic string theory. This talk will conta
in joint works with T.C. Collins\, J.-X. Fu\, J. Li\, and S. Picard.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Atsushi Ito (Nagoya University)
DTSTART:20210225T100000Z
DTEND:20210225T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/98
DESCRIPTION:Title: Linear systems on abelian varieties via M-regularity of Q-twisted shea
ves\nby Atsushi Ito (Nagoya University) as part of ZAG (Zoom Algebraic
Geometry) seminar\n\n\nAbstract\nFor an ample line bundle $L$ on an abeli
an variety $X$\, it is known that $L^n$ is basepoint free if $n \\geq 2$\,
projectively normal if $n \\geq 3$\, and the ideal of $X$ embedded by $|L
^n|$ is generated by quadrics if $n \\geq 4$. As a generalization of these
results\, Lazarsfeld conjectures that $L^n$ satisfies property $(N_p)$ if
$n \\geq p+3$.\nThis conjecture is affirmatively proved by Pareschi and s
trengthen by Pareschi-Popa by the theory of M-regularity. Recently\, Jiang
and Pareschi consider (variants of) M-regularity of $\\mathbb{Q}$-twisted
sheaves and it turns out that this is very useful when we study the linea
r system $|L|$ of $L$ itself\, not only $L^n$ for $n \\geq 2$. In this tal
k\, I will explain this topic and some recent results.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Cukierman (University of Buenos Aires)
DTSTART:20210302T150000Z
DTEND:20210302T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/99
DESCRIPTION:Title: Deformations of exterior differential ideals and applications\nby
Fernando Cukierman (University of Buenos Aires) as part of ZAG (Zoom Algeb
raic Geometry) seminar\n\n\nAbstract\nThe main theme of this talk is the g
eometry of moduli spaces of algebraic singular foliations on smooth projec
tive algebraic varieties over the complex numbers. A motivating problem is
the determination of the irreducible components of such moduli spaces. We
plan to discuss some basic facts on deformations of exterior differential
ideals. With these tools we study deformations of several types of Pfaff
ideals\, obtaining some new irreducible components of spaces of singular f
oliations of any codimension. This is based on joint work with Cesar Massr
i.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiwamu Watanabe (Chuo University)
DTSTART:20210304T100000Z
DTEND:20210304T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/100
DESCRIPTION:Title: Positivity of the exterior power of the tangent bundles\nby Kiwam
u Watanabe (Chuo University) as part of ZAG (Zoom Algebraic Geometry) semi
nar\n\n\nAbstract\nBy Mori's solution of the Hartshorne conjecture\, the o
nly smooth projective variety with ample tangent bundle is the projective
space. As a generalization of the Hartshorne conjecture\, Demially\, Peter
nell and Schneider studied smooth projective varieties with nef tangent bu
ndle. They proved that such variety X admits an étale cover Y such that t
he Albanese map Y \\to Alb(Y) is a smooth morphism whose fibers are smooth
Fano varieties with nef tangent bundle. In this talk\, we will study smoo
th projective varieties such that the r-th exterior power of the tangent b
undle is nef\, paying special attention to the case r=2. This talk is base
d on the paper arXiv:2011.01427.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunsuke Takagi (University of Tokyo)
DTSTART:20210309T110000Z
DTEND:20210309T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/101
DESCRIPTION:Title: Deformations of F-pure and F-regular singularities\nby Shunsuke T
akagi (University of Tokyo) as part of ZAG (Zoom Algebraic Geometry) semin
ar\n\n\nAbstract\nF-regular and F-pure singularities are singularities in
positive characteristic defined in terms of Frobenius splitting properties
. Ma and Schwede recently proved that a normal Q-Gorenstein complex variet
y has log terminal singularities if its reduction modulo p has F-regular s
ingularities for a single prime p. I will discuss the analog of their resu
lt for log canonical singularities. I will also explain how F-regular sing
ularities behave under equal and mixed characteristic deformations. This t
alk is based on joint work with Kenta Sato.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolina Araujo (IMPA)
DTSTART:20210311T150000Z
DTEND:20210311T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/102
DESCRIPTION:Title: Birational geometry of Calabi-Yau pairs and 3-dimensional Cremona tra
nsformations\nby Carolina Araujo (IMPA) as part of ZAG (Zoom Algebraic
Geometry) seminar\n\n\nAbstract\nAbstract: Recently\, Oguiso addressed th
e following question\, attributed to Gizatullin: ``Which automorphisms of
a smooth quartic K3 surface $D\\subset \\mathbb{P}^3$ are induced by Cremo
na transformations of the ambient space $\\mathbb{P}^3$?'' When $D\\subset
\\mathbb{P}^3$ is a quartic surface\, $(\\mathbb{P}^3\,D)$ is an example
of a \\emph{Calabi-Yau pair}\, that is\, a pair $(X\,D)$ consisting of a
normal projective variety $X$ and an effective Weil divisor $D$ on $X$ suc
h that $K_X+D\\sim 0$. In this talk\, I will explain a general framework t
o study the birational geometry of mildly singular Calabi-Yau pairs. Then
I will focus on the case of singular quartic surfaces $D\\subset \\mathbb{
P}^3$. Our results illustrate how the appearance of increasingly worse sin
gularities in $D$ enriches the birational geometry of the pair $(\\mathbb{
P}^3\, D)$\, and lead to interesting subgroups of the Cremona group of $\\
mathbb{P}^3$. This is a joint work with Alessio Corti and Alex Massarenti.
\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taro Sano (Kobe University)
DTSTART:20210316T100000Z
DTEND:20210316T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/103
DESCRIPTION:Title: Birational boundedness of some Calabi-Yau hypersurfaces\nby Taro
Sano (Kobe University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\
n\nAbstract\nIt is well-known that complex projective K3 surfaces are conn
ected by analytic deformations\, but they are algebraically unbounded. Nev
ertheless\, Reid\, Iano-Fletcher and Kollar-Johnson showed the finiteness
of weighted Calabi-Yau hypersurfaces. Motivated by this\, we study plt Cal
abi-Yau pairs (X\,D) and show finiteness of D in some cases. In particular
\, we show that anticanonical K3 surfaces form a birationally bounded fami
ly. We also exhibit examples of K3 surfaces of a fixed degree whose birati
onal contractions form an unbounded family\, thus the birational boundedne
ss is optimal in a sense.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Lazda (University of Warwick)
DTSTART:20210318T150000Z
DTEND:20210318T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/104
DESCRIPTION:Title: A Neron-Ogg-Shafarevich criterion for K3 surfaces\nby Chris Lazda
(University of Warwick) as part of ZAG (Zoom Algebraic Geometry) seminar\
n\n\nAbstract\nThe naive analogue of the Néron-Ogg-Shafarevich criterion
fails for K3 surfaces\, that is\, there exist K3 surfaces over Henselian\,
discretely valued fields K\, with unramified etale cohomology groups\, bu
t which do not admit good reduction over K. Assuming potential semi-stable
reduction\, I will show how to correct this by proving that a K3 surface
has good reduction if and only if is second cohomology is unramified\, and
the associated Galois representation over the residue field coincides wit
h the second cohomology of a certain “canonical reduction” of X. This
is joint work with B. Chiarellotto and C. Liedtke.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Lesieutre (Pennsylvania State University)
DTSTART:20210323T100000Z
DTEND:20210323T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/105
DESCRIPTION:Title: Rational surface automorphisms without periodic curves\nby John L
esieutre (Pennsylvania State University) as part of ZAG (Zoom Algebraic Ge
ometry) seminar\n\n\nAbstract\nAlthough there are many examples known of i
nfinite-order automorphisms of rational surfaces\, in most cases these aut
omorphisms have at least one periodic curve C (a curve for which f^n(C) =
C for some n). I will explain the construction of a class of rational sur
faces which admit a large group of automorphisms with no invariant curves.
The example makes use of several classical constructions\, and the surfa
ces admit contructions down to three different Coble surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulia Sacca (Columbia University)
DTSTART:20210325T150000Z
DTEND:20210325T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/106
DESCRIPTION:Title: Fano manifolds associated to hyperkahler manifolds\nby Giulia Sac
ca (Columbia University) as part of ZAG (Zoom Algebraic Geometry) seminar\
n\n\nAbstract\nIt is known that to some Fano manifolds whose cohomology lo
oks like that of a K3 surface\, one can associate\, via geometric construc
tions\, examples of hyperkahler manifolds. In this talk I will report on t
he first steps of a program whose aim is to reverse this construction: sta
rting from a hyperkahler manifold how to recover geometrically a Fano mani
fold? This is joint work with L. Flapan\, E. Macri\, and K. O'Grady.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katsuhisa Furukawa (Josai University)
DTSTART:20210330T100000Z
DTEND:20210330T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/107
DESCRIPTION:Title: On the singular loci of higher secant varieties of Veronese embedding
s\nby Katsuhisa Furukawa (Josai University) as part of ZAG (Zoom Algeb
raic Geometry) seminar\n\n\nAbstract\nFor a projective variety X in P^N\,
the k-secant variety \\sigma_k(X) is defined to be the closure of the unio
n of k-planes in P^N spanned by k-points of X. It is well known that \\sig
ma_{k-1}(X) is contained in the singular locus of \\sigma_k(X). Let us con
sider the case when X is the image of the Veronese embedding P^n to P^N of
degree d\, where N = \\binom{d+N}{d}-1. In the case of k=3\, K. Han showe
d that \\Sing(\\sigma_3(X)) = \\sigma_2(X)\, except when d=4 and n > 2. In
the exceptional case\, \\Sing(\\sigma_3(X)) is the union of \\sigma_2(X)
and D\, where D is an irreducible subset. In this talk\, we first give a g
eometric description of this D for k = 3\, and next study the case of k >
3. In particular\, I will explain projective techniques with respect to an
explicit calculation of the Gauss map of X and the projection from the in
cidence correspondence of \\sigma_k(X). This is a joint work with Kangjin
Han.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vyacheslav Shokurov (Johns Hopkins University)
DTSTART:20210401T150000Z
DTEND:20210401T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/108
DESCRIPTION:Title: Around a-n-complements\nby Vyacheslav Shokurov (Johns Hopkins Uni
versity) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nA
general conjecture about a-n-complements will be discussed in connection
with strict $\\delta$-lc singularities\, generalized pairs and McKernan co
njecture.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takehiko Yasuda (Osaka University)
DTSTART:20210406T100000Z
DTEND:20210406T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/109
DESCRIPTION:Title: Stringy motives and local fundamental groups of klt surface singulari
ties in arbitrary characteristic\nby Takehiko Yasuda (Osaka University
) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn this
talk\, I will speak about an application of stringy motives to local funda
mental groups of klt surface singularities. Xu proved that klt singulariti
es in characteristic zero have finite local fundametal groups. I will expl
ain how to prove that the same is true in arbitrary characteristic and in
dimension two\, which had been unknown in characteristics two and three. T
he key of the proof is to study the behavior of stringy motives under quas
i-etale Galois covers of klt singularities. This is a joint work with Javi
er Carvajal-Rojas.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Langer (Institute of Mathematics\, University of Warsaw\, P
oland)
DTSTART:20210408T130000Z
DTEND:20210408T140000Z
DTSTAMP:20260404T111217Z
UID:ZAG/110
DESCRIPTION:Title: Chern classes of vector bundles\nby Adrian Langer (Institute of M
athematics\, University of Warsaw\, Poland) as part of ZAG (Zoom Algebraic
Geometry) seminar\n\n\nAbstract\nI will talk about various restrictions o
n Chern classes of vector bundles on algebraic varieties. One of the most
important is Bogomolov's inequality saying that the degree of the discri
minant of a semistable vector bundle on a smooth complex algebraic variety
is non-negative. The degree zero case essentially corresponds to flat ve
ctor bundles. There are also versions of this inequality for Higgs bundle
s and in positive characteristic. I will talk about some applications of B
ogomolov's inequality and its possible variants in the Chow ring of the va
riety.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karl Schwede (University of Utah)
DTSTART:20210413T170000Z
DTEND:20210413T180000Z
DTSTAMP:20260404T111217Z
UID:ZAG/111
DESCRIPTION:Title: Recent progress in mixed characteristic higher dimensional algebraic
geometry\nby Karl Schwede (University of Utah) as part of ZAG (Zoom Al
gebraic Geometry) seminar\n\n\nAbstract\nIn characteristic zero birational
algebraic geometry\, Kawamata-Viehweg vanishing is a centrally important
tool. For some applications in characteristic p > 0\, one may use Frobeni
us and perturbations as a replacement for resolution of singularities and
Kawamata-Viehweg vanishing. This talk will show how to use Bhatt's vanish
ing theorem for absolute integral closures mixed characteristic as a repla
cement for resolutions and Kawamata-Viehweg vanishing theorems in a number
of applications. This is joint work with B. Bhatt\, L. Ma\, Z. Patakfalv
i\, K. Tucker\, J. Waldron and J. Witaszek.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yasunari Nagai (Waseda University)
DTSTART:20210415T100000Z
DTEND:20210415T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/112
DESCRIPTION:Title: Rational normal quintic curves on a cubic fourfold\nby Yasunari N
agai (Waseda University) as part of ZAG (Zoom Algebraic Geometry) seminar\
n\n\nAbstract\nWe study the moduli of rational normal quintic curves on a
cubic fourfold and its compactifications with a view toward projective sym
plectic geometry. This is a work in progress with Manfred Lehn and Duco va
n Straten.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakub Witaszek (University of Michigan)
DTSTART:20210420T170000Z
DTEND:20210420T180000Z
DTSTAMP:20260404T111217Z
UID:ZAG/113
DESCRIPTION:Title: Relative semiampleness in mixed characteristic.\nby Jakub Witasze
k (University of Michigan) as part of ZAG (Zoom Algebraic Geometry) semina
r\n\n\nAbstract\nIn this talk we will discuss the existence of contraction
s and base point freeness of line bundles in mixed characteristic in the c
ontext of the arithmetic Minimal Model Program.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandor Kovacs (University of Washington)
DTSTART:20210422T170000Z
DTEND:20210422T180000Z
DTSTAMP:20260404T111217Z
UID:ZAG/114
DESCRIPTION:Title: Hodge sheaves for singular families\nby Sandor Kovacs (University
of Washington) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbst
ract\nThis is a report on joint work with Behrouz Taji. Given a flat proje
ctive morphism [f:X\\to B] of complex varieties\, assuming that [B] is s
mooth\, we construct a system of reflexive Hodge sheaves on [B] . If in ad
dition [X] is also smooth then this system gives an extension of the Hodg
e bundle underlying the VHS of the smooth locus of [f] . This in turn prov
ides a criterion that all VHSs of geometric origin must satisfy. As an ind
ependent application we prove a singular version of Viehweg's conjecture a
bout base spaces of families of maximal variation.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Tschinkel (Courant Institute of Mathematical Sciences\, New Y
ork University)
DTSTART:20210427T150000Z
DTEND:20210427T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/115
DESCRIPTION:Title: Equivariant birational types\nby Yuri Tschinkel (Courant Institut
e of Mathematical Sciences\, New York University) as part of ZAG (Zoom Alg
ebraic Geometry) seminar\n\n\nAbstract\nI will discuss joint work with A.
Kresch and B. Hassett concerning new invariants in equivariant birational
geometry and their applications.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margarida Melo (University of Roma Tre)
DTSTART:20210429T120000Z
DTEND:20210429T130000Z
DTSTAMP:20260404T111217Z
UID:ZAG/116
DESCRIPTION:Title: On the top weight cohomology of the moduli space of abelian varieties
\nby Margarida Melo (University of Roma Tre) as part of ZAG (Zoom Alge
braic Geometry) seminar\n\n\nAbstract\nThe moduli space of abelian varieti
es Ag admits well behaved toroidal compactifications whose dual complex ca
n be given a tropical interpretation. Therefore\, one can use the techniqu
es recently developed by Chan-Galatius-Payne in order to understand part o
f the topology of Ag via tropical geometry. In this talk\, which is based
in joint work with Madeleine Brandt\, Juliette Bruce\, Melody Chan\, Gwyne
th Moreland and Corey Wolfe\, I will explain how to use this setup\, and i
n particular computations in the perfect cone compactification of Ag\, in
order to describe its top weight cohomology for g up to 7.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Pe Pereira (Universidad Complutense de Madrid)
DTSTART:20210504T140000Z
DTEND:20210504T150000Z
DTSTAMP:20260404T111217Z
UID:ZAG/117
DESCRIPTION:Title: Moderately Discontinuous Algebraic Topology\nby Maria Pe Pereira
(Universidad Complutense de Madrid) as part of ZAG (Zoom Algebraic Geometr
y) seminar\n\n\nAbstract\nAn algebraic or complex analytic subset in C^n h
as 2 natural metrics: the outer metric (restriction of the euclidean metri
c) and the inner metric (natural extension of the riemannian metric on the
smooth part). These metrics considered up to bilipschitz mappings are ana
lytic invariants\, that is\, they do not depend on the complex analytic em
bedding.\nRecently there is an intense activity in bilipschitz geometry of
germs and degenerations\, enriching and providing finer information on\np
roblems that were studied previously from the topological viewpoint (for m
ultiplicity invariance of the germ or certain equisingularity notions).\nI
n the works [1] and [2] we develop a new metric algebraic topology\, calle
d the Moderately Discontinuous Homology and Homotopy\, in the context of s
ubanalytic germs in R^n (with a supplementary metric structure) and more g
enerally of (degenerating) subanalytic families. This theory captures bili
pschitz information\, or in other words\, quasi isometric invariants\, and
aims to codify\, in an algebraic way\, part of the bilipschitz geometry.\
nA subanalytic germ is topologically a cone over its link and the moderate
ly discontinuous theory captures the different speeds\, with respect to th
e distance to the origin\, in which the topology of the link collapses tow
ards the origin. Similarly\, in a degenerating subanalytic family\, it cap
tures the different speeds of collapsing with respect to the family parame
ter.\nThe MD algebraic topology satisfies all the analogues of the usual t
heorems in Algebraic Topology: long exact sequences for the relative case\
, Mayer Vietoris and Seifert van Kampen for special coverings...\nIn this
talk\, I will present the most important concepts in the theory and some
results or applications that we got until the present.\n[1] (with J. Ferna
ndez de Bobadilla\, S. Heinze\, E. Sampaio) Moderately discontinuous homol
ogy. To appear in Comm. Pure App. Math.. Available in arXiv: 1910.12552\
n[2] (with J. Fernández de Bobadilla\, S. Heinze) Moderately discontinu
ous homotopy. Submitted. Available in ArXiv:2007.01538\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mara Ungureanu (University of Freiburg)
DTSTART:20210506T140000Z
DTEND:20210506T150000Z
DTSTAMP:20260404T111217Z
UID:ZAG/118
DESCRIPTION:Title: Counts of secant planes to varieties\, Virasoro algebras\, and univer
sal polynomials\nby Mara Ungureanu (University of Freiburg) as part of
ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nFor a curve in proje
ctive space\, the varieties parametrising its secant planes are among the
most studied objects in classical enumerative geometry. We shall start wi
th an introduction to secant varieties and explain the role of degeneratio
n arguments in understanding their geometry. We shall then explore the co
nnection between the enumerative geometry of secant varieties and Virasoro
algebras on one side\, and tautological integrals on the other.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Kebekus (University of Freiburg)
DTSTART:20210511T130000Z
DTEND:20210511T140000Z
DTSTAMP:20260404T111217Z
UID:ZAG/119
DESCRIPTION:Title: Brauer-Manin obstruction on a simply connected fourfold and a Mordell
theorem in the orbifold setting\nby Stefan Kebekus (University of Fre
iburg) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAlm
ost one decade ago\, Poonen constructed the first examples of algebraic va
rieties over global fields for which Skorobogatov's etale Brauer-Manin obs
truction does not explain the failure of the Hasse principle. By now\, sev
eral constructions are known\, but they all share common geometric feature
s such as large fundamental groups. In this paper\, we construct simply co
nnected fourfolds over global fields of positive characteristic for which
the Brauer-Manin machinery fails. Contrary to earlier work in this directi
on\, our construction does not rely on major conjectures. Instead\, we est
ablish a new diophantine result of independent interest: a Mordell-type th
eorem for Campana's "geometric orbifolds" over function fields of positive
characteristic. Along the way\, we also construct the first example of si
mply connected surface of general type over a global field with a non-empt
y\, but non-Zariski dense set of rational points. This is joint work with
Jorge Pereira (IMPA) and Arne Smeets (Nijmegen)\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jack Rogers (University of Manchester)
DTSTART:20210513T140000Z
DTEND:20210513T150000Z
DTSTAMP:20260404T111217Z
UID:ZAG/120
DESCRIPTION:Title: K-stability of smooth Fano SL2-threefolds\nby Jack Rogers (Univer
sity of Manchester) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n
Abstract\nThere has been much interest in K-stability since it was shown t
o be equivalent to the existence of Kähler-Einstein metrics by Chen-Donal
dson-Sun. The theory of K-stability is now well developed\, but practical
methods to check whether a given variety is K-stable are hard to come by.
Equivariant K-stability\, introduced by Datar-Székelyhidi\, makes finding
such criteria easier for varieties with large automorphism groups.\n\nIf
an algebraic group G acts on a variety X\, the complexity of the action is
the minimal codimension in X of the orbits of a Borel subgroup B of G (e.
g. if T is a torus\, the complexity zero T-varieties are the toric varieti
es). Conditions for K-stability have been found for toric varieties by Wan
g-Zhu\, for complexity one T-varieties by Ilten-Süss and for all complexi
ty zero varieties by Delcroix.\n\nWe will discuss the combinatorial descri
ption due to Timashev of complexity one G-varieties\, and describe a pract
ical method to check K-stability in the particular case of smooth Fano SL2
-threefolds. In particular\, this method proves the K-stability of several
varieties not previously known to be K-stable\, e.g. projective 3-space b
lown up along three disjoint lines. This is joint work with Hendrik Süss.
\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jørgen Vold Rennemo (University of Oslo)
DTSTART:20210518T110000Z
DTEND:20210518T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/121
DESCRIPTION:Title: K-theoretic sheaf counting invariants on C^4\nby Jørgen Vold Ren
nemo (University of Oslo) as part of ZAG (Zoom Algebraic Geometry) seminar
\n\n\nAbstract\nOh and Thomas have recently defined a K-theoretic sheaf co
unting invariant for moduli spaces of sheaves on a Calabi-Yau 4-fold. One
of the simplest examples of such a moduli scheme is the Hilbert scheme of
n points on C^4. The topic of this talk is a proof of a formula for the ge
nerating functions of invariants of these Hilbert schemes\, confirming a c
onjecture of Nekrasov (as well a generalisation to Quot schemes of C^4\, c
onjectured by Nekrasov and Piazzalunga). This is joint work with Martijn K
ool.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marta Pieropan (Utrecht University)
DTSTART:20210520T150000Z
DTEND:20210520T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/122
DESCRIPTION:Title: Campana points on Fano varieties\nby Marta Pieropan (Utrecht Univ
ersity) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nWe
call Campana points an arithmetic notion of points on Campana's orbifolds
that has been first studied by Campana and Abramovich\, and that interpol
ates between the notions of rational and integral points. In this talk we
introduce Campana points and a Manin type conjecture for Campana points on
Fano varieties\, and we present results for equivariant compactifications
of vector groups (joint work with A. Smeets\, S. Tanimoto\, T. Várilly-A
lvarado) and for toric varieties (joint work with D. Schindler).\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brendan Hassett (Brown University)
DTSTART:20210525T150000Z
DTEND:20210525T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/123
DESCRIPTION:Title: Rationality of even-dimensional intersections of two real quadrics\nby Brendan Hassett (Brown University) as part of ZAG (Zoom Algebraic Ge
ometry) seminar\n\n\nAbstract\nWe consider rationality constructions for s
mooth complete intersections of two quadrics over nonclosed fields. Over t
he real numbers\, we establish a criterion for rationality in dimension fo
ur and discuss open cases in higher dimensions. (joint with János Kollár
and Yuri Tschinkel)\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthony Varilly-Alvarado (Rice University)
DTSTART:20210527T150000Z
DTEND:20210527T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/124
DESCRIPTION:Title: Quasi-hyperbolicity via explicit symmetric differentials\nby Anth
ony Varilly-Alvarado (Rice University) as part of ZAG (Zoom Algebraic Geom
etry) seminar\n\n\nAbstract\nA surface X is algebraically quasi-hyperbolic
if it contains finitely many curves of genus 0 or 1. In 2006\, Bogomolov
and de Oliveira used asymptotic computations to show that sufficiently no
dal surfaces of high degree in projective three-space carry symmetric diff
erentials\, and they used this to prove quasi-hyperbolicity of these surfa
ces. We explain how a granular analysis of their ideas\, combined with co
mputational tools and insights\, yield explicit results for the existence
of symmetric differentials\, and we show how these results can be used to
give constraints on the locus of rational curves on surfaces like the Bart
h Decic\, Buechi's surface\, and certain complete intersections of general
type\, including the surface parametrizing perfect cuboids\, and the surf
ace parametrizing magic squares of squares. This is joint work with Nils
Bruin and Jordan Thomas.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Livia Campo (University of Birmingham)
DTSTART:20210601T110000Z
DTEND:20210601T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/125
DESCRIPTION:Title: Fano 3-folds and double covers\nby Livia Campo (University of Bir
mingham) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI
will propose a method to explicitly construct 52 deformation families of
terminal Q-Fano 3-folds in codimension 4 and Fano index 2. Their structure
descends from suitably crafted double covers. If time allows\, I will bri
efly discuss the non-solidity of some of such families (in a joint work in
progress with T. Guerreiro).\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrico Fatighenti (Sapienza - Università di Roma)
DTSTART:20210603T160000Z
DTEND:20210603T170000Z
DTSTAMP:20260404T111217Z
UID:ZAG/126
DESCRIPTION:Title: Fano varieties from homogeneous vector bundles\nby Enrico Fatighe
nti (Sapienza - Università di Roma) as part of ZAG (Zoom Algebraic Geomet
ry) seminar\n\n\nAbstract\nThe idea of classifying Fano varieties using ho
mogeneous vector bundles was behind Mukai's classification of prime Fano 3
-folds. In this talk\, we give a survey of some recent progress along the
same lines\, including a biregular rework of the non-prime Mori-Mukai 3-fo
lds classification and some examples of higher-dimensional Fano varieties
with special Hodge-theoretical properties.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Borisov (Rutgers University)
DTSTART:20210608T150000Z
DTEND:20210608T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/127
DESCRIPTION:Title: Explicit equations of surfaces of general type\nby Lev Borisov (R
utgers University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nA
bstract\nI will talk about progress in finding equations of special surfac
es of general type\, notably fake projective planes. This work was done ov
er the last several years\, in a series of joint papers with JongHae Keum\
, Sai Kee Yeung\, Enrico Fatighenti and Anders Buch.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fumiaki Suzuki (UCLA Mathematics)
DTSTART:20210610T160000Z
DTEND:20210610T170000Z
DTSTAMP:20260404T111217Z
UID:ZAG/128
DESCRIPTION:Title: An O-acyclic variety of even index\nby Fumiaki Suzuki (UCLA Mathe
matics) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI
will construct a family of Enriques surfaces parametrized by P^1 such that
any multi-section has even degree over the base P^1. Over the function fi
eld of a complex curve\, this gives the first example of an O-acyclic vari
ety (H^i(X\,O)=0 for i>0) whose index is not equal to one\, and an affirma
tive answer to a question of Colliot-Thélène and Voisin. I will also dis
cuss applications to related problems\, including the integral Hodge conje
cture and Murre’s question on universality of the Abel-Jacobi maps. This
is joint work with John Christian Ottem.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eveline Legendre (Institut de Mathématiques de Toulouse)
DTSTART:20210615T110000Z
DTEND:20210615T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/129
DESCRIPTION:Title: Valuative stability for polarised varieties\nby Eveline Legendre
(Institut de Mathématiques de Toulouse) as part of ZAG (Zoom Algebraic Ge
ometry) seminar\n\n\nAbstract\nI will talk about a recent joint work with
Ruadhai Dervan where we introduced a notion of valuative stability for pol
arised variety. This extends Fujita's valuative stability of Fano varietie
s. We show that valuative stability is equivalent to K-stability with resp
ect to test configurations with integral central fibre.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Cascini (Imperial College London)
DTSTART:20210617T160000Z
DTEND:20210617T170000Z
DTSTAMP:20260404T111217Z
UID:ZAG/130
DESCRIPTION:Title: Birational geometry of foliations on a complex threefold\nby Paol
o Cascini (Imperial College London) as part of ZAG (Zoom Algebraic Geometr
y) seminar\n\n\nAbstract\nMany results in the classical minimal model prog
ram\, such as the existence of flips and the base point free theorem\, adm
it a natural generalisation to the category of foliations defined over a c
omplex threefold. Other results\, instead\, seem to behave differently\, s
uch as existence of flops and canonical models. I will survey about some o
f the recent progress in this direction. Joint work with C. Spicer.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krishna Hanumanthu (Chennai Mathematical Institute)
DTSTART:20210622T110000Z
DTEND:20210622T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/131
DESCRIPTION:Title: Rationality questions on Seshadri constants.\nby Krishna Hanumant
hu (Chennai Mathematical Institute) as part of ZAG (Zoom Algebraic Geometr
y) seminar\n\n\nAbstract\nLet X be a projective variety and let L be an am
ple line bundle on X. For a point x in X\, the Seshadri constant of L at x
is the infimum\, over all curves C passing through x\, of the ratios (L.C
)/m\, where (L.C) denotes the intersection product of L and C and m is the
multiplicity of C at x. These constants were defined by J.-P. Demailly i
n 1990 and they shed light on the local behaviour of L at x and even say s
omething about the nature of L and X. An important question about Seshadr
i constants is whether they can be irrational. They are expected to be irr
ational often\, even though currently no examples are known. In this talk\
, we will focus on rational surfaces. We will discuss certain conjectures
on linear systems of plane curves and show that Seshadri constants of some
ample line bundles are irrational if these conjectures are true. This tal
k is based on joint works with B. Harbourne\, \\L. Farnik\, J. Huizenga\,
D. Schmitz and T. Szemberg.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Howard Nuer (Technion\, Israel Institute of Technology)
DTSTART:20210624T110000Z
DTEND:20210624T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/132
DESCRIPTION:Title: The cohomology of the general stable sheaf on a K3 surface\nby H
oward Nuer (Technion\, Israel Institute of Technology) as part of ZAG (Zoo
m Algebraic Geometry) seminar\n\n\nAbstract\nLet X be a K3 surface of Pica
rd rank one and degree 2n with ample generator H. Let M_H(v) be the moduli
space of Gieseker semistable sheaves on X with Mukai vector v. In this ta
lk\, we consider the weak Brill-Noether property for v\, namely that the g
eneral sheaf in M_H(v) has at most one nonzero cohomology group. We show
that given any positive rank r\, there are only finitely many Mukai vecto
rs of rank r failing weak Brill-Noether over all K3 surfaces of Picard ran
k one. We discuss our algorithm for finding the potential counterexamples
and demonstrate the utility of our approach by discussing how we were able
to classify all such counterexamples up to rank 20 and calculate the coho
mology of the general sheaf in each case. Moreover\, for fixed rank r\, w
e give sharp bounds on n\, d\, and a that guarantee that a Mukai vector v=
(r\,dH\,a) satisfies weak Brill-Noether. As a corollary\, we provide anot
her proof of the classification of Ulrich bundles on K3 surfaces of Picard
rank one. In addition\, we discuss the question of when the general sheaf
in M_H(v) is globally generated. This joint work with Izzet Coskun and Ko
ta Yoshioka makes crucial use of Bridgeland stability conditions and wall-
crossing.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Fernandez de Bobadilla (Basque Center for Applied Mathemati
cs)
DTSTART:20210629T110000Z
DTEND:20210629T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/133
DESCRIPTION:Title: The Brasselet-Schurmann-Yokura conjecture for L-classes on singular v
arieties\nby Javier Fernandez de Bobadilla (Basque Center for Applied
Mathematics) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstrac
t\nThe Brasselet-Schurmann-Yokura conjecture predicts the equality between
the Hodge L-class and the Goresky-MacPherson L-class for compact complex
algebraic varieties that are rational homology manifolds. In this talk\, w
e give two different proofs of this conjecture. The first proof is for pro
jective varieties\, and it is based on cubical hyperresolutions\, the Deco
mposition Theorem\, and classical Hodge theory. This is a joint work with
I. Pallares. The second proof is for general compact algebraic varieties b
y using the theory of mixed Hodge modules. This is a joint work with I. Pa
llares and M. Saito.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sheng Meng (Korea Institute for Advanced Study)
DTSTART:20210701T110000Z
DTEND:20210701T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/134
DESCRIPTION:Title: Automorphism group and its Jordan property\nby Sheng Meng (Korea
Institute for Advanced Study) as part of ZAG (Zoom Algebraic Geometry) sem
inar\n\n\nAbstract\nA group is said to have Jordan property if there exist
s a Jordan constant J such that any finite subgroup has an abelian subgrou
p with index bounded by J. I will survey known results for Jordan property
on certain automorphism groups and birational automorphism groups of vari
eties. I will also explain our recent progress on automorphism groups of c
ompact spaces in Fujiki’s class C. This is a joint work with Fabio Perro
ni and De-Qi Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taku Suzuki (Utsunomiya University)
DTSTART:20210706T100000Z
DTEND:20210706T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/135
DESCRIPTION:Title: Higher order minimal families of rational curves on Fano manifolds\nby Taku Suzuki (Utsunomiya University) as part of ZAG (Zoom Algebraic G
eometry) seminar\n\n\nAbstract\nThe purpose of my talk is to introduce the
notion of higher order minimal families of rational curves on Fano manifo
lds and to explain two results concerning it. One is that Fano manifolds a
re covered by higher rational manifolds if their Chern characters satisfy
some positivity conditions. The other is a classification of embedded Fano
manifolds covered by higher linear spaces.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aline Zanardini (Leiden University)
DTSTART:20210708T150000Z
DTEND:20210708T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/136
DESCRIPTION:Title: Stability of pencils of plane curves\nby Aline Zanardini (Leiden
University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract
\nIn this talk I will discuss some recent results on the problem of classi
fying pencils of plane curves up to projective equivalence. We will see ho
w the stability of a pencil is related to the stability of its generators\
, to the log canonical threshold\, and to the multiplicities of a base poi
nt. In particular\, I will present complete stability criteria for certain
pencils of plane sextics called Halphen pencils of index two.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zheng Zhang (ShanghaiTech)
DTSTART:20210713T100000Z
DTEND:20210713T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/137
DESCRIPTION:Title: The moduli space of cubic surface pairs via the intermediate Jacobian
s of Eckardt cubic threefolds\nby Zheng Zhang (ShanghaiTech) as part o
f ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nWe study the moduli
space of pairs consisting of a smooth cubic surface and a transverse plan
e via a period map. More specifically\, the construction associates to a c
ubic surface pair a so-called Eckardt cubic threefold which admits an invo
lution\, and the period map sends the pair to the anti-invariant part of t
he intermediate Jacobian. Our main result is that the global Torelli theor
em holds for the period map (in other words\, the period map is injective)
. The key ingredients of the proof include a description of the anti-invar
iant part of the intermediate Jacobian as a Prym variety of a branched cov
er and a detailed study of certain positive dimensional fibers of the corr
esponding Prym map. This is joint work with S. Casalaina-Martin.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicole Lemire (University of Western Ontario)
DTSTART:20210715T160000Z
DTEND:20210715T170000Z
DTSTAMP:20260404T111217Z
UID:ZAG/138
DESCRIPTION:Title: Codimension 2 cycles of classifying spaces of low-dimensional algebra
ic tori\nby Nicole Lemire (University of Western Ontario) as part of Z
AG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nLet T be an algebraic
torus over a field F\, and let CH^2(BT) be the Chow group of codimension 2
cycles in its classifying space. Following work of Blinstein and Merkurje
v on the structure of the torsion part of CH^2(BT)\, Scavia\, in a recent
preprint\, found an example of an algebraic torus with non-trivial torsion
in CH^2(BT). In joint work with Alexander Neshitov\, we show computationa
lly that the group CH^2(BT) is torsion-free for all algebraic tori of dime
nsion at most 5 and determine the conjugacy classes of finite subgroups of
GL_6(Z) which correspond to 6-dimensional tori with nontrivial torsion in
CH^2(BT). Some interesting properties of the structure of low-dimensional
algebraic tori are involved.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eiji Inoue (RIKEN iTHEMS)
DTSTART:20210720T110000Z
DTEND:20210720T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/139
DESCRIPTION:Title: Perelman's entropy and optimal degeneration\nby Eiji Inoue (RIKEN
iTHEMS) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nA
lgebraic optimal degeneration of Fano variety along Kahler-Ricci flow was
originally constructed by Chen-Sun-Wang and was deepened by Dervan-Szekely
hidi\, Han-Li and recent Blum-Liu-Xu-Zhuang. The degeneration is a substan
tial intermediate for studying a Fano variety with Kahler-Ricci soliton ap
pearing in the Gromov-Hausdorff limit of Kahler-Ricci flow. The degenerati
on is characterized by a valuation which maximizes `H-entropy' among all v
aluations. Motivated by these works\, I would like to explain my ongoing a
ttempt to optimal degeneration of polarized variety with respect to `mu-en
tropy'. The mu-entropy appears in my study on mu-cscK metrics and muK-stab
ility\, which I introduced to understand cscK metrics and Kahler-Ricci sol
iton in a unified way. Going deep into the story\, we encounter Perelman's
entropy\, which turns out to be the origin of our story.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swarnava Mukhopadhyay (Tata Institute of Fundamental Research)
DTSTART:20210722T110000Z
DTEND:20210722T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/140
DESCRIPTION:Title: Hitchin connection for parabolic bundles\nby Swarnava Mukhopadhya
y (Tata Institute of Fundamental Research) as part of ZAG (Zoom Algebraic
Geometry) seminar\n\n\nAbstract\nIn a fundamental paper in1990\, Hitchin c
onsidered the space of non-abelian theta functions/conformal blocks/Verlin
de spaces from the view point of geometric-quantization (Konstant-Kirillov
-Soureau) for the moduli space of principal bundles on a smooth projecti
ve curve. Hitchin found a flat projective connection that can be interpret
ed as identification of these spaces via a parallel transport along a path
joining different curves in the Teichmuller space. In this talk\, we will
discuss a generalization of Hitchin's construction to the parabolic set-u
p. Namely we consider punctured curves and the moduli space of parabolic $
G$ bundles and produce a flat projective connection that identifies sectio
ns of parabolic determinant bundles as the puncture curve varies. This is
a joint work with Indranil Biswas and Richard Wentworth.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenneth Ascher (Princeton University)
DTSTART:20210727T160000Z
DTEND:20210727T170000Z
DTSTAMP:20260404T111217Z
UID:ZAG/141
DESCRIPTION:Title: K-stability and birational geometry of moduli spaces of quartic K3 su
rfaces\nby Kenneth Ascher (Princeton University) as part of ZAG (Zoom
Algebraic Geometry) seminar\n\n\nAbstract\nWe discuss various compactifica
tions of moduli spaces of quartic K3 surfaces constructed using GIT\, hodg
e theory\, and K-stability. This is based on joint work with Kristin DeVle
ming and Yuchen Liu.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anand Sawant (Tata Institute of Fundamental Research)
DTSTART:20210729T110000Z
DTEND:20210729T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/142
DESCRIPTION:Title: Near-rationality properties of norm varieties\nby Anand Sawant (T
ata Institute of Fundamental Research) as part of ZAG (Zoom Algebraic Geom
etry) seminar\n\n\nAbstract\nThe standard norm varieties played a crucial
role in Voevodsky's proof of the Bloch-Kato conjecture. I will discuss va
rious near-rationality concepts for smooth projective varieties and descri
be known near-rationality results for standard norm varieties. I will the
n outline an argument showing that a standard norm variety over a field of
characteristic 0 is universally R-trivial after passing to the algebraic
closure of the base field. The talk is based on joint work with Chetan Ba
lwe and Amit Hogadi.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Fanelli (Institut de Mathématiques de Bordeaux)
DTSTART:20210902T110000Z
DTEND:20210902T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/143
DESCRIPTION:Title: Rational simple connectedness and Fano threefolds\nby Andrea Fane
lli (Institut de Mathématiques de Bordeaux) as part of ZAG (Zoom Algebrai
c Geometry) seminar\n\n\nAbstract\nThe notion of rational simple connected
ness can be seen as an algebro-geometric analogue of simple connectedness
in topology. The work of de Jong\, He and Starr has already produced sever
al recent studies to understand this notion. \nIn this talk I will discuss
the joint project with Laurent Gruson and Nicolas Perrin to study rationa
l simple connectedness for Fano threefolds via explicit methods from birat
ional geometry.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Schnell (Stony Brook University)
DTSTART:20210907T090000Z
DTEND:20210907T100000Z
DTSTAMP:20260404T111217Z
UID:ZAG/144
DESCRIPTION:Title: A new finiteness theorem for variations of Hodge structure\nby Ch
ristian Schnell (Stony Brook University) as part of ZAG (Zoom Algebraic Ge
ometry) seminar\n\n\nAbstract\nI will talk about a new finiteness theorem
for variations of Hodge structure. It is a generalization of the Cattani-D
eligne-Kaplan theorem from Hodge classes to so-called self-dual (and anti-
self-dual) classes. For example\, among integral cohomology classes of deg
ree 4\, those of type (4\,0) + (2\,2) + (0\,4) are self-dual\, and those o
f type (3\,1) + (1\,3) are anti-self-dual. The result is suggested by cons
iderations in theoretical physics\, and the proof uses o-minimality and th
e definability of period mappings. This is joint work with Benjamin Bakker
\, Thomas Grimm\, and Jacob Tsimerman.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Filipazzi (École polytechnique fédérale de Lausanne)
DTSTART:20210909T150000Z
DTEND:20210909T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/145
DESCRIPTION:Title: On the boundedness of elliptically fibered varieties\nby Stefano
Filipazzi (École polytechnique fédérale de Lausanne) as part of ZAG (Zo
om Algebraic Geometry) seminar\n\n\nAbstract\nIn this talk\, we will surve
y some ideas to address the boundedness of varieties admitting an elliptic
fibration. After introducing general ideas\, we will discuss how they app
ly concretely to special classes of varieties: n-folds of Kodaira dimensio
n n-1\, and elliptic Calabi--Yau varieties. Part of this talk is based on
current work in progress joint with C.D. Hacon and R. Svaldi.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaroslaw Wisniewski (Institute of Mathematics\, University of Wars
aw)
DTSTART:20210914T140000Z
DTEND:20210914T150000Z
DTSTAMP:20260404T111217Z
UID:ZAG/146
DESCRIPTION:Title: Rational maps via C* actions\nby Jaroslaw Wisniewski (Institute o
f Mathematics\, University of Warsaw) as part of ZAG (Zoom Algebraic Geome
try) seminar\n\n\nAbstract\nI will recall old results and present new fact
s linking varieties with C^* action to birational maps. I particular I wil
l talk about recent results obtained together with Michalek\, Monin\, Occh
etta\, Romano\, and Sola Conde.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geordie Williamson (Sydney Mathematical Research Institute)
DTSTART:20210916T210000Z
DTEND:20210916T220000Z
DTSTAMP:20260404T111217Z
UID:ZAG/147
DESCRIPTION:Title: Geometric extensions\nby Geordie Williamson (Sydney Mathematical
Research Institute) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n
Abstract\nThe Decomposition Theorem is probably my favourite theorem. I'll
start by recalling the statement and trying to explain a little of why it
is so remarkable. One consequence is that one could imagine an alternate
history of the subject\, in which intersection cohomology complexes were d
iscovered without knowing about perverse sheaves. I'll explain how this mi
ght have occurred\, and how it led Soergel and Juteau-Mautner-Williamson t
o the study of parity sheaves. Parity sheaves need strong parity vanishing
assumptions\, which somewhat restrict their utility (particularly for app
lications outside of geometric representation theory). The final goal of m
y talk is to explain a recent theorem (joint with Chris Hone) which proves
the existence and uniqueness of "geometric extensions" in broad generalit
y. The upshot is that parity sheaves probably don't need parity after all.
\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Perry (University of Michigan)
DTSTART:20210921T130000Z
DTEND:20210921T140000Z
DTSTAMP:20260404T111217Z
UID:ZAG/148
DESCRIPTION:Title: Serre functors of semiorthogonal components\nby Alexander Perry (
University of Michigan) as part of ZAG (Zoom Algebraic Geometry) seminar\n
\n\nAbstract\nThe Serre functor of a triangulated category is one of its m
ost important invariants\, playing the role of the dualizing complex of a
variety in noncommutative algebraic geometry. I will explain how to descri
be the Serre functors of many semiorthogonal components of varieties in te
rms of spherical twists. In the case of Kuznetsov components of Fano compl
ete intersections\, this leads to a proof of a conjecture of Katzarkov and
Kontsevich on the dimensions of such categories\, and implies the nonexis
tence of Serre invariant stability conditions when the degrees of the comp
lete intersection do not all coincide. This is joint work with Alexander K
uznetsov.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:June Huh (Princeton University)
DTSTART:20210923T150000Z
DTEND:20210923T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/149
DESCRIPTION:Title: Lorentzian polynomials\nby June Huh (Princeton University) as par
t of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nLorentzian polyn
omials link continuous convex analysis and discrete convex analysis via tr
opical geometry. The tropical connection is used to produce Lorentzian pol
ynomials from discrete convex functions. Specific examples can be construc
ted from graphs\, convex bodies\, stable polynomials\, irreducible represe
ntations of general linear groups\, and in particular\, projective varieti
es. I will explain the main ideas from the viewpoint of algebraic geometry
. Based on joint work with Petter Branden.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulia Sacca (Columbia University)
DTSTART:20210928T150000Z
DTEND:20210928T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/150
DESCRIPTION:Title: Compactification of Lagrangian fibrations\nby Giulia Sacca (Colum
bia University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbst
ract\nLagrangian fibered Hyper-Kahler manifolds are the natural generaliza
tion of elliptic K3 surfaces and have been used to study and construct exa
mples of compact Hyper-Kahler manifolds and (possibly singular) symplectic
varieties. In this talk I will talk about some recent compactification te
chniques I introduced for quasi-projective Lagrangian fibrations\, with ap
plications to the study of Prym\, Intermediate Jacobian\, and Albanese fib
rations.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amnon Neeman (Australian National University)
DTSTART:20210930T210000Z
DTEND:20210930T220000Z
DTSTAMP:20260404T111217Z
UID:ZAG/151
DESCRIPTION:Title: Uniqueness theorems for dg enhancements\nby Amnon Neeman (Austral
ian National University) as part of ZAG (Zoom Algebraic Geometry) seminar\
n\n\nAbstract\nAbstract: The study of Fourier-Mukai transforms has led to
many fascinating developments\, and in this talk we will focus on just one
of them. In a 2004 article Bondal\, Larsen and Lunts made the daring conj
ecture that geometric categories should have unique enhancements\, and thi
s remarkable conjecture turns out to be true. We will describe the series
of theorems that have come out of this conjecture. The recent work\, which
we will get to at the end of the talk\, is joint with Alberto Canonaco an
d Paolo Stellari.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Caraiani (Imperial College London)
DTSTART:20211005T100000Z
DTEND:20211005T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/152
DESCRIPTION:Title: On the cohomology of Hilbert modular varieties with torsion coefficie
nts\nby Ana Caraiani (Imperial College London) as part of ZAG (Zoom Al
gebraic Geometry) seminar\n\n\nAbstract\nShimura varieties are certain mod
uli spaces equipped with many symmetries\, that play an important role in
the Langlands programme. For example\, Hilbert modular varieties are quoti
ents of the product of several copies of the upper-half plane by certain a
rithmetic groups. I will discuss a general conjecture on the cohomology of
Shimura varieties with torsion coefficients\, which states that the non-d
egenerate part of their cohomology is concentrated in the middle degree. I
will give an overview of an approach to this conjecture introduced in joi
nt work with Peter Scholze. This approach relies on the geometry of the Ho
dge-Tate period morphism\, which I will describe\, and on certain technica
l computations. I will then specialise to the case of Hilbert modular vari
eties and explain a modified version of this approach that relies on an in
stance of geometric Jacquet-Langlands functoriality for the fibers of the
Hodge-Tate period morphism. This is joint work with Matteo Tamiozzo.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yongnam Lee (Korea Advanced Institute of Science and Technology)
DTSTART:20211007T110000Z
DTEND:20211007T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/153
DESCRIPTION:Title: Dominant rational maps from a very general hypersurface\nby Yongn
am Lee (Korea Advanced Institute of Science and Technology) as part of ZAG
(Zoom Algebraic Geometry) seminar\n\n\nAbstract\nThere has been recent in
terest in studying measures of irrationality for hypersurfaces $X$ of high
degree in $\\mathbb P^{n+1}$. The degree of irrationality of $X$ is defin
ed as the minimal degree of dominant rational maps from $X$ to $\\mathbb P
^n$. It is known that the degree of irrationality of $X$ is $d-1$ if $X$ i
s a very general hypersurface of degree $d\\ge 2n+1$. In this talk\, from
a different point of view we will discuss dominant rational maps of finite
degree from a very general hypersurface $X$ of degree $d\\ge n+3$ in $\\m
athbb P^{n+1}$ to any smooth projective variety $Z$. The finite theorem st
ates that these form a finite set\, up to birational equivalence of $Z$\,
if $Z$ is a variety of general type. It is an interesting question to dete
rmine $Z$ when $Z$ is not birational to $X$. It is conjecturally expected
that $Z$ is rationally connected if $X$ is a very general hypersurface of
degree $d\\ge n+3$. In this talk\, I will present some partial results for
this expectation. This talk combines the joint work with Gian Pietro Piro
la and the joint work with De-Qi Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Thomas (Imperial College London)
DTSTART:20211012T160000Z
DTEND:20211012T170000Z
DTSTAMP:20260404T111217Z
UID:ZAG/154
DESCRIPTION:Title: Higher rank DT theory from curve counting\nby Richard Thomas (Imp
erial College London) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n
\nAbstract\nFix a Calabi-Yau 3-fold X. Its DT invariants count stable bund
les and sheaves on X. The generalised DT invariants of Joyce-Song count se
mistable bundles and sheaves on X. I will describe work with Soheyla Feyzb
akhsh showing these generalised DT invariants in any rank r can be written
in terms of rank 1 invariants. By the MNOP conjecture the latter are dete
rmined by the GW invariants of X. Along the way we also show they are dete
rmined by rank 0 invariants counting sheaves supported on surfaces in X. T
hese invariants are predicted by S-duality to be governed by (vector-value
d\, mock) modular forms.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/154/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fei Hu (University of Oslo)
DTSTART:20211014T120000Z
DTEND:20211014T130000Z
DTSTAMP:20260404T111217Z
UID:ZAG/155
DESCRIPTION:Title: A dynamical approach to generalized Weil's Riemann hypothesis\nby
Fei Hu (University of Oslo) as part of ZAG (Zoom Algebraic Geometry) semi
nar\n\n\nAbstract\nInspired by a result of Esnault and Srinivas on automor
phisms of surfaces and recent advances in complex dynamics\, Truong raised
a question on the comparison of two dynamical degrees\, which are defined
using pullback actions of dynamical correspondences on numerical cycle cl
ass groups and cohomology groups\, respectively. An affirmative answer to
his question would surprisingly imply Weil’s Riemann hypothesis. In this
talk\, I shall discuss some partial results in the cases of Abelian varie
ties and surfaces. This is based on joint work with Tuyen Truong.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/155/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ronan Terpereau (Université de Bourgogne)
DTSTART:20211019T150000Z
DTEND:20211019T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/156
DESCRIPTION:Title: Real structures on almost homogeneous varieties\nby Ronan Terpere
au (Université de Bourgogne) as part of ZAG (Zoom Algebraic Geometry) sem
inar\n\n\nAbstract\nIn this talk\, we will be interested in the real struc
tures on the almost homogeneous varieties\; these are the complex algebrai
c varieties X endowed with an action of a reductive algebraic group G such
that G acts on X with a dense open orbit. We will see how to determine wh
en a real structure on X exists and\, if so\, how to describe and count al
l of them. In particular\, we will try to illustrate our approach on two c
lassical families of almost homogeneous varieties: the horospherical varie
ties (which include toric manifolds and flag varieties) and the SL(2)-almo
st homogeneous threefolds (which include the Fano threefolds P3\, Q3\, V5\
, and V22). This is a joint work with Lucy Moser-Jauslin (IMB\, Dijon).\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/156/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Donu Arapura (Purdue University)
DTSTART:20211021T170000Z
DTEND:20211021T180000Z
DTSTAMP:20260404T111217Z
UID:ZAG/157
DESCRIPTION:Title: Euler characteristics of aspherical Kähler manifolds\nby Donu Ar
apura (Purdue University) as part of ZAG (Zoom Algebraic Geometry) seminar
\n\n\nAbstract\nThis is joint work with Botong Wang. I want to start by re
calling the Hopf-Singer conjecture on the sign of the Euler characteristic
of a compact aspherical manifold. In the K\\”ahler setting\, we have a
stronger conjecture involving Euler characteristics of perverse sheaves. O
ur results are that the stronger conjecture holds when X is compact K\\”
ahler with nonpositive curvature\, or X is aspherical projective with a
faithful rigid local system. I will sketch the proofs\, and describe with
some illustrative examples.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/157/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fenglong You (University of Oslo)
DTSTART:20211026T130000Z
DTEND:20211026T140000Z
DTSTAMP:20260404T111217Z
UID:ZAG/158
DESCRIPTION:Title: Degenerations\, fibrations and mirror symmetry\nby Fenglong You (
University of Oslo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n
Abstract\nGiven a Tyurin degeneration of a Calabi-Yau variety to a union o
f two quasi-Fano varieties\, Doran-Harder-Thompson conjectured that the La
ndau-Ginzburg models of two quasi-Fano varieties can be glued to the mirro
r Calabi-Yau variety which admits a P^1-fibration. I will talk about a gen
eralization of this conjecture to degenerations of quasi-Fano varieties. I
will explain some evidence of this conjecture including a gluing formula
for (relative) periods.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/158/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viatcheslav Kharlamov (University of Strasbourg)
DTSTART:20211028T140000Z
DTEND:20211028T150000Z
DTSTAMP:20260404T111217Z
UID:ZAG/159
DESCRIPTION:Title: New examples of surgery invariant counts in real algebraic geometry\nby Viatcheslav Kharlamov (University of Strasbourg) as part of ZAG (Zo
om Algebraic Geometry) seminar\n\n\nAbstract\nInitial Welschinger invarian
ts\, as well as their various generalizations\, are very sensitive\, in ge
neral \, to a change of topology of the underlying real structure. However
\, it was soon noticed that some natural combinations of them have a stron
ger invariance property (remaining also non-trivial in many interesting ca
ses)\, the property that I call "surgery invariance": for a given complex
deformation class of a variety\, they no more depend on a chosen real st
ructure. The starting example is the signed count of real lines on cub
ic surfaces in accordance with B.~Segre's division of such lines in 2 kin
ds\, hyperbolic and elliptic. It is this example that originated a discov
ery of similar counts on higher dimensional hypersurfaces and complete in
tersections\, and served as one of the impulses for a development of an i
nteger valued real Schubert calculus. In this talk (based on a work in pro
gress\, joint with Sergey Finashin) I intend to discuss extending of the a
bove cubic surface example in a bit different direction: from lines on a c
ubic surface to lines\, and even higher degree rational curves\, on other
del Pezzo surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/159/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elana Kalashnikov (Harvard University)
DTSTART:20211102T170000Z
DTEND:20211102T180000Z
DTSTAMP:20260404T111217Z
UID:ZAG/160
DESCRIPTION:Title: Undoing toric degenerations: an analogue of Greene-Plesser mirror sym
metry for the Grassmannian\nby Elana Kalashnikov (Harvard University)
as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nThe most b
asic construction of mirror symmetry compares the Calabi–Yau hypersurfac
es of projective space and projective space quotient a finite group G. The
re is a natural analogue of this finite group action on the Grassmannian G
r(n\, r). In this talk\, I'll explain how toric degenerations\, blow-ups\,
variation of GIT and mirror symmetry relate the Calabi–Yau hypersurface
s of Gr(n\,r) and Gr(n\,r)/G. This is joint work with Tom Coates and Charl
es Doran.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/160/
END:VEVENT
BEGIN:VEVENT
SUMMARY:François Loeser (Sorbonne Université)
DTSTART:20211104T140000Z
DTEND:20211104T150000Z
DTSTAMP:20260404T111217Z
UID:ZAG/161
DESCRIPTION:Title: A motivic version of topological mirror symmetry\nby François Lo
eser (Sorbonne Université) as part of ZAG (Zoom Algebraic Geometry) semin
ar\n\n\nAbstract\nHausel and Thaddeus have conjectured that the moduli spa
ces of twisted SL_n- and PGL_n-Higgs bundles on a smooth projective curve
have the same (twisted) stringy Hodge numbers. This was recently proven by
Groechenig\, Wyss and Ziegler using $p$-adic integration. In this talk we
shall explain how we can prove using motivic integration that the result
holds in the Grothendieck ring of rational Chow motives. This is joint wor
k with D. Wyss.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/161/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farbod Shokrieh (University of Washington)
DTSTART:20211109T170000Z
DTEND:20211109T180000Z
DTSTAMP:20260404T111217Z
UID:ZAG/162
DESCRIPTION:Title: Heights and moments of abelian varieties\nby Farbod Shokrieh (Uni
versity of Washington) as part of ZAG (Zoom Algebraic Geometry) seminar\n\
n\nAbstract\nWe give a formula which\, for a principally polarized abelian
variety $(A\, \\lambda)$ over a number field (or a function field)\, rela
tes the stable Faltings height of $A$ with the N\\'eron--Tate height of a
symmetric theta divisor on $A$. Our formula involves invariants arising fr
om tropical geometry. We also discuss the case of Jacobians in some detail
\, where graphs and electrical networks will play a key role. (Based on jo
int works with Robin de Jong.)\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/162/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rosa Winter (King's College London)
DTSTART:20211111T130000Z
DTEND:20211111T140000Z
DTSTAMP:20260404T111217Z
UID:ZAG/163
DESCRIPTION:Title: Concurrent exceptional curves on del Pezzo surfaces of degree one and
torsion points on elliptic fibrations\nby Rosa Winter (King's College
London) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nL
et S be a del Pezzo surface of degree one. Then S contains 240 exceptional
curves over an algebraically closed field. After blowing up a specific po
int one obtains an elliptic surface E\, where the exceptional curves corre
spond to 240 sections. At most 16 exceptional curves gan go through the sa
me point on S\, and when this happens\, the corresponding point on E is to
rsion on its fiber. In this talk I will consider the question how many exc
eptional curves can go through a point on S for which the corresponding po
int on E is non-torsion on its fiber. First of all I will explain how this
question came up when studying the density of the set of rational points
on del Pezzo surfaces of degree one. I will then show that if at least 9 e
xceptional curves intersect in a point on~S\, the corresponding point on E
is torsion on its fiber. This is less trivial than one might think by loo
king at the Mordell--Weil rank of E. Finally\, in joint work with Julie De
sjardins we show that 7 exceptional curves can go through a non-torsion po
int\, and the question if 8 exceptional curves can go through a non-torsio
n point is still work in progress. I will show how one might try to tackle
this.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/163/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Gross (University of Cambridge)
DTSTART:20211116T150000Z
DTEND:20211116T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/164
DESCRIPTION:Title: Open FJRW theory\nby Mark Gross (University of Cambridge) as part
of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will describe j
oint work with Tyler Kelly and Ran Tessler. FJRW (Fan-Jarvis-Ruan-Witten)
theory is an enumerative theory of quasi-homogeneous singularities\, or al
ternatively\, of Landau-Ginzburg models. It associates to a potential W:C^
n -> C given by a quasi-homogeneous polynomial moduli spaces of (orbi-)cur
ves of some genus and marked points along with some extra structure\, and
these moduli spaces carry virtual fundamental classes as constructed by Fa
n-Jarvis-Ruan. Here we specialize to the case W=x^r+y^s and construct an a
nalogous enumerative theory for disks. We show that these open invariants
provide perturbations of the potential W in such a way that mirror symmetr
y becomes manifest. Further\, these invariants are dependent on certain ch
oices of boundary conditions\, but satisfy a beautiful wall-crossing forma
lism.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/164/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Garcia-Prada (ICMAT)
DTSTART:20211118T150000Z
DTEND:20211118T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/165
DESCRIPTION:Title: Higgs bundles and higher Teichmüller spaces\nby Oscar Garcia-Pra
da (ICMAT) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\
nIt is well-known that the Teichmüller space of a compact real surface ca
n be identified with a connected component of the moduli space of represen
tations of the fundamental group of the surface in PSL(2\,R). Higher Teich
müller spaces are generalizations of this\, where PSL(2\,R) is replaced
by certain simple non-compact real Lie groups of higher rank. As for the u
sual Teichmüller space\, these spaces consist entirely of discrete and fa
ithful representations. Several cases have been identified over the years.
First\, the Hitchin components for split groups\, then the maximal Toledo
invariant components for Hermitian groups\, and more recently certain com
ponents for SO(p\,q). In this talk\, I will describe a general constructio
n of all possible higher Teichmüller spaces\, and a parametrization of th
em using the theory of Higgs bundles\, given in joint work with Bradlow\,
Collier\, Gothen and Oliveira.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/165/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sung Rak Choi (Yonsei University)
DTSTART:20211123T100000Z
DTEND:20211123T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/166
DESCRIPTION:Title: Subadditivity theorem for Okounkov bodies\nby Sung Rak Choi (Yons
ei University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstr
act\nWe will investigate the subadditivity theorem of Okounkov bodies for
algebraic fiber spaces. As an application\, we obtain some numerical vari
ants of the Iitaka conjecture. As a byproduct\, we also obtain a criterion
of birational isotriviality in terms of Okounkov bodies when the general
fiber is of general type. We expect that our results will provide a new ap
proach toward the Iitaka conjecture. This is a joint work with Jinhyung Pa
rk.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/166/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Urech (École polytechnique fédérale de Lausanne)
DTSTART:20211125T150000Z
DTEND:20211125T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/167
DESCRIPTION:Title: Actions of Cremona groups on CAT(0) cube complexes\nby Christian
Urech (École polytechnique fédérale de Lausanne) as part of ZAG (Zoom A
lgebraic Geometry) seminar\n\n\nAbstract\nRecently\, in geometric group th
eory\, isometric actions of groups on CAT(0) cube complexes have turned ou
t to be powerful tools to study a broad range of groups. In this talk\, I
will explain the construction of CAT(0) cube complexes on which groups of
birational transformations act by isometries and explain how to use these
actions to deduce new and old group theoretical and dynamical results abou
t Cremona groups. This is joint work with Anne Lonjou.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/167/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatemeh Rezaee (Loughborough University)
DTSTART:20211130T150000Z
DTEND:20211130T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/168
DESCRIPTION:Title: Wall-crossing pathologies in dimension three\nby Fatemeh Rezaee (
Loughborough University) as part of ZAG (Zoom Algebraic Geometry) seminar\
n\n\nAbstract\nRunning wall-crossing (with respect to Bridgeland stability
conditions)\, I will describe the geometry of associated moduli spaces to
canonical genus four curves\, including the moduli space of PT stable pai
rs and the Hilbert scheme. Along the way\, I will introduce a new wall-cro
ssing phenomenon that induces non-Q-factorial singularities\; hence\, it c
annot be detected as an operation in the Minimal Model Program of the corr
esponding moduli space\, unlike the case for many surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/168/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Lehmann (Boston College)
DTSTART:20211202T130000Z
DTEND:20211202T140000Z
DTSTAMP:20260404T111217Z
UID:ZAG/169
DESCRIPTION:Title: Rational curves on del Pezzo surfaces in characteristic p\nby Bri
an Lehmann (Boston College) as part of ZAG (Zoom Algebraic Geometry) semin
ar\n\n\nAbstract\nTesta classified the components of the moduli space of r
ational curves on a del Pezzo surface over an algebraically closed field o
f characteristic 0. In characteristic p\, new pathologies can appear. I wi
ll explain how such pathologies are predicted by Geometric Manin's Conject
ure and how this perspective leads to a description of "problematic" surfa
ces. When no pathologies occur\, we can completely classify the components
of the moduli space of rational curves. This is joint work with Roya Behe
shti\, Eric Riedl\, and Sho Tanimoto.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/169/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jun-Muk Hwang (Korea Institute for Advanced Study)
DTSTART:20211207T100000Z
DTEND:20211207T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/170
DESCRIPTION:Title: Minimal rational curves and 1-flat irreducible G-structures\nby
Jun-Muk Hwang (Korea Institute for Advanced Study) as part of ZAG (Zoom Al
gebraic Geometry) seminar\n\n\nAbstract\n1-flat irreducible G-structures\,
equivalently\, irreducible G-structures admitting torsion-free affine con
nections\, have been studied extensively in differential geometry\, espec
ially in connection with the theory of affine holonomy groups. In a joint
work with Qifeng Li\, we study them in a setting in algebraic geometry\, w
here they arise from varieties of minimal rational tangents (VMRT) associa
ted to families of minimal rational curves on uniruled projective manifold
s. We prove that such a structure is locally symmetric when the dimension
of the uniruled projective manifold is at least 5. By the classification r
esult of Merkulov and Schwachhoefer on irreducible affine holonomy\, the p
roblem is reduced to the case when the VMRT at a general point of the unir
uled projective manifold is isomorphic to a subadjoint variety. In the lat
ter situation\, we prove a stronger result that\, without the assumption o
f 1-flatness\, the structure arising from VMRT is always locally flat.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/170/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helge Ruddat (University of Hamburg)
DTSTART:20211209T150000Z
DTEND:20211209T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/171
DESCRIPTION:Title: Fano manifolds from smoothing toroidal crossing varieties\nby Hel
ge Ruddat (University of Hamburg) as part of ZAG (Zoom Algebraic Geometry)
seminar\n\n\nAbstract\nI am reporting on a joint work with Corti\, Felten
\, Petracci where we put particular singular log structures on toroidal cr
ossing spaces. We prove various properties of the resulting reflexive log
differential forms from using local log smooth log crepant resolutions. Th
e properties give the ingredients to conclude the Hodge to de Rham degener
ation and the smoothability of the toroidal crossing Fano variety. All Fan
os with very amply anticanonical divisor are obtained from so called "admi
ssible" log singularties by this method. We believe that yet more general
log singularities give all Fano manifolds with non-empty anticanonical cla
ss by similar methods.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/171/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Schaposnik (University of Illinois at Chicago)
DTSTART:20211214T150000Z
DTEND:20211214T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/172
DESCRIPTION:Title: The geometry of Generalized Hyperpolygons\, Hitchin systems and other
scientific advances\nby Laura Schaposnik (University of Illinois at C
hicago) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn
this talk we will introduce generalized hyperpolygons\, which arise as Na
kajima-type representations of a comet-shaped quiver\, following recent wo
rk joint with Steven Rayan. After showing how to identify these representa
tions with pairs of polygons\, we shall associate to the data an explicit
meromorphic Higgs bundle on a genus-g Riemann surface\, where g is the num
ber of loops in the comet. We shall see that\, under certain assumptions o
n flag types\, the moduli space of generalized hyperpolygons admits the st
ructure of a completely integrable Hamiltonian system. Having made the con
nection to Hitchin moduli spaces\, we will consider different geometric me
thods developed within that set up to study geometric properties of integr
able systems and their dualities. Finally\, we shall conclude the talk men
tioning other directions in which one can apply geometric insights to make
scientific advances.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/172/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Ballard (University of South Carolina)
DTSTART:20211216T150000Z
DTEND:20211216T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/173
DESCRIPTION:Title: Stratified Mukai flops revisited\nby Matthew Ballard (University
of South Carolina) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nA
bstract\nWe will describe how constructing Fourier-Mukai kernels for strat
ified Mukai flops fits into a general framework. Joint with N. Chidambaram
and D. Favero.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/173/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linquan Ma (Purdue University)
DTSTART:20211221T170000Z
DTEND:20211221T180000Z
DTSTAMP:20260404T111217Z
UID:ZAG/174
DESCRIPTION:Title: The cohomology table of coherent sheaves on singular projective varie
ties\nby Linquan Ma (Purdue University) as part of ZAG (Zoom Algebraic
Geometry) seminar\n\n\nAbstract\nThe cohomology table of a coherent sheaf
on a projective variety is numerical data of the dimension of each cohomo
ogy group of each twist of the sheaf. Eisenbud--Schreyer give a descriptio
n of the cone of cohomology table of vector bundles and coherent sheaves o
n projective spaces. This leads to their proof of the Boij--Soderberg theo
ry which describes the cone spanned by the Betti tables of graded modules
over polynomial rings. In this talk\, we give some extensions of these res
ults of Eisenbud--Schreyer to singular projective varieties and singular s
tandard graded rings. Our central technique is to use a sequence of cohere
nt sheaves that behave like an Ulrich sheave asymptotically. We call such
sequence a lim Ulrich sequence of sheaves and we can prove their existence
in positive characteristic. This talk is largely based on joint work in p
rogress with Srikanth Iyengar and Mark Walker.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/174/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Okounkov (Columbia University)
DTSTART:20220203T090000Z
DTEND:20220203T100000Z
DTSTAMP:20260404T111217Z
UID:ZAG/175
DESCRIPTION:Title: The unramified Eisenstein spectrum\nby Andrei Okounkov (Columbia
University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract
\nI will report on joint work with David Kazhdan\, in which we determine t
he unramified Eisenstein spectrum for\nall split reductive groups over a g
lobal field. Our methods are rooted in topology and algebraic geometry.\nS
pecifically\, we relate the spectral decomposition to a decomposition of $
T^*(B \\backslash G / B)$ in in a certain cobordism group\, where $G$ is t
he Langlands dual group. This works equally well for fields of positive an
d zero characteristic.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/175/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takumi Murayama (Princeton University)
DTSTART:20220111T170000Z
DTEND:20220111T180000Z
DTSTAMP:20260404T111217Z
UID:ZAG/176
DESCRIPTION:Title: The Kawamata–Viehweg vanishing theorem for schemes\nby Takumi M
urayama (Princeton University) as part of ZAG (Zoom Algebraic Geometry) se
minar\n\n\nAbstract\nIn 1953\, Kodaira proved what is now called the Kodai
ra vanishing theorem\, which states that if L is an ample divisor on a com
plex projective manifold X\, then H^i(X\,-L) = 0 for all i < dim(X). Since
then\, Kodaira's theorem and its generalizations for complex projective v
arieties – in particular\, the Kawamata–Viehweg vanishing theorem and
its relative version due to Kawamata–Matsuda–Matsuki – have become i
ndispensable tools in algebraic geometry over fields of characteristic zer
o\, in particular in birational geometry and the minimal model program. Ho
wever\, while the goal in the minimal model program is to study birational
equivalences between projective varieties\, recent progress in the minima
l model program has shown that it would be very useful to have a version o
f the Kawamata–Viehweg vanishing theorem that holds for schemes that are
not necessarily projective varieties. Recently\, I proved the relative Ka
wamata–Viehweg vanishing theorem for schemes of equal characteristic zer
o. My results are optimal given known counterexamples to vanishing theorem
s in positive and mixed characteristic\, and have many applications to bot
h algebraic geometry and commutative algebra. In this talk\, I will discus
s my vanishing theorem and several of its applications.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/176/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kris Shaw (University of Oslo)
DTSTART:20220113T150000Z
DTEND:20220113T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/177
DESCRIPTION:Title: A tropical approach to the enriched count of bitangents to quartic cu
rves\nby Kris Shaw (University of Oslo) as part of ZAG (Zoom Algebraic
Geometry) seminar\n\n\nAbstract\nUsing A1 enumerative geometry Larson and
Vogt have provided an enriched count of the 28 bitangents to a quartic cu
rve. In this talk\, I will explain how these enriched counts can be comput
ed combinatorially using tropical geometry. I will also introduce an arith
metic analogue of Viro’s patchworking for real algebraic curves which\,
in some cases\, retains enough data to recover the enriched counts. This t
alk is based on joint work with Hannah Markwig and Sam Payne.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/177/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eunjeong Lee (Institute for Basic Science\, Center for Geometry an
d Physics)
DTSTART:20220118T100000Z
DTEND:20220118T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/178
DESCRIPTION:Title: On smooth toric Richardson varieties\nby Eunjeong Lee (Institute
for Basic Science\, Center for Geometry and Physics) as part of ZAG (Zoom
Algebraic Geometry) seminar\n\n\nAbstract\nSchubert varieties and Richards
on varieties are some of the most interesting subvarieties of the full fla
g varieties. A maximal torus acts on the full flag variety and these subva
rieties are stable under the action. Considering the restriction of the mo
ment map on Richardson varieties\, we obtain Bruhat interval polytopes. Th
e combinatorics of Bruhat interval polytopes play an important role in stu
dying toric Richardson varieties. In this talk\, we consider an interestin
g family of smooth toric Richardson varieties each element of which is ass
ociated with a cubic Bruhat interval polytope\, called a toric variety \\t
extit{of Catalan type}. We study the relationship between the isomorphism
classes of toric varieties of Catalan type and polygon triangulations. Mor
eover\, we consider the isomorphism classes of toric Schubert varieties wh
ich may not be of Catalan type. This talk is based on joint work with Miki
ya Masuda and Seonjeong Park.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/178/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ehud Hrushovski (University of Oxford)
DTSTART:20220120T113000Z
DTEND:20220120T123000Z
DTSTAMP:20260404T111217Z
UID:ZAG/179
DESCRIPTION:Title: Old and new results in the model theory of finite fields\nby Ehud
Hrushovski (University of Oxford) as part of ZAG (Zoom Algebraic Geometry
) seminar\n\n\nAbstract\nAx's determination of the first-order theory of
finite fields in 1968 was the starting point of a rich chapter of model
theory\; highlights include the Denef-Loeser connection between definable
sets over pseudo-finite fields and motives\, their use in motivic integra
tion\, the Chatzidakis-Van den Dries-Macintyre measure theory\, the str
ong Szemeredi regularity lemma for definable sets and applications to expa
nsion due to Terry Tao. I will sketch a path through some of this materi
al\, aiming to touch on recent work of Levi and Chevalier on higher regu
larity\, and on open problems that arise when an additive character is a
dded to the structure.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/179/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Larson (Stanford University)
DTSTART:20220125T170000Z
DTEND:20220125T180000Z
DTSTAMP:20260404T111217Z
UID:ZAG/180
DESCRIPTION:Title: The rational Chow rings of M_7\, M_8\, and M_9\nby Hannah Larson
(Stanford University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n
\nAbstract\nThe rational Chow ring of the moduli space M_g of curves of ge
nus g is known for g up to 6. In each of these cases\, the Chow ring is ta
utological (generated by certain natural classes known as kappa classes).
In joint work with Sam Canning\, we prove that the rational Chow ring of M
_g is tautological for g = 7\, 8\, 9\, thereby determining the Chow rings
by earlier work of Faber. In this talk\, I will give an overview of our ap
proach\, with particular focus on the locus of tetragonal curves (special
curves admitting a degree 4 map to P^1).\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/180/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sukmoon Huh (Sungkyunkwan Universityok)
DTSTART:20220127T100000Z
DTEND:20220127T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/181
DESCRIPTION:Title: Torelli problem on logarithmic sheaves\nby Sukmoon Huh (Sungkyunk
wan Universityok) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAb
stract\nThe logarithmic sheaf associated to a reduced divisor\, is the she
af of differential 1-forms with logarithmic poles along the divisor\, and
it was introduced by P. Deligne to define a mixed Hodge structure on the c
omplement of the divisor. There have been a great deal of study on this su
bject\, and one of the questions is whether the sheaf determines the divis
or or not\, which we call the Torelli problem. In case of general hyperpla
ne arrangements on projective spaces\, I. Dolgachev and M. Kapranov gave a
positive answer to the Torelli problem when the number of hyperplanes is
big enough\, and then later J. Valles gave a complete answer. In this talk
we give several other results on the Torelli problem\, and report our rec
ent result\, in which we introduce two different approachs to have a posit
ive answer on the problem. This is a joint work with S. Marchesi\, J. Pons
-Llopis and J. Valles.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/181/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soheyla Feyzbakhsh (Imperial College London)
DTSTART:20220201T150000Z
DTEND:20220201T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/182
DESCRIPTION:Title: Moduli spaces of stable objects in the Kuznetsov component of cubic t
hreefolds\nby Soheyla Feyzbakhsh (Imperial College London) as part of
ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nWe will first discuss
a general criterion that ensures a fractional Calabi-Yau category of dime
nsion less than or equal to 2 admits a unique Serre-invariant stability co
ndition up to the action of the universal cover of GL+(2\, R). This result
can be applied to a certain triangulated subcategory (called the Kuznetso
v component) of the bounded derived category of coherent sheaves on a cubi
c threefold. As an application\, we will prove (i) a categorical version o
f the Torelli theorem holds for cubic threefolds\, and (ii) the moduli spa
ce of Ulrich bundles of fixed rank r greater than or equal to 2 on a cubic
threefold is irreducible. The talk is based on joint work with Laura Pert
usi and a group project with A. Bayer\, S.V. Beentjes\, G. Hein\, D. Marti
nelli\, F. Rezaee and B. Schmidt.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/182/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Keel (The University of Texas at Austin)
DTSTART:20220208T170000Z
DTEND:20220208T180000Z
DTSTAMP:20260404T111217Z
UID:ZAG/183
DESCRIPTION:Title: Mirror symmetry and analytic disks\nby Sean Keel (The University
of Texas at Austin) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n
Abstract\nI will explain my recent construction\, joint with Tony Yu\, of
the mirror to an affine log CY manifold as the spectrum of an algebra with
a canonical basis and structure constants naive counts of Berkovich analy
tic disks. I wont assume any previous knowledge of Berkovich geometry.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/183/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Kummer (TU Dresden)
DTSTART:20220210T150000Z
DTEND:20220210T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/184
DESCRIPTION:Title: Secant varieties of real curves\nby Mario Kummer (TU Dresden) as
part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAfter an intr
oduction to hyperbolic polynomials and their relevance in convex optimizat
ion\, I will explain a construction of hyperbolic polynomials using secant
varieties of curves. Further\, I will relate this to the theory of Ulrich
sheaves.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/184/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alena Pirutka (Courant Institute of Mathematical Sciences\, New Yo
rk University)
DTSTART:20220215T150000Z
DTEND:20220215T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/185
DESCRIPTION:Title: On local-global principles and Galois cohomology\nby Alena Pirutk
a (Courant Institute of Mathematical Sciences\, New York University) as pa
rt of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn this talk we
will review several questions of local-global type for schemes of dimensi
on 3 in the arithmetic (curves over semi-global fields) and geometric (thr
eefolds over a finite field) settings.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/185/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Favero (University of Alberta)
DTSTART:20220217T160000Z
DTEND:20220217T170000Z
DTSTAMP:20260404T111217Z
UID:ZAG/186
DESCRIPTION:Title: Path Homotopy Quiver Algebras and Mirror Symmetry\nby David Faver
o (University of Alberta) as part of ZAG (Zoom Algebraic Geometry) seminar
\n\n\nAbstract\nGiven a quiver (directed graph) embedded in a topological
space\, one can consider the algebra of directed paths up to homotopy. Co
nversely\, given a certain type of algebra\, I will construct a quiver and
a topological space which recovers this algebra by the above procedure.
These constructions induce an equivalence between the derived category of
the algebra and a certain subcategory of the derived category of sheaves o
n the topological space. As applications\, I will recover some examples o
f homological mirror symmetry for Berglund-Hubsch-Krawitz mirrors and for
toric varieties following work of Bondal and Fan-Lui-Treumann-Zaslow.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/186/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alicia Dickenstein (Universidad de Buenos Aires)
DTSTART:20220222T150000Z
DTEND:20220222T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/187
DESCRIPTION:Title: Iterated and mixed discriminants\nby Alicia Dickenstein (Universi
dad de Buenos Aires) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\
nAbstract\nClassical work by Salmon and Bromwich classified singular inter
sections of two quadric surfaces. The basic idea of these results was alre
ady pursued by Cayley in connection with tangent intersections of conics i
n the plane and used by Schafli for the study of hyperdeterminants. More r
ecently\, the problem has been revisited with similar tools in the context
of geometric modeling and a generalization to the case of two higher dime
nsional quadric hypersurfaces was given by Ottaviani. In joint work with S
andra di Rocco and Ralph Morrison\, we propose and study a generalization
of this question for systems of Laurent polynomials with support on a fixe
d point configuration. In the non-defective case\, the closure of the locu
s of coefficients giving a non-degenerate multiple root of the system is d
efined by a polynomial called the mixed discriminant. We define a related
polynomial called the multivariate iterated discriminant. This iterated di
scriminant is easier to compute and we prove that it is always divisible b
y the mixed discriminant. We show that tangent intersections can be comput
ed via iteration if and only if the singular locus of a corresponding dual
variety has sufficiently high codimension. We also study when point confi
gurations corresponding to Segre-Veronese varieties and to the lattice poi
nts of planar smooth polygons\, have their iterated discriminant equal to
their mixed discriminant.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/187/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diane Maclagan (University of Warwick)
DTSTART:20220224T150000Z
DTEND:20220224T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/188
DESCRIPTION:Title: Toric and tropical Bertini theorems in arbitrary characteristic\n
by Diane Maclagan (University of Warwick) as part of ZAG (Zoom Algebraic G
eometry) seminar\n\n\nAbstract\nThe classical Bertini theorem on irreducib
ility when intersecting by hyperplanes is a standard part of the algebraic
geometry toolkit. This was generalised recently\, in characteristic zero\
, by Fuchs\, Mantova\, and Zannier to a toric Bertini theorem for subvarie
ties of an algebraic torus\, with hyperplanes replaced by subtori. I will
discuss joint work with Gandini\, Hering\, Mohammadi\, Rajchgot\, Wheeler\
, and Yu in which we give a different proof of this theorem that removes t
he characteristic assumption. An application is a tropical Bertini theorem
.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/188/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georg Oberdieck (Hausdorff Center for Mathematics)
DTSTART:20220301T110000Z
DTEND:20220301T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/189
DESCRIPTION:Title: Holomorphic anomaly equations for the Hilbert schemes of points of a
K3 surface\nby Georg Oberdieck (Hausdorff Center for Mathematics) as p
art of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nHolomorphic an
omaly equations are certain structural properties predicted by physics for
the Gromov-Witten theory of Calabi-Yau manifolds. In this talk I will exp
lain the conjectural form of these equations for the Hilbert scheme of poi
nts of a K3 surface\, and explain how to prove them for genus 0 and up to
three markings. As a corollary\, for fixed n\, the (reduced) quantum cohom
ology of Hilb^n K3 is determined up to finitely many coefficients.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/189/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Nordstrom (University of Bath)
DTSTART:20220303T110000Z
DTEND:20220303T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/190
DESCRIPTION:Title: K3 surfaces and twisted connected sum G2-manifolds\nby Johannes N
ordstrom (University of Bath) as part of ZAG (Zoom Algebraic Geometry) sem
inar\n\n\nAbstract\nThe twisted connected sum construction of Kovalev prod
uces many examples of closed Riemannian 7-manifolds with holonomy group G_
2 (a special class of Ricci-flat manifolds)\, starting from complex algebr
aic geometry data like Fano 3-folds. If the pieces admit automorphisms\, t
hen adding an extra twist to the construction yields examples with a wider
variety of topological features. I will outline the constructions\, and d
escribe how a good understanding of moduli of K3 surfaces appearing as ant
icanonical divisors in Fano 3-folds is used in a crucial way to match the
pieces in the gluing procedure. This is joint work with Diarmuid Crowley a
nd Sebastian Goette.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/190/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Bragg (University of California\, Berkeley)
DTSTART:20220308T170000Z
DTEND:20220308T180000Z
DTSTAMP:20260404T111217Z
UID:ZAG/191
DESCRIPTION:Title: Compact supersingular twistor spaces\nby Daniel Bragg (University
of California\, Berkeley) as part of ZAG (Zoom Algebraic Geometry) semina
r\n\n\nAbstract\nSupersingular twistor spaces are certain families of K3 s
urfaces over A^1 associated to a supersingular K3 surface. We will describ
e a geometric construction that produces families of K3 surfaces over P^1
which compactify supersingular twistor spaces. The key input is a construc
tion relating Brauer classes of order p on a scheme of characteristic p to
certain sheaves of twisted differential operators. We will give some resu
lts on the geometry of compactified supersingular twistor spaces\, and som
e applications.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/191/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Yves Welschinger (Institut Camille Jordan\, Université Lyon
1)
DTSTART:20220310T150000Z
DTEND:20220310T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/192
DESCRIPTION:Title: Shellable tilings on simplicial complexes\nby Jean-Yves Welsching
er (Institut Camille Jordan\, Université Lyon 1) as part of ZAG (Zoom Alg
ebraic Geometry) seminar\n\n\nAbstract\nI will introduce a notion of shell
able tilings on finite simplicial complexes\, prove their existence after
finitely many stellar subdivisions and discuss their relations with discre
te Morse theory and h-vectors. Every shelled tiling computes the (co)homol
ogy of the complex via two spectral sequences. As a consequence\, I deduce
the existence of piecewise-linear pinched handle decompositions for all c
losed triangulated manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/192/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guolei Zhong (Institute for Basic Science)
DTSTART:20220315T090000Z
DTEND:20220315T100000Z
DTSTAMP:20260404T111217Z
UID:ZAG/193
DESCRIPTION:Title: Compact Kähler threefolds with the action of an abelian group of max
imal dynamical rank\nby Guolei Zhong (Institute for Basic Science) as
part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nLet X be a co
mpact Kaehler manifold. It is proved by Dinh and Sibony that\, for any abe
lian subgroup G of the automorphism group Aut(X)\, if G is of positive ent
ropy\, then G is free abelian with rank no more than dim(X)-1. In the past
decade\, when X is projective\, the extremal case rank(G)=dim(X)-1 (being
maximal) has been intensively studied by Zhang. In this talk\, we conside
r the case when X is a general compact Kaehler 3-fold and rank(G)=2. By ru
nning the G-equivariant log minimal model program\, we show that such X is
either rationally connected\, or bimeromorphic to a quasi-etale quotient
of a complex 3-torus.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/193/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lawrence Jack Barrott (University of Leiden)
DTSTART:20220317T150000Z
DTEND:20220317T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/194
DESCRIPTION:Title: Fibrations and degenerations of Calabi-Yau varieties via tropical geo
metry\nby Lawrence Jack Barrott (University of Leiden) as part of ZAG
(Zoom Algebraic Geometry) seminar\n\n\nAbstract\nOne expectation from the
Doran-Harder-Thompson is that certain degenerations of Calabi-Yau's should
correspond under mirror symmetry to fibrations by lower dimensional Calab
i-Yau's. I will make this expectation precise\, and explain how to prove i
t under certain assumptions using the Gross-Siebert program. The proof use
s an old result of Deligne-Illusie together with modern deformation theory
from Chan-Leung-Ma and Felten-Filip-Ruddat.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/194/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Bridgeland (University of Sheffield)
DTSTART:20220322T140000Z
DTEND:20220322T150000Z
DTSTAMP:20260404T111217Z
UID:ZAG/195
DESCRIPTION:Title: Geometric structures on spaces of quadratic differentials\nby Tom
Bridgeland (University of Sheffield) as part of ZAG (Zoom Algebraic Geome
try) seminar\n\n\nAbstract\nThis talk is part of a long-running saga which
aims to encode the Donaldson-Thomas invariants of a CY3 triangulated cate
gory in a geometric structure on its stability space. I will focus on a cl
ass of examples of such categories whose stability spaces are known to par
ameterise compact Riemann surfaces equipped with quadratic differentials.
I will explain exactly what geometric structure we should look for on thes
e spaces\, and then use moduli spaces of Higgs bundles\, flat connections\
, etc to construct it.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/195/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masafumi Hattori (Kyoto University)
DTSTART:20220324T100000Z
DTEND:20220324T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/196
DESCRIPTION:Title: On K-stability of Calabi-Yau fibrations\nby Masafumi Hattori (Kyo
to University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstr
act\nIn K-stability\, the characterization of K-stable varieties is well-s
tudied when K_X is ample or X is a Calabi-Yau or Fano variety. However\, K
-stability of Fano fibrations or Calabi-Yau fibrations (i.e.\, K_X is rela
tively trivial) is not known much in algebraic geometry. On the other hand
\, cscK problems on fibrations are studied by Fine\, Jian-Shi-Song and Der
van-Sektnan in Kahler geometry. We introduce adiabatic K-stability (If f:(
X\,H)\\to (B\,L) is a fibration of polarized varieties\, this means that K
-stability of (X\,aH+L) for sufficiently small a) and show that adiabatic
K-semistability of Calabi-Yau fibration implies log-twisted K-semistabilit
y of the base variety by applying the canonical bundle formula. If the bas
e is a curve\, we also obtain a partial converse. In this talk\, I would l
ike to explain our main results and their applications to rational ellipti
c surfaces and the conjecture of Miranda on Chow-stability of rational Wei
erstrass fibrations.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/196/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Collins (Massachusetts Institute of Technology)
DTSTART:20220329T140000Z
DTEND:20220329T150000Z
DTSTAMP:20260404T111217Z
UID:ZAG/197
DESCRIPTION:Title: SYZ mirror symmetry for some Calabi-Yau surface pairs\nby Tristan
Collins (Massachusetts Institute of Technology) as part of ZAG (Zoom Alge
braic Geometry) seminar\n\n\nAbstract\nI will discuss a proof of a strong
form of the SYZ mirror symmetry conjecture for Calabi-Yau surfaces pairs c
onstructed from del Pezzo surfaces and rational elliptic surfaces. Time pe
rmitting\, I will also mention some applications\, including to the Torell
i theorem for ALH* gravitational instantons. This is joint work with A. Ja
cob and Y.-S. Lin.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/197/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julius Ross (University of Illinois Chicago)
DTSTART:20220331T160000Z
DTEND:20220331T170000Z
DTSTAMP:20260404T111217Z
UID:ZAG/198
DESCRIPTION:Title: Hodge-Riemann Classes and Schur Polynomials\nby Julius Ross (Univ
ersity of Illinois Chicago) as part of ZAG (Zoom Algebraic Geometry) semin
ar\n\n\nAbstract\nThe classical Hodge-Riemann bilinear relations are state
ments about the intersection form associated to the self-wedge product of
a K\\"ahler form on a compact complex manifold. Gromov initiated the que
stion as to whether there are other cohomology that give rise these same b
ilinear relations\, and proved that this is the case for the intersection
of (possibly different) K\\"ahler classes. In this talk I will discuss j
oint work with Matei Toma in which we prove that the Schur classes of ampl
e vector bundles have the Hodge-Riemann bilinear relations (at least on $H
^{1\,1}$). This gives rise to a number of new inequalities among charact
eristic classes of ample vector bundles that should be thought of as gener
alizations of the Khovanskii-Tessier inequalities. And if time allows I w
ill also discuss how this extends to the non-projective case and beyond.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/198/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulio Codogni (Università di Roma Tor Vergata)
DTSTART:20220405T110000Z
DTEND:20220405T120000Z
DTSTAMP:20260404T111217Z
UID:ZAG/199
DESCRIPTION:Title: Ample cone of KSB and K- moduli spaces\nby Giulio Codogni (Univer
sità di Roma Tor Vergata) as part of ZAG (Zoom Algebraic Geometry) semina
r\n\n\nAbstract\nI will present some quantitative results about the ample
cone of the moduli spaces of KSB stable and K-stable varieties of any dime
nsion. These results follow from various higher dimensional generalization
s of the Xiao-Cornalba-Harris slope inequality. Our proofs combine some ne
w Noether and Castelnuovo inequalities with a careful study of the Harder-
Narasimhan filtration of the push-forward of the log pluri-canonical bundl
es. The talk is based on a joint work with Luca Tasin and Filippo Viviani.
\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/199/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Laface (Universidad de Concepción)
DTSTART:20220407T150000Z
DTEND:20220407T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/200
DESCRIPTION:Title: On effective cones of rational surfaces\nby Antonio Laface (Unive
rsidad de Concepción) as part of ZAG (Zoom Algebraic Geometry) seminar\n\
n\nAbstract\nEffective cones of rational surfaces have been intensively st
udied in the past few years\, especially in the context of Nagata conjectu
re and Seshadri constants. After reviewing recent results on blow-ups of t
he projective plane at points in very general position\, I will focus on b
low-ups of toric surfaces at a general point\, discussing examples of poly
hedral and non-polyhedral effective cones. This is joint work with A-M. Ca
stravet\, J. Tevelev and L. Ugaglia.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/200/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Ignacio Burgos Gil (Instituto de Ciencias Matemáticas)
DTSTART:20220412T140000Z
DTEND:20220412T150000Z
DTSTAMP:20260404T111217Z
UID:ZAG/201
DESCRIPTION:Title: Chern-Weil theory and Hilbert-Samuel theorem for semi-positive singul
ar toroidal metrics on line bundles\nby Jose Ignacio Burgos Gil (Insti
tuto de Ciencias Matemáticas) as part of ZAG (Zoom Algebraic Geometry) se
minar\n\n\nAbstract\nIn this talk I will report on joint work with A. Bote
ro\, D. Holmes and R. de Jong. Using the theory of b-divisors and non-plur
ipolar products we show that Chen-Weil theory and a Hilbert Samuel theorem
can be extended to a wide class of singular semi-positive metrics. We app
ly the techniques relating semipositive metrics on line bundles to b-divis
ors to study the line bundle of Siegel-Jacobi forms with the Peterson metr
ic. On the one hand we prove that the ring of Siegel-Jacobi forms of const
ant positive relative index is never finitely generated\, and we recover a
formula of Tai giving the asymptotic growth of the dimension of the space
s of Siegel-Jacobi modular forms.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/201/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Lieblich (University of Washington)
DTSTART:20220414T170000Z
DTEND:20220414T180000Z
DTSTAMP:20260404T111217Z
UID:ZAG/202
DESCRIPTION:Title: Infinite rank vector bundles and applications\nby Max Lieblich (U
niversity of Washington) as part of ZAG (Zoom Algebraic Geometry) seminar\
n\n\nAbstract\nThis is a report on joint work with Johan de Jong and Minse
on Shin. Grothendieck famously asked whether the Brauer group and cohomolo
gical Brauer group of a scheme coincide\, a question which still lacks a g
ood answer. Modern methods reduce this question to a question about the ex
istence of non-zero vector bundles of finite rank on certain stacks. I wil
l discuss what happens if one allows vector bundles of infinite rank\, and
how this infinite-rank version of the question is related to the resoluti
on property for schemes. I will also discuss some basic questions about ve
ctor bundles of infinite rank on varieties\, including the potential exist
ence of some mysterious invariants.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/202/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erik Paemurru (International Center for Mathematical Sciences –
Sofia)
DTSTART:20220419T140000Z
DTEND:20220419T150000Z
DTSTAMP:20260404T111217Z
UID:ZAG/203
DESCRIPTION:Title: Counting Divisorial Contractions with Centre a cAn-singularity\nb
y Erik Paemurru (International Center for Mathematical Sciences – Sofia)
as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nFirst\, w
e simplify the existing classification due to Kawakita and Yamamoto of 3-d
imensional divisorial contractions with centre a cA_n-singularity. Next we
consider divisorial contractions of discrepancy at least 2 to a fixed var
iety with centre a cA_n-singularity. We show that if there exists one such
divisorial contraction\, then there exist uncountably many such divisoria
l contractions.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/203/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Elduque (Universidad Autónoma de Madrid)
DTSTART:20220426T120000Z
DTEND:20220426T130000Z
DTSTAMP:20260404T111217Z
UID:ZAG/204
DESCRIPTION:Title: Eigenspace decomposition of mixed Hodge structures on Alexander modul
es\nby Eva Elduque (Universidad Autónoma de Madrid) as part of ZAG (Z
oom Algebraic Geometry) seminar\n\n\nAbstract\nIn previous work jointly wi
th Geske\, Herradón Cueto\, Maxim and Wang\, we constructed a mixed Hodge
structure (MHS) on the torsion part of Alexander modules\, which generali
zes the MHS on the cohomology of the Milnor fiber for weighted homogeneous
polynomials. The cohomology of a Milnor fiber carries a monodromy action\
, whose semisimple part is an isomorphism of MHS. The natural question of
whether this result still holds for Alexander modules was then posed. In t
his talk\, we will talk about the solution to this question\, as well as s
ome consequences and explicit computations. Joint work with Moises Herrad
ón Cueto.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/204/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodoros Papazachariou (University of Essex)
DTSTART:20220426T140000Z
DTEND:20220426T150000Z
DTSTAMP:20260404T111217Z
UID:ZAG/205
DESCRIPTION:Title: K-moduli for log Fano complete intersections\nby Theodoros Papaza
chariou (University of Essex) as part of ZAG (Zoom Algebraic Geometry) sem
inar\n\n\nAbstract\nAn important category of geometric objects in algebrai
c geometry is smooth Fano varieties\, which have positive curvature. These
have been classified in 1\, 10 and 105 families in dimensions 1\, 2 and 3
respectively\, while in higher dimensions the number of Fano families is
yet unknown\, although we know that their number is bounded. An important
problem is compactifying these families into moduli spaces via K-stability
. In this talk\, I will describe the compactification of the family of Fan
o threefolds\, which is obtained by blowing up the projective space along
a complete intersection of two quadrics which is an elliptic curve\, into
a K-moduli space using Geometric Invariant Theory (GIT). A more interestin
g setting occurs in the case of pairs of varieties and a hyperplane sectio
n where the K-moduli compactifications tessellate depending on a parameter
. In this case it has been shown recently that the K-moduli decompose into
a wall-chamber decomposition depending on a parameter\, but wall-crossing
phenomena are still difficult to describe explicitly. Using GIT\, I will
describe an explicit example of wall-crossing in the K-moduli spaces\, wh
ere both variety and divisor differ in the deformation families before and
after the wall\, given by log pairs of Fano surfaces of degree 4 and a hy
perplane section.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/205/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arman Sarikyan (University of Edinburgh)
DTSTART:20220428T100000Z
DTEND:20220428T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/206
DESCRIPTION:Title: Equivariant pliability of the projective space\nby Arman Sarikyan
(University of Edinburgh) as part of ZAG (Zoom Algebraic Geometry) semina
r\n\n\nAbstract\nWe classify finite subgroups $G\\subset\\mathrm{PGL}_4(\\
mathbb{C})$ such that $\\mathbb{P}^3$ is not $G$-birational to conic bundl
es and del Pezzo fibrations\, and explicitly describe all $G$-Mori fibre s
paces that are $G$-birational to $\\mathbb{P}^3$ for these subgroups. This
is a joint work with I. Cheltsov\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/206/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kyoung-Seog Lee (University of Miami)
DTSTART:20220503T150000Z
DTEND:20220503T160000Z
DTSTAMP:20260404T111217Z
UID:ZAG/207
DESCRIPTION:Title: Derived categories and motives of moduli spaces of vector bundles on
curves\nby Kyoung-Seog Lee (University of Miami) as part of ZAG (Zoom
Algebraic Geometry) seminar\n\n\nAbstract\nDerived categories and motives
are important invariants of algebraic varieties invented by Grothendieck a
nd his collaborators around the 1960s. In 2005\, Orlov conjectured that th
ey will be closely related and now there are several evidences supporting
his conjecture. On the other hand\, moduli spaces of vector bundles on cur
ves provide attractive and important examples of algebraic varieties and t
here have been intensive works studying them. In this talk\, I will discus
s derived categories and motives of moduli spaces of vector bundles on cur
ves and how they are related. Part of this talk is based on several joint
works with I. Biswas\, T. Gomez\, H.-B. Moon and M. S. Narasimhan.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/207/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ariyan Javanpeykar (Johannes Gutenberg University of Mainz)
DTSTART:20220505T100000Z
DTEND:20220505T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/208
DESCRIPTION:Title: Shafarevich's conjecture for canonically polarized varieties revisite
d\nby Ariyan Javanpeykar (Johannes Gutenberg University of Mainz) as p
art of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAbstract: Arak
elov-Parshin proved Shafarevich's conjecture for the (actual) moduli space
M_g of curves of genus g (g>1). Namely\, for every curve C\, the set of
isomorphism classes of non-isotrivial morphisms C \\to M_g is finite. This
finiteness result is similar to the theorem of De Franchis: for every hyp
erbolic curve X\, the set of non-constant morphisms C->X is finite. Intere
stingly\, M_g is hyperbolic (in any reasonable sense of the word "hyperbol
ic"). Is maybe the theorem of Arakelov-Parshin and De Franchis an instance
of a more general finiteness property for hyperbolic varieties/stacks? Th
e answer is no. The conclusion of the theorem of De Franchis fails for hyp
erbolic surfaces (such as X x X) and the conclusion of Arakelov-Parshin's
theorem fails for the moduli space of canonically polarized surfaces (beca
use it contains copies of X x X). How to remedy this? Guided by finiteness
properties of compact hyperbolic varieties\, we establish new finiteness
properties for the moduli space CanPol of canonically polarized varieties
by proving rigidity properties of pointed maps. Applications include bound
s on dimensions of moduli spaces of maps to CanPol. Joint work with Steven
Lu\, Ruiran Sun\, and Kang Zuo.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/208/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emma Brakkee (University of Amsterdam)
DTSTART:20220510T120000Z
DTEND:20220510T130000Z
DTSTAMP:20260404T111217Z
UID:ZAG/209
DESCRIPTION:Title: General type results for moduli of hyperkahler varieties\nby Emma
Brakkee (University of Amsterdam) as part of ZAG (Zoom Algebraic Geometry
) seminar\n\n\nAbstract\nIn 2007\, Gritsenko\, Hulek and Sankaran proved t
hat the moduli space of K3 surfaces of degree 2d is of general type when d
>61. Their strategy is to reduce the question to the existence of a certai
n cusp form for an orthogonal modular variety. This method has been applie
d successfully to prove general type results for\, among others\, some mod
uli of higher-dimensional hyperkähler varieties. In this talk\, we sketch
the reduction argument and give general type results for some more types
of hyperkähler moduli spaces. We also explain what the challenges are whe
n trying to imitate the strategy for other moduli spaces of hyperkähler v
arieties. This is joint work in progress with I. Barros\, P. Beri and L. F
lapan.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/209/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Chan (UNSW Sydney)
DTSTART:20220512T210000Z
DTEND:20220512T220000Z
DTSTAMP:20260404T111217Z
UID:ZAG/210
DESCRIPTION:Title: The minimal model program for arithmetic surfaces enriched by a Braue
r class\nby Daniel Chan (UNSW Sydney) as part of ZAG (Zoom Algebraic G
eometry) seminar\n\n\nAbstract\nMori's minimal model program is a major or
ganising principle for studying and classifying varieties $X$. It has been
generalised in many directions\, and in this talk\, we examine a ``noncom
mutative'' one where $X$ is enriched by a Brauer class $\\beta \\in K(X)$.
We focus on some new results where $X$ is a surface whose residue fields
are finite. When the order of $\\beta$ is a prime >5\, we recover most of
standard surface theory including existence of terminal resolutions\, Cast
elnuovo contraction and Zariski factorisation. However\, interesting new e
xamples of terminal singularities and Castelnuovo contractions appear\, wh
ich have no characteristic zero analogue.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/210/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoit Claudon (Université de Rennes 1)
DTSTART:20220517T100000Z
DTEND:20220517T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/211
DESCRIPTION:Title: Numerical characterization of complex tori\nby Benoit Claudon (Un
iversité de Rennes 1) as part of ZAG (Zoom Algebraic Geometry) seminar\n\
n\nAbstract\nIn this talk I will explain how to recognize complex tori amo
ng Kahler klt spaces (smooth in codimension 2) in terms of vanishing of Ch
ern numbers. It requires first to define Chern classes on singular spaces
(a rather unstable notion). On the way\, we will establish a singular vers
ion of the Bogomolov--Gieseker inequality for stable sheaves and study wha
t can be said in the equality case. Joint work with Patrick Graf and Henri
Guenancia.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/211/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Bakker (University of Illinois at Chicago)
DTSTART:20220524T220000Z
DTEND:20220524T230000Z
DTSTAMP:20260404T111217Z
UID:ZAG/212
DESCRIPTION:Title: Period integrals of algebraic varieties\nby Benjamin Bakker (Univ
ersity of Illinois at Chicago) as part of ZAG (Zoom Algebraic Geometry) se
minar\n\n\nAbstract\nPeriod integrals on complex algebraic varieties are t
he integrals of algebraic differential forms along topological cycles. Th
ey are at the heart of Hodge theory. In this talk I will survey some rece
nt results on the behavior of the functions obtained by taking period inte
grals in algebraic families\, including their transcendence\, their relati
on to the derivatives of the associated period map\, and some geometric ap
plications. This is joint work with J. Pila and J. Tsimerman.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/212/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Sophie Kaloghiros (Brunel University)
DTSTART:20220519T140000Z
DTEND:20220519T150000Z
DTSTAMP:20260404T111217Z
UID:ZAG/213
DESCRIPTION:Title: 1-dimensional K-moduli spaces of Fano 3-folds\nby Anne-Sophie Kal
oghiros (Brunel University) as part of ZAG (Zoom Algebraic Geometry) semin
ar\n\n\nAbstract\nRecent advances in the study of K-stability have shown t
hat there is a projective good moduli space of K-polystable Q-Gorenstein s
moothable Q-Fano varieties of dimension n and volume V. The classification
of smooth Fano 3-folds is due to Iskovshikh\, Mori and Mukai and dates ba
ck to the 80s. While the classification is non-modular\, it contains rich
information on the geometry of Fano 3-folds. Fano 3-folds offer a rich sou
rce of examples in which we can explicitly construct and understand some K
-moduli spaces. In this talk\, I will discuss some examples of 1-dimension
al K-moduli spaces of Fano 3-folds. This is joint work with Abban\, Chelts
ov\, Jiao\, Martinez-Garcia\, Papazachariou and Sarikyan.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/213/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Shinder (University of Sheffield)
DTSTART:20220526T140000Z
DTEND:20220526T150000Z
DTSTAMP:20260404T111217Z
UID:ZAG/214
DESCRIPTION:Title: Motivic invariants of birational maps\nby Evgeny Shinder (Univers
ity of Sheffield) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAb
stract\nI will introduce invariants of birational maps with values in the
Grothendieck ring of varieties and their applications to groups of biratio
nal isomorphisms\, in particular the Cremona groups. This is joint work wi
th Hsueh-Yung Lin.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/214/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Shepherd-Barron (King’s College London)
DTSTART:20220531T100000Z
DTEND:20220531T110000Z
DTSTAMP:20260404T111217Z
UID:ZAG/215
DESCRIPTION:Title: Periods of elliptic surfaces\nby Nicholas Shepherd-Barron (King
’s College London) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\
nAbstract\nThe derivative of the period map for elliptic surfaces has a de
scription in terms of where the j-invariant ramifies. This leads to a natu
ral orthonormal basis of the (1\,1) part of the primitive cohomology\, exp
ressed in terms of meromorphic 2-forms of the 2nd kind\, and to a generic
Torelli theorem. This extends to certain other families of varieties fibre
d in Calabi-Yau varieties.\n
LOCATION:https://stable.researchseminars.org/talk/ZAG/215/
END:VEVENT
END:VCALENDAR