BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Tim Logvinenko (Cardiff)
DTSTART:20200423T120000Z
DTEND:20200423T130000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/1
DESCRIPTION:Title: CANCELLED - Skein-triangulated representations of generalised brai
ds\nby Tim Logvinenko (Cardiff) as part of Online Nottingham algebraic
geometry seminar\n\n\nAbstract\nOrdinary braid group $\\mathrm{Br}_n$ is
a well-known algebraic structure which encodes configurations of n non-tou
ching strands ("braids") up to continuous transformations ("isotopies"). A
classical result of Khovanov and Thomas states that there is a natural ca
tegorical action of $\\mathrm{Br}_n$ on the derived category of the cotang
ent bundle of the variety of complete flags in $\\mathbb{C}^n$.\nIn this t
alk\, I will introduce a new structure: the category $\\mathrm{GBr}_n$ of
generalised braids. These are the braids whose strands are allowed to touc
h in a certain way. They have multiple endpoint configurations and can be
non-invertible\, thus forming a category rather than a group. In the conte
xt of triangulated categories\, it is natural to impose certain relations
which result in the notion of a skein-triangulated representation of $\\ma
thrm{GBr}_n$.\nA decade-old conjecture states that there a skein-triangula
ted action of $\\mathrm{GBr}_n$ on the cotangent bundles of the varieties
of full and partial flags in $\\mathbb{C}^n$. We prove this conjecture for
$n = 3$. We also show that any categorical action of $\\mathrm{Br}_n$ can
be lifted to a skein-triangulated action of $\\mathrm{GBr}_n$\, which beh
aves like a categorical nil Hecke algebra. This is a joint work with Rina
Anno and Lorenzo De Biase.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Kohl (Aalto)
DTSTART:20200430T083000Z
DTEND:20200430T093000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/2
DESCRIPTION:Title: Unconditional Reflexive Polytopes\nby Florian Kohl (Aalto) as
part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nA conv
ex body is unconditional if it is symmetric with respect to reflections in
all coordinate hyperplanes. In this talk\, we investigate unconditional l
attice polytopes with respect to geometric\, combinatorial\, and algebraic
properties. In particular\, we characterize unconditional reflexive polyt
opes in terms of perfect graphs. As a prime example\, we study a type-$B$
analogue of the Birkhoff polytope. This talk is based on joint work with M
cCabe Olsen and Raman Sanyal.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Livia Campo (Nottingham)
DTSTART:20200506T090000Z
DTEND:20200506T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/3
DESCRIPTION:Title: On a high pliability quintic hypersurface\nby Livia Campo (Not
tingham) as part of Online Nottingham algebraic geometry seminar\n\n\nAbst
ract\nIn this talk we exhibit an example of a quintic hypersurface with a
certain compound singularity that has pliability at least $2$. We also sho
w that\, while a non-trivial sequence of birational transformations can be
constructed between the two elements of the pliability set\, the Sarkisov
link connecting them is not evident. This is done by studying birational
links for codimension $4$ index $1$ Fano $3$-folds having Picard rank $2$.
\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Ducat (Imperial)
DTSTART:20200513T120000Z
DTEND:20200513T130000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/4
DESCRIPTION:Title: A Laurent phenomenon for $\\mathrm{OGr}(5\,10)$ and explicit mirro
r symmetry for the Fano $3$-fold $V_{12}$\nby Tom Ducat (Imperial) as
part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nThe $5
$-periodic birational map $(x\, y) -> (y\, (1+y)/x)$ can be interpreted as
a mutation between five open torus charts in a del Pezzo surface of degre
e $5$\, coming from a cluster algebra structure on the Grassmannian $\\mat
hrm{Gr}(2\,5)$. This can used to construct a rational elliptic fibration w
hich is the Landau-Ginzburg mirror to $\\mathrm{dP}_5$. I will briefly rec
ap this\, and then explain the following $3$-dimensional generalisation: t
he $8$-periodic birational map $(x\, y\, z) -> (y\, z\, (1+y+z)/x)$ can be
used to exhibit a Laurent phenomenon for the orthogonal Grassmannian $\\m
athrm{OGr}(5\,10)$ and construct a completely explicit $K3$ fibration whic
h is mirror to the Fano $3$-fold $V_{12}$\, as well as some other Fano $3$
-folds.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Thompson (Loughborough)
DTSTART:20200514T090000Z
DTEND:20200514T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/5
DESCRIPTION:Title: Threefolds fibred by sextic double planes\nby Alan Thompson (L
oughborough) as part of Online Nottingham algebraic geometry seminar\n\n\n
Abstract\nI will discuss the theory of threefolds fibred by K3 surfaces mi
rror to the sextic double plane. This theory is unexpectedly rich\, in par
t due to the presence of a polarisation-preserving involution on such K3 s
urfaces. I will present an explicit birational classification result for s
uch threefolds\, along with computations of several of their basic invaria
nts. Along the way we will uncover several (perhaps) surprising links betw
een this theory and Kodaira's theory of elliptic surfaces. This is joint w
ork with Remkes Kooistra.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesús Martinez Garcia (Essex)
DTSTART:20200521T123000Z
DTEND:20200521T133000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/6
DESCRIPTION:Title: The moduli continuity method for log Fano pairs\nby Jesús Mar
tinez Garcia (Essex) as part of Online Nottingham algebraic geometry semin
ar\n\n\nAbstract\nThe moduli continuity method\, pioneered by Odaka\, Spot
ti and Sun\, allows us to explicitly provide algebraic charts of the Gromo
v-Hausdorff compactification of (possibly singular) Kähler-Einstein metri
cs. Assuming we can provide a homeomorphism to some 'known' algebraic comp
actification (customarily\, a GIT one) the method allows us to determine w
hich Fano varieties (or more generally log Fano pairs) are K-polystable in
a given deformation family. In this talk we provide the first examples of
compactification of the moduli of log Fano pairs for the simplest deforma
tion family: that of projective space and a hypersurface\, and mention rel
ated results for cubic surfaces. This is joint work with Patricio Gallardo
and Cristiano Spotti.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Sutherland (Lisbon)
DTSTART:20200528T090000Z
DTEND:20200528T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/7
DESCRIPTION:Title: Mirror symmetry for Painlevé surfaces\nby Tom Sutherland (Lis
bon) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract
\nThis talk will survey aspects of mirror symmetry for ten families of non
-compact hyperkähler manifolds on which the dynamics of one of the Painle
vé equations is naturally defined. They each have a pair of natural reali
sations: one as the complement of a singular fibre of a rational elliptic
surface and another as the complement of a triangle of lines in a (singula
r) cubic surface. The two realisations relate closely to a space of stabil
ity conditions and a cluster variety of a quiver respectively\, providing
a perspective on SYZ mirror symmetry for these manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karin Schaller (FU Berlin)
DTSTART:20200611T090000Z
DTEND:20200611T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/8
DESCRIPTION:Title: Polyhedral divisors and orbit decompositions of normal affine vari
eties with torus action\nby Karin Schaller (FU Berlin) as part of Onli
ne Nottingham algebraic geometry seminar\n\n\nAbstract\nNormal affine vari
eties of dimension $n$ with an effective action of a $k$-dimensional algeb
raic torus can be described completely in terms of proper polyhedral divis
ors living on semiprojective varieties of dimension $n−k$. We use the la
nguage of polyhedral divisors to study the collection of $T$-orbits and $T
$-orbit closures of a normal affine $T$-variety in terms of its defining p
p-divisor. This is based on previous work of Klaus Altmann and Jürgen Hau
sen complemented by work in progress with Klaus Altmann.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuliano Gagliardi (Hannover and MPI Bonn)
DTSTART:20200604T123000Z
DTEND:20200604T133000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/9
DESCRIPTION:Title: The Manin-Peyre conjecture for smooth spherical Fano varieties of
semisimple rank one\nby Giuliano Gagliardi (Hannover and MPI Bonn) as
part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nThe Ma
nin-Peyre conjecture is established for a class of smooth spherical Fano v
arieties of semisimple rank one. This includes all smooth spherical Fano t
hreefolds of type T as well as some higher-dimensional smooth spherical Fa
no varieties.\n\nJoint work with Valentin Blomer\, Jörg Brüdern\, and Ul
rich Derenthal.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Monin (Bristol)
DTSTART:20200618T123000Z
DTEND:20200618T133000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/10
DESCRIPTION:Title: Inversion of matrices\, a $\\C^*$ action on Grassmannians and the
space of complete quadrics\nby Leonid Monin (Bristol) as part of Onli
ne Nottingham algebraic geometry seminar\n\n\nAbstract\nLet $\\Gamma$ be t
he closure of the set of pairs $(A\,A^{-1})$ of symmetric matrices of size
$n$. In other words\, $\\Gamma$ is the graph of the inversion map on the
space $\\mathrm{Sym}_n$ of symmetric matrices of size $n$. What is the coh
omology class of $\\Gamma$ in the product of projective spaces? Equivalent
ly\, what is the degree of the variety $L^{-1}$ obtained as the closure of
the set of inverses of matrices from a generic linear subspace $L$ of $\\
mathrm{Sym}_n$. This question is interesting in its own right but it is al
so motivated by algebraic statistics. In my talk\, I will explain how to i
nvert a matrix using a $\\C^*$ action on Grassmannians\, relate the above
question to classical enumerative problems about quadrics\, and give sever
al possible answers.\n\nThis is joint work in progress with Laurent Manive
l\, Mateusz Michalek\, Tim Seynnaeve\, Martin Vodicka\, Andrzej Weber\, an
d Jaroslaw A. Wisniewski.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Klaus Altmann (FU Berlin)
DTSTART:20200625T090000Z
DTEND:20200625T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/11
DESCRIPTION:Title: Displaying the cohomology of toric line bundles\nby Klaus Alt
mann (FU Berlin) as part of Online Nottingham algebraic geometry seminar\n
\n\nAbstract\nLine bundles $L$ on projective toric varieties can be unders
tood as formal differences $(\\Delta^+ − \\Delta^-)$ of convex polyhedra
in the character lattice. We show how it is possible to use this language
for understanding the cohomology of $L$ by studying the set-theoretic dif
ference $(\\Delta^- \\setminus \\Delta^+)$. Moreover\, when interpreting t
hese cohomology groups as certain Ext-groups\, we demonstrate how the appr
oach via $(\\Delta^-\\setminus \\Delta^+)$ leads to a direct description o
f the associated extensions. The first part is joint work with Jarek Buczi
nski\, Lars Kastner\, David Ploog\, and Anna-Lena Winz\; the second is wor
k in progress with Amelie Flatt.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Logvinenko (Cardiff)
DTSTART:20200519T130000Z
DTEND:20200519T140000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/12
DESCRIPTION:Title: Skein-triangulated representations of generalised braids\nby
Tim Logvinenko (Cardiff) as part of Online Nottingham algebraic geometry s
eminar\n\n\nAbstract\nOrdinary braid group $\\mathrm{Br}_n$ is a well-know
n algebraic structure which encodes configurations of $n$ non-touching str
ands ("braids") up to continuous transformations ("isotopies"). A classica
l result of Khovanov and Thomas states that there is a natural categorical
action of $\\mathrm{Br}_n$ on the derived category of the cotangent bundl
e of the variety of complete flags in $\\mathbb{C}^n$. In this talk\, I wi
ll introduce a new structure: the category $\\mathrm{GBr}_n$ of generalise
d braids. These are the braids whose strands are allowed to touch in a cer
tain way. They have multiple endpoint configurations and can be non-invert
ible\, thus forming a category rather than a group. In the context of tria
ngulated categories\, it is natural to impose certain relations which resu
lt in the notion of a skein-triangulated representation of $\\mathrm{GBr}_
n$. A decade-old conjecture states that there a skein-triangulated action
of $\\mathrm{GBr}_n$ on the cotangent bundles of the varieties of full and
partial flags in $\\mathbb{C}^n$. We prove this conjecture for $n = 3$. W
e also show that any categorical action of $\\mathrm{Br}_n$ can be lifted
to a skein-triangulated action of $\\mathrm{GBr}_n$\, which behaves like a
categorical nil Hecke algebra. This is a joint work with Rina Anno and Lo
renzo De Biase.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregory Smith (Queen's University)
DTSTART:20200702T123000Z
DTEND:20200702T133000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/13
DESCRIPTION:Title: Geometry of smooth Hilbert schemes\nby Gregory Smith (Queen's
University) as part of Online Nottingham algebraic geometry seminar\n\n\n
Abstract\nHow can we understand the subvarieties of a fixed projective spa
ce? Hilbert schemes provide the geometric answer to this question. After
surveying some features of these natural parameter spaces\, we will classi
fy the smooth Hilbert schemes. Time permitting\, we will also describe the
geometry of nonsingular Hilbert schemes by interpreting them as suitable
generalizations of partial flag varieties. This talk is based on joint wo
rk with Roy Skjelnes (KTH).\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ed Segal (University College London)
DTSTART:20200708T123000Z
DTEND:20200708T133000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/14
DESCRIPTION:Title: Semi-orthogonal decompositions and discriminants\nby Ed Segal
(University College London) as part of Online Nottingham algebraic geomet
ry seminar\n\n\nAbstract\nThe derived category of a toric variety can usua
lly be decomposed into smaller pieces\, by passing through different birat
ional models and applying the "windows" theory relating VGIT and derived c
ategories. There are many choices involved and the decompositions are not
unique. We prove a Jordan-Hölder result\, that the multiplicities of the
pieces are independent of choices. If the toric variety is Calabi-Yau then
there are no decompositions\, instead the theory produces symmetries of t
he derived category. Physics predicts that these all these symmetries form
an action of the fundamental group of the "FI parameter space". I'll expl
ain why our Jordan-Hölder result is necessary for this prediction to work
\, and state a conjecture (based on earlier work of Aspinwall-Plesser-Wang
) relating our multiplicities to the geometry of the FI parameter space. T
his is joint work with Alex Kite.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Lazda (Warwick)
DTSTART:20200715T090000Z
DTEND:20200715T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/15
DESCRIPTION:Title: A Neron-Ogg-Shafarevich criterion for $K3$ surfaces\nby Chris
Lazda (Warwick) as part of Online Nottingham algebraic geometry seminar\n
\n\nAbstract\nThe naive analogue of the Néron-Ogg-Shafarevich criterion f
ails for $K3$ surfaces\, that is\, there exist $K3$ surfaces over Henselia
n\, discretely valued fields $\\mathbb{K}$\, with unramified étale cohomo
logy groups\, but which do not admit good reduction over $\\mathbb{K}$. As
suming potential semi-stable reduction\, I will show how to correct this b
y proving that a $K3$ surface has good reduction if and only if is second
cohomology is unramified\, and the associated Galois representation over t
he residue field coincides with the second cohomology of a certain "canoni
cal reduction" of $X$. This is joint work with B. Chiarellotto and C. Lied
tke.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hendrik Süß (Manchester)
DTSTART:20200716T123000Z
DTEND:20200716T133000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/16
DESCRIPTION:Title: Normalised volumes of singularities\nby Hendrik Süß (Manche
ster) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstrac
t\nThe notion of the normalised volume of a singularity has been introduce
d relatively recently\, but plays a crucial role in the context of Einstei
n metrics and $K$-stability. After introducing this invariant my plan is t
o specialise quickly to the case of toric singularities and show that even
in this relatively simple setting interesting phenomena occur.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elana Kalashnikov (Harvard)
DTSTART:20200724T150000Z
DTEND:20200724T160000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/17
DESCRIPTION:Title: Constructing Laurent polynomial mirrors for quiver flag zero loci
\nby Elana Kalashnikov (Harvard) as part of Online Nottingham algebrai
c geometry seminar\n\n\nAbstract\nAll smooth Fano varieties of dimension a
t most three can be constructed as either toric complete intersections (su
bvarieties of toric varieties) or quiver flag zero loci (subvarieties of
quiver flag varieties). Conjecturally\, Fano varieties are expected to mi
rror certain Laurent polynomials. The construction of mirrors of Fano tori
c complete intersections is well-understood. In this talk\, I'll discuss e
vidence for this conjecture by proposing a method of constructing mirrors
for Fano quiver flag zero loci. A key step of the construction is via fin
ding toric degenerations of the ambient quiver flag varieties. These dege
nerations generalise the Gelfand-Cetlin degeneration of flag varieties\, w
hich in the Grassmannian case has an important role in the cluster structu
re of its coordinate ring.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Braun (University of Kentucky)
DTSTART:20200730T140000Z
DTEND:20200730T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/18
DESCRIPTION:Title: The integer decomposition property and Ehrhart unimodality for we
ighted projective space simplices\nby Benjamin Braun (University of Ke
ntucky) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstr
act\nWe consider lattice simplices corresponding to weighted projective sp
aces where one of the weights is $1$. We study the integer decomposition p
roperty and Ehrhart unimodality for such simplices by focusing on restrict
ions regarding the multiplicity of each weight. We introduce a necessary c
ondition for when a simplex satisfies the integer decomposition property\,
and classify those simplices that satisfy it in the case where there are
no more than three distinct weights. We also introduce the notion of refle
xive stabilizations of a simpex of this type\, and show that higher-order
reflexive stabilizations fail to be Ehrhart unimodal and fail to have the
integer decomposition property. This is joint work with Robert Davis\, Mor
gan Lane\, and Liam Solus.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang-Hui He (City and Oxford)
DTSTART:20200806T090000Z
DTEND:20200806T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/19
DESCRIPTION:Title: Universes as Big Data: Superstrings\, Calabi-Yau Manifolds and Ma
chine-Learning\nby Yang-Hui He (City and Oxford) as part of Online Not
tingham algebraic geometry seminar\n\n\nAbstract\nWe review how historical
ly the problem of string phenomenology lead theoretical physics first to a
lgebraic/diffenretial geometry\, and then to computational geometry\, and
now to data science and AI. With the concrete playground of the Calabi-Yau
landscape\, accumulated by the collaboration of physicists\, mathematicia
ns and computer scientists over the last 4 decades\, we show how the lates
t techniques in machine-learning can help explore problems of physical and
mathematical interest.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Ilten (Simon Fraser)
DTSTART:20200813T150000Z
DTEND:20200813T160000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/20
DESCRIPTION:Title: Type D associahedra are unobstructed\nby Nathan Ilten (Simon
Fraser) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstr
act\nGeneralized associahedra associated to any root system were introduce
d by Fomin and Zelevinsky in their study of cluster algebras. For type $\\
mathsf{A}$ root systems\, one recovers the classical associahedron paramet
rizing triangulations of a regular $n$-gon. For type $\\mathsf{D}$ root sy
stems\, one obtains a polytope parametrizing centrally symmetric triangula
tions of a $2n$-gon. In previous work\, Jan Christophersen and I showed th
at the Stanley-Reisner ring of the simplicial complex dual to the boundary
of the classical associahedron is unobstructed\, that is\, has vanishing
second cotangent cohomology. This could be used to find toric degeneration
s of the Grassmannian $\\mathrm{Gr}(2\,n)$. In this talk\, I will describe
work-in-progress that generalizes this unobstructedness result to the typ
e $\\mathsf{D}$ associahedron.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Man-Wai "Mandy" Cheung (Harvard)
DTSTART:20200820T130000Z
DTEND:20200820T140000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/21
DESCRIPTION:Title: Polytopes\, wall crossings\, and cluster varieties\nby Man-Wa
i "Mandy" Cheung (Harvard) as part of Online Nottingham algebraic geometry
seminar\n\n\nAbstract\nCluster varieties are log Calabi-Yau varieties whi
ch are a union of algebraic tori glued by birational "mutation" maps. Part
ial compactifications of the varieties\, studied by Gross\, Hacking\, Keel
\, and Kontsevich\, generalize the polytope construction of toric varietie
s. However\, it is not clear from the definitions how to characterize the
polytopes giving compactifications of cluster varieties. We will show how
to describe the compactifications easily by broken line convexity. As an a
pplication\, we will see the non-integral vertex in the Newton Okounkov bo
dy of $\\mathrm{Gr}(3\,6)$ comes from broken line convexity. Further\, we
will also see certain positive polytopes will give us hints about the Baty
rev mirror in the cluster setting. The mutations of the polytopes will be
related to the almost toric fibration from the symplectic point of view. F
inally\, we can see how to extend the idea of gluing of tori in Floer theo
ry which then ended up with the Family Floer Mirror for the del Pezzo surf
aces of degree $5$ and $6$. The talk will be based on a series of joint wo
rks with Bossinger\, Lin\, Magee\, Najera-Chavez\, and Vienna.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Petracci (FU Berlin)
DTSTART:20200827T123000Z
DTEND:20200827T133000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/22
DESCRIPTION:Title: $K$-moduli stacks and $K$-moduli spaces are singular\nby Andr
ea Petracci (FU Berlin) as part of Online Nottingham algebraic geometry se
minar\n\n\nAbstract\nOnly recently a separated moduli space for (some) Fan
o varieties has been constructed by several algebraic geometers: this is t
he $K$-moduli stack which parametrises $K$-semistable Fano varieties and h
as a separated good moduli space. A natural question is: are these stacks
and spaces smooth? This question makes sense because deformations of smoot
h Fano varieties are unobstructed\, so moduli stacks of smooth Fano variet
ies are smooth. In this talk I will explain how to use toric geometry to c
onstruct examples of non-smooth points in the $K$-moduli stack and the $K$
-moduli space of Fano $3$-folds. This is joint work with Anne-Sophie Kalog
hiros.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Harder (Lehigh)
DTSTART:20200904T140000Z
DTEND:20200904T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/23
DESCRIPTION:Title: Log symplectic pairs and mixed Hodge structures\nby Andrew Ha
rder (Lehigh) as part of Online Nottingham algebraic geometry seminar\n\n\
nAbstract\nA log symplectic pair is a pair $(X\,Y)$ consisting of a smooth
projective variety $X$ and a divisor $Y$ in $X$ so that there is a non-de
generate log $2$-form on $X$ with poles along $Y$. I will discuss the rela
tionship between log symplectic pairs and degenerations of hyperkaehler va
rieties\, and how this naturally leads to a class of log symplectic pairs
called log symplectic pairs of "pure weight". I will discuss results which
show that the classification of log symplectic pairs of pure weight is an
alogous to the classification of log Calabi-Yau surfaces. Time permitting\
, I'll discuss two classes of log symplectic pairs which are related to re
al hyperplane arrangements and which admit cluster type structures.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lara Bossinger (Oaxaca)
DTSTART:20200910T150000Z
DTEND:20200910T160000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/24
DESCRIPTION:Title: Families of Gröbner degenerations\, Grassmannians\, and universa
l cluster algebras\nby Lara Bossinger (Oaxaca) as part of Online Notti
ngham algebraic geometry seminar\n\n\nAbstract\nLet $V$ be the weighted pr
ojective variety defined by a weighted homogeneous ideal $J$ and $C$ a max
imal cone in the Gröbner fan of $J$ with m rays. We construct a flat fami
ly over affine $m$-space that assembles the Gröbner degenerations of $V$
associated with all faces of $C$. This is a multi-parameter generalization
of the classical one-parameter Gröbner degeneration associated to a weig
ht. We show that our family can be constructed from Kaveh-Manon's recent w
ork on the classification of toric flat families over toric varieties: it
is the pullback of a toric family defined by a Rees algebra with base $X_C
$ (the toric variety associated to $C$) along the universal torsor $\\math
bb{A}^m \\to X_C$. If time permits I will explain how to apply this constr
uction to the Grassmannians $\\mathrm{Gr}(2\,n)$ (with Plücker embedding)
and $\\mathrm{Gr}(3\,6)$ (with "cluster embedding"). In each case there e
xists a unique maximal Gröbner cone whose associated initial ideal is the
Stanley-Reisner ideal of the cluster complex. We show that the correspond
ing cluster algebra with universal coefficients arises as the algebra defi
ning the flat family associated to this cone. Further\, for $\\mathrm{Gr}(
2\,n)$ we show how Escobar-Harada's mutation of Newton-Okounkov bodies can
be recovered as tropicalized cluster mutation. This is joint work with Fa
temeh Mohammadi and Alfredo Nájera Chávez.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ronan Terpereau (Bourgogne)
DTSTART:20200917T090000Z
DTEND:20200917T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/25
DESCRIPTION:Title: Actions of connected algebraic groups on rational 3-dimensional M
ori fibrations\nby Ronan Terpereau (Bourgogne) as part of Online Notti
ngham algebraic geometry seminar\n\n\nAbstract\nIn this talk we will study
the connected algebraic groups acting on Mori fibrations $X \\to Y$ with
$X$ a rational threefold and $Y$ a curve or a surface. We will see how the
se groups can be classified\, using the minimal model program (MMP) and th
e Sarkisov program\, and how our results make possible to recover most of
the classification of the connected algebraic subgroups of the Cremona gro
up $\\mathrm{Bir}(\\mathbb{P}^3)$ obtained by Hiroshi Umemura in the 1980'
s when the base field is the field of complex numbers.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renato Vianna (Rio de Janeiro)
DTSTART:20200903T140000Z
DTEND:20200903T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/26
DESCRIPTION:Title: Sharp ellipsoid embeddings and almost-toric mutations\nby Ren
ato Vianna (Rio de Janeiro) as part of Online Nottingham algebraic geometr
y seminar\n\n\nAbstract\nWe will show how to construct volume filling elli
psoid embeddings in some $4$-dimensional toric domain using mutations of a
lmost toric compactifications of those. In particular we recover the resul
ts of McDuff-Schlenk for the ball\, Fenkel-Müller for product of symplect
ic disks and Cristofaro-Gardiner for $E(2\,3)$\, giving a more explicit ge
ometric perspective for these results. To be able to represent certain div
isors\, we develop the idea of symplectic tropical curves in almost toric
fibrations\, inspired by Mikhalkin's work for tropical curves. This is joi
nt work with Roger Casals.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Navid Nabijou (Cambridge)
DTSTART:20200924T140000Z
DTEND:20200924T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/27
DESCRIPTION:Title: Degenerating tangent curves\nby Navid Nabijou (Cambridge) as
part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nIt is
well-known that a smooth plane cubic $E$ supports $9$ flex lines. In highe
r degrees we may ask an analogous question: "How many degree $d$ curves in
tersect $E$ in a single point?" The problem of calculating such numbers ha
s fascinated enumerative geometers for decades. Despite being an extremely
classical and concrete problem\, it was not until the advent of Gromov-Wi
tten invariants in the 1990s that a general method was discovered. The res
ulting theory is incredibly rich\, and the curve counts satisfy a suite of
remarkable properties\, some proven and some still conjectural. In this t
alk I will discuss joint work with Lawrence Barrott\, in which we study th
e behaviour of these tangent curves as the cubic $E$ degenerates to a cycl
e of lines. Using the machinery of logarithmic Gromov-Witten theory\, we o
btain detailed information concerning how the tangent curves degenerate al
ong with $E$. The theorems we obtain are purely classical\, with no refere
nce to Gromov-Witten theory\, but they do not appear to admit a classical
proof. No prior knowledge of Gromov-Witten theory will be assumed.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Smirnov (Augsburg)
DTSTART:20201001T140000Z
DTEND:20201001T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/28
DESCRIPTION:Title: Residual categories of Grassmannians\nby Maxim Smirnov (Augsb
urg) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract
\nExceptional collections in derived categories of coherent sheaves have a
long history going back to the pioneering work of A. Beilinson. After rec
alling the general setup\, I will concentrate on some recent developments
inspired by the homological mirror symmetry. Namely\, I will define residu
al categories of Lefschetz decompositions and discuss a conjectural relati
on between the structure of quantum cohomology and residual categories. I
will illustrate this relationship in the case of some isotropic Grassmanni
ans. This is a joint work with Alexander Kuznetsov.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiroshi Iritani (Kyoto)
DTSTART:20201007T130000Z
DTEND:20201007T140000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/29
DESCRIPTION:Title: Quantum cohomology of blow-ups: a conjecture\nby Hiroshi Irit
ani (Kyoto) as part of Online Nottingham algebraic geometry seminar\n\n\nA
bstract\nIn this talk\, I discuss a conjecture that a semiorthogonal decom
position of topological $K$-groups (or derived categories) due to Orlov sh
ould induce a relationship between quantum cohomology under blowups. The r
elationship between quantum cohomology can be described in terms of soluti
ons to a Riemann-Hilbert problem.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Kaplan (Birmingham)
DTSTART:20201015T120000Z
DTEND:20201015T130000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/30
DESCRIPTION:Title: Exceptional collections for invertible polynomials using VGIT
\nby Daniel Kaplan (Birmingham) as part of Online Nottingham algebraic geo
metry seminar\n\n\nAbstract\nA sum of n monomials in n variables is said t
o be invertible if it is quasi-homogeneous and quasi-smooth (i.e. it has a
unique singularity at the origin). To an invertible polynomial w\, one ca
n associate a maximal symmetry group\, and consider the derived category o
f equivariant matrix factorizations of w. Joint with David Favero and Tyle
r Kelly\, we prove this category has a full exceptional collection\, using
a variation of GIT result of Ballard—Favero—Katzarkov. Our proof addi
tionally utilizes the Kreuzer-Skarke classification of invertible polynomi
als as Thom—Sebastiani sums of Fermat\, chain\, and loop polynomials. I
’ll present a friendly\, example-oriented illustration of our approach\,
review related literature\, and discuss applications to mirror symmetry.\
n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tyler Kelly (Birmingham)
DTSTART:20201022T140000Z
DTEND:20201022T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/31
DESCRIPTION:Title: What is an exoflop?\nby Tyler Kelly (Birmingham) as part of O
nline Nottingham algebraic geometry seminar\n\n\nAbstract\nAspinwall state
d in 2014 that an exoflop "occurs in the gauged linear sigma-model by vary
ing the Kähler form so that a subspace appears to shrink to a point and t
hen reemerge 'outside' the original manifold." This description may be int
angible at first for us to sink our hands into but it turns out to be a gr
eat concrete technique that relates to many things we care about as algebr
aic geometers! We will interpret it in this talk. I will explain in toric
geometry concretely what this means for us. Afterwards\, I will explain wh
y it’s yet another reason we should listen to our string theoretic frien
ds. Namely\, I hope to have enough time to explain how it gives us applica
tions in mirror symmetry and derived categories. Exoflops are a recurring
character in my joint work with David Favero (Alberta)\, Chuck Doran (Albe
rta)\, and Dan Kaplan (Birmingham).\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Cannizzo (Simons Center)
DTSTART:20201029T150000Z
DTEND:20201029T160000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/32
DESCRIPTION:Title: Towards global homological mirror symmetry for genus 2 curves
\nby Catherine Cannizzo (Simons Center) as part of Online Nottingham algeb
raic geometry seminar\n\n\nAbstract\nThe first part of the talk will discu
ss work in arXiv:1908.04227 [math.SG] on constructing a Donaldson-Fukaya-S
eidel type category for the generalized SYZ mirror of a genus $2$ curve. W
e will explain the categorical mirror correspondence on the cohomological
level. The key idea uses that a $4$-torus is SYZ mirror to a $4$-torus. So
if we view the complex genus $2$ curve as a hypersurface of a $4$-torus $
V$\, a mirror can be constructed as a symplectic fibration with fiber give
n by the dual $4$-torus $V^\\vee$. Hence on categories\, line bundles on $
V$ are restricted to the genus $2$ curve while fiber Lagrangians of $V^\\v
ee$ are parallel transported over $U$-shapes in the base of the mirror. Ne
xt we describe ongoing work with H. Azam\, H. Lee\, and C-C. M. Liu on ext
ending the result to a global statement\, namely allowing the complex and
symplectic structures to vary in their real six-dimensional families. The
mirror statement for this more general result relies on work of A. Kanazaw
a and S-C. Lau.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Barbacovi (UCL)
DTSTART:20201105T133000Z
DTEND:20201105T143000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/33
DESCRIPTION:Title: Understanding the flop-flop autoequivalence using spherical funct
ors\nby Federico Barbacovi (UCL) as part of Online Nottingham algebrai
c geometry seminar\n\n\nAbstract\nThe homological interpretation of the Mi
nimal Model Program conjectures that flips should correspond to embeddings
of derived categories\, and flops to equivalences. Even if the conjecture
doesn’t provide us with a preferred functor\, there is an obvious choic
e: the pull-push via the fibre product. When this approach work\, we obtai
n an interesting autoequivalence of either side of the flop\, known as the
“flop-flop autoequivalence”. Understanding the structure of this func
tor (e.g. does it split as the composition of simpler functors?) is an int
eresting problem\, and it has been extensively studied. In this talk I wil
l explain that there is a natural\, i.e. arising from the geometry\, way t
o realise the “flop-flop autoequivalence” as the inverse of a spherica
l twist\, and that this presentation can help us shed light on the structu
re of the autoequivalence itself.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arkadij Bojko (Oxford)
DTSTART:20201112T133000Z
DTEND:20201112T143000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/34
DESCRIPTION:Title: Orientations for DT invariants on quasi-projective Calabi-Yau $4$
-folds\nby Arkadij Bojko (Oxford) as part of Online Nottingham algebra
ic geometry seminar\n\n\nAbstract\nDonaldson-Thomas type invariants in com
plex dimension $4$ have attracted a lot of attention in the past few years
. I will give a brief overview of how one can count coherent sheaves on Ca
labi-Yau $4$-folds. Inherent to the definition of DT4 invariants is the no
tion of orientations on moduli spaces of sheaves/ perfect complexes. For v
irtual fundamental classes and virtual structure sheaves to be well-define
d\, one needs to prove orientability. The result of Cao-Gross-Joyce does t
his for projective CY $4$-folds. However\, computations are more feasible
in the non-compact setting using localization formulae\, where the fixed p
oint loci inherit orientations from global ones\, and orientations of the
virtual normal bundles come into play. I will explain how to use real dete
rminant line bundles of Dirac operators on the double of the original Cala
bi-Yau manifold to construct orientations on the moduli stack of compactly
supported perfect complexes\, moduli schemes of stable pairs and Hilbert
schemes. These are controlled by choices of orientations in K-theory and s
atisfy compatibility under direct sums. If time allows\, I will discuss th
e connection between the sings obtained from comparing orientations and un
iversal wall-crossing formulae of Joyce using vertex algebras.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrico Fatighenti (Toulouse)
DTSTART:20201111T100000Z
DTEND:20201111T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/35
DESCRIPTION:Title: Fano varieties from homogeneous vector bundles\nby Enrico Fat
ighenti (Toulouse) as part of Online Nottingham algebraic geometry seminar
\n\n\nAbstract\nThe idea of classifying Fano varieties using homogeneous v
ector 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-folds classif
ication and some examples of higher-dimensional Fano varieties with specia
l Hodge-theoretical properties.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naoki Fujita (University of Tokyo)
DTSTART:20201119T100000Z
DTEND:20201119T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/36
DESCRIPTION:Title: Newton-Okounkov bodies arising from cluster structures\nby Na
oki Fujita (University of Tokyo) as part of Online Nottingham algebraic ge
ometry seminar\n\n\nAbstract\nA toric degeneration is a flat degeneration
from a projective variety to a toric variety\, which can be used to apply
the theory of toric varieties to other projective varieties. In this talk\
, we discuss relations among the following three constructions of toric de
generations: representation theory\, Newton-Okounkov bodies\, and cluster
algebras. More precisely\, we construct Newton-Okounkov bodies using clust
er structures\, and realize representation-theoretic and cluster-theoretic
toric degenerations from this framework. As an application\, we connect t
wo kinds of representation-theoretic polytopes (string polytopes and Nakas
hima-Zelevinsky polytopes) by tropicalized cluster mutations. We also disc
uss relations with combinatorial mutations which was introduced in the con
text of mirror symmetry for Fano varieties. More precisely\, we relate dua
l polytopes of these representation-theoretic polytopes by combinatorial m
utations. This talk is based on joint works with Hironori Oya and Akihiro
Higashitani.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Peón-Nieto (Birmingham/Côte d'Azur)
DTSTART:20201120T100000Z
DTEND:20201120T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/37
DESCRIPTION:Title: Pure codimensionality of wobbly bundles\nby Ana Peón-Nieto (
Birmingham/Côte d'Azur) as part of Online Nottingham algebraic geometry s
eminar\n\n\nAbstract\nHiggs bundles on smooth projective curves were intro
duced by Hitchin as solutions to gauge equations motivated by physics. The
y can be seen as points of $T^*N$\, where N is the moduli space of vector
bundles on the curve. The topology of the moduli space of Higgs bundles is
determined by the nilpotent cone\, which is a reducible scheme containing
the zero section of $T^*N\\dashrightarrow N$. Inside this section\, wobbl
y bundles are particularly important\, as this is the locus where any othe
r component intersects $N$. In fact\, this implies that the geometry of th
e nilpotent cone can be described in terms of wobbly bundles. In this talk
I will explain an inductive method to prove pure codimensionality of the
wobbly locus\, as announced in a paper by Laumon from the 80's. We expect
our method to yield moreover a description of the irreducible components o
f the nilpotent cone in arbitrary rank.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Okke van Garderen (Glasgow)
DTSTART:20201126T133000Z
DTEND:20201126T143000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/38
DESCRIPTION:Title: Refined Donaldson-Thomas theory of threefold flops\nby Okke v
an Garderen (Glasgow) as part of Online Nottingham algebraic geometry semi
nar\n\n\nAbstract\nDT invariants are virtual counts of semistable objects
in the derived category of a Calabi-Yau variety\, which can be calculated
at various levels of refinement. An interesting family of CY variety which
are of particular interest to the MMP are threefold flopping curves\, and
in this talk I will explain how to understand their DT theory. The key po
int is that the stability conditions on the derived categories can be unde
rstood via tilting equivalences\, which can be seen as the analogue of clu
ster mutations in this setting. I will show that these equivalences induce
wall-crossing formulas\, and use this to reduce the DT theory of a flop t
o a comprehensible set of curve-counting invariants\, which can be compute
d for several examples. These computations produce new evidence for a conj
ecture of Pandharipande-Thomas\, and show that refined DT invariants are n
ot enough to completely classify flops.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Magee (Birmingham)
DTSTART:20201203T133000Z
DTEND:20201203T143000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/39
DESCRIPTION:Title: Convexity in tropical spaces and compactifications of cluster var
ieties\nby Timothy Magee (Birmingham) as part of Online Nottingham alg
ebraic geometry seminar\n\n\nAbstract\nCluster varieties are a relatively
new\, broadly interesting class of geometric objects that generalize toric
varieties. Convexity is a key notion in toric geometry. For instance\, pr
ojective toric varieties are defined by convex lattice polytopes. In this
talk\, I'll explain how convexity generalizes to the cluster world\, where
"polytopes" live in a tropical space rather than a vector space and "conv
ex polytopes" define projective compactifications of cluster varieties. Ti
me permitting\, I'll conclude with two exciting applications of this more
general notion of convexity: 1) an intrinsic version of Newton-Okounkov bo
dies and 2) a possible cluster version of a classic toric mirror symmetry
construction due to Batyrev. Based on joint work with Man-Wai Cheung and
Alfredo Nájera Chávez.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Eur (Stanford)
DTSTART:20201210T163000Z
DTEND:20201210T173000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/40
DESCRIPTION:Title: Tautological bundles of matroids\nby Christopher Eur (Stanfor
d) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\n
Recent advances in matroid theory via tropical geometry broadly fall into
two themes: One concerns the K-theory of Grassmannians\, and the other con
cerns the intersection theory of wonderful compactifications. How do thes
e two themes talk to each other? We introduce the notion of tautological
bundles of matroids to unite these two themes. As a result\, we give a ge
ometric interpretation of the Tutte polynomial of a matroid that unifies s
everal previous works as its corollaries\, deduce new log-concavity statem
ents\, and answer few conjectures in the literature. This is an ongoing p
roject with Andrew Berget\, Hunter Spink\, and Dennis Tseng.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lawrence Barrott (Boston College)
DTSTART:20210114T150000Z
DTEND:20210114T160000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/41
DESCRIPTION:Title: Log geometry and Chow theory\nby Lawrence Barrott (Boston Col
lege) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstrac
t\nLog geometry has become a central tool in enumerative geometry over the
past years\, providing means to study many degenerations situations. Unfo
rtunately much of the theory is complicated by the fact that products of l
og schemes differ from products of schemes.\n\nIn this talk I will introdu
ce a gadget which replaces Chow theory for log schemes\, reproducing many
familiar tools such as virtual pullback in the context of log geometry.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel Van Garrel (Birmingham)
DTSTART:20210121T100000Z
DTEND:20210121T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/42
DESCRIPTION:Title: Stable maps to Looijenga pairs\nby Michel Van Garrel (Birming
ham) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract
\nStart with a rational surface $Y$ admitting a decomposition of its antic
anonical divisor into at least 2 smooth nef components. We associate 5 cur
ve counting theories to this Looijenga pair: 1) all genus stable log maps
with maximal tangency to each boundary component\; 2) genus 0 stable maps
to the local Calabi-Yau surface obtained by twisting $Y$ by the sum of the
line bundles dual to the components of the boundary\; 3) the all genus op
en Gromov-Witten theory of a toric Calabi-Yau threefold associated to the
Looijenga pair\; 4) the Donaldson-Thomas theory of a symmetric quiver spec
ified by the Looijenga pair and 5) BPS invariants associated to the variou
s curve counting theories. In this joint work with Pierrick Bousseau and A
ndrea Brini\, we provide closed-form solutions to essentially all of the a
ssociated invariants and show that the theories are equivalent. I will sta
rt by describing the geometric transitions from one geometry to the other\
, then give an overview of the curve counting theories and their relations
. I will end by describing how the scattering diagrams of Gross and Sieber
t are a natural place to count stable log maps.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matej Filip (Ljubljana)
DTSTART:20210128T100000Z
DTEND:20210128T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/43
DESCRIPTION:Title: The miniversal deformation of an affine toric Gorenstein threefol
d\nby Matej Filip (Ljubljana) as part of Online Nottingham algebraic g
eometry seminar\n\n\nAbstract\nWe are going to describe the reduced minive
rsal deformation of an affine toric Gorenstein threefold. The reduced defo
rmation components correspond to special Laurent polynomials. There is can
onical bijective map between the set of the smoothing components and the s
et of the corresponding Laurent polynomials\, which we are going to analys
e in more details.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pieter Belmans (Bonn)
DTSTART:20210204T100000Z
DTEND:20210204T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/44
DESCRIPTION:Title: Hochschild cohomology of partial flag varieties and Fano 3-folds<
/a>\nby Pieter Belmans (Bonn) as part of Online Nottingham algebraic geome
try seminar\n\n\nAbstract\nThe Hochschild-Kostant-Rosenberg decomposition
gives a description of the Hochschild cohomology of a smooth projective va
riety in terms of the sheaf cohomology of exterior powers of the tangent b
undle. In all but a few cases it is a non-trivial task to compute this dec
omposition\, and understand the extra algebraic structure which exists on
Hochschild cohomology. I will give a general introduction to Hochschild co
homology and this decomposition\, and explain what it looks like for parti
al flag varieties (joint work with Maxim Smirnov) and Fano 3-folds (joint
work with Enrico Fatighenti and Fabio Tanturri).\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrica Mazzon (Bonn)
DTSTART:20210211T110000Z
DTEND:20210211T120000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/45
DESCRIPTION:Title: Non-archimedean approach to mirror symmetry and to degenerations
of varieties\nby Enrica Mazzon (Bonn) as part of Online Nottingham alg
ebraic geometry seminar\n\n\nAbstract\nMirror symmetry is a fast-moving re
search area at the boundary between mathematics and theoretical physics. O
riginated from observations in string theory\, it suggests that complex Ca
labi-Yau manifolds should come in mirror pairs\, in the sense that geometr
ical information of a Calabi-Yau manifold can be read through invariants o
f its mirror.\n\nIn the first part of the talk\, I will introduce some geo
metrical ideas inspired by mirror symmetry. In particular\, I will go thro
ugh the main steps which relate mirror symmetry to non-archimedean geometr
y and the theory of Berkovich spaces.\n\nIn the second part\, I will descr
ibe a combinatorial object\, the so-called dual complex of a degeneration
of varieties. This emerges in many contexts of algebraic geometry\, includ
ing mirror symmetry where moreover it comes equipped with an integral affi
ne structure. I will show how the techniques of Berkovich geometry give a
new insight into the study of dual complexes and their integral affine str
ucture. This is based on a joint work with Morgan Brown and a work in prog
ress with Léonard Pille-Schneider.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Zucconi (Udine)
DTSTART:20210218T100000Z
DTEND:20210218T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/46
DESCRIPTION:Title: Fujita decomposition and Massey product for fibered varieties
\nby Francesco Zucconi (Udine) as part of Online Nottingham algebraic geom
etry seminar\n\n\nAbstract\nLet $f\\colon X \\to B$ be a semistable fibrat
ion where $X$ is a smooth variety of dimension $n ≥ 2$ and $B$ is a smoo
th curve. We give an interpretation of the second Fujita decomposition of
$f_∗\\omega_{X/B}$ in terms of local systems of the relative 1-forms and
of the relative top forms. We show the existence of higher irrational pen
cils under natural hypothesis on local subsystems.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatemeh Rezaee (Loughborough)
DTSTART:20210304T100000Z
DTEND:20210304T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/47
DESCRIPTION:Title: Wall-crossing does not induce MMP\nby Fatemeh Rezaee (Loughbo
rough) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstra
ct\nI will describe a new wall-crossing phenomenon of sheaves on the proje
ctive 3-space that induces singularities that are not allowed in the sense
of the Minimal Model Program (MMP). Therefore\, it cannot be detected as
an operation in the MMP of the moduli space\, unlike the case for many sur
faces.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diane Maclagan (Warwick)
DTSTART:20210311T130000Z
DTEND:20210311T140000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/48
DESCRIPTION:Title: Toric and tropical Bertini theorems in arbitrary characteristic\nby Diane Maclagan (Warwick) as part of Online Nottingham algebraic geo
metry seminar\n\n\nAbstract\nThe classical Bertini theorem on irreducibili
ty when intersecting by hyperplanes is a standard part of the algebraic ge
ometry toolkit. This was generalised recently\, in characteristic zero\, b
y Fuchs\, Mantova\, and Zannier to a toric Bertini theorem for subvarietie
s of an algebraic torus\, with hyperplanes replaced by subtori. I will dis
cuss joint work with Gandini\, Hering\, Mohammadi\, Rajchgot\, Wheeler\, a
nd Yu in which we give a different proof of this theorem that removes the
characteristic assumption. An application is a tropical Bertini theorem.\
n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taro Sano (Kobe)
DTSTART:20210318T100000Z
DTEND:20210318T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/49
DESCRIPTION:Title: Construction of non-Kähler Calabi-Yau manifolds by log deformati
ons\nby Taro Sano (Kobe) as part of Online Nottingham algebraic geomet
ry seminar\n\n\nAbstract\nCalabi-Yau manifolds (in the strict sense) form
an important class in the classification of algebraic varieties. One can a
lso consider its generalisation by removing the projectivity assumption. I
t was previously known that there are infinitely many topological types of
non-Kähler Calabi-Yau 3-folds. In this talk\, I will present constructio
n of such examples in higher dimensions by smoothing normal crossing varie
ties. The key tools of the construction are some isomorphisms between gene
ral rational elliptic surfaces which induce isomorphisms between Calabi-Ya
u manifolds of Schoen type.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michał Kapustka (IMPAN and Stavanger)
DTSTART:20210325T100000Z
DTEND:20210325T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/50
DESCRIPTION:Title: Nikulin orbifolds\nby Michał Kapustka (IMPAN and Stavanger)
as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nThe
theory of K3 surfaces with symplectic involutions and their quotients is
now a well understood classical subject thanks to foundational works of Ni
kulin\, and van Geemen and Sarti. In this talk we will try to develop an a
nalogous theory in the context of hyperkahler fourfolds of K3${}^{[2]}$ ty
pe. First\, we will present a latttice theoretic classification of such fo
urfolds which admit a symplectic involution. Then we will investigate the
associated quotients that we call Nikulin orbifolds. These are orbifolds w
hich admit a symplectic form on the smooth locus and hence are special cas
es of so called hyperkahler orbifolds. Finally\, we shall discuss families
of Nikulin orbifolds and their deformations called hyperkahler orbifolds
of Nikulin type. As an application\, we will provide a description of the
first known example of a complete family of projective hyperkahler orbifol
ds. This is joint work with A. Garbagnati\, C. Camere and G. Kapustka.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiarui Fei (Shanghai Jiao Tong)
DTSTART:20210401T120000Z
DTEND:20210401T130000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/51
DESCRIPTION:Title: Tropical $F$-polynomials and Cluster Algebras\nby Jiarui Fei
(Shanghai Jiao Tong) as part of Online Nottingham algebraic geometry semin
ar\n\n\nAbstract\nThe representation-theoretic interpretations of $g$-vect
ors and $F$-polynomials are two fundamental ingredients in the (additive)
categorification of cluster algebras. We knew that the $g$-vectors are rel
ated to the presentation spaces. We introduce the tropical $F$-polynomial
$f_M$ of a quiver representation $M$\, and explain its interplay with the
general presentation for any finite-dimensional basic algebra. As a conseq
uence\, we give a presentation of the Newton polytope $N(M)$ of $M$. We pr
opose an algorithm to determine the generic Newton polytopes\, and show it
works for path algebras. As an application\, we give a representation-the
oretic interpretation of Fock-Goncharov's cluster duality pairing. We also
study many combinatorial aspects of $N(M)$\, such as faces\, the dual fan
and $1$-skeleton. We conjecture that the coefficients of a cluster monomi
al corresponding to vertices are all $1$\, and the coefficients inside the
Newton polytope are saturated. We show the conjecture holds for acyclic c
luster algebras. We specialize the above general results to the cluster-fi
nite algebras and the preprojective algebras of Dynkin type.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Gräfnitz (Hamburg)
DTSTART:20210408T090000Z
DTEND:20210408T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/52
DESCRIPTION:Title: Tropical correspondence for smooth del Pezzo log Calabi-Yau pairs
\nby Tim Gräfnitz (Hamburg) as part of Online Nottingham algebraic ge
ometry seminar\n\n\nAbstract\nIn this talk I will present the main results
of my thesis\, a tropical correspondence theorem for log Calabi-Yau pairs
$(X\,D)$ consisting of a smooth del Pezzo surface $X$ of degree $\\ge3$ a
nd a smooth anticanonical divisor $D$. The easiest example of such a pair
is $(\\mathbb{P}^2\,E)$\, where $E$ is an elliptic curve. I will explain h
ow the genus zero logarithmic Gromov-Witten invariants of $X$ with maximal
tangency to $D$ are related to tropical curves in the dual intersection c
omplex of $(X\,D)$ and how they can be read off from the consistent wall s
tructure appearing in the Gross-Siebert program. The novelty in this corre
spondence is that $D$ is smooth but non-toric\, leading to log singulariti
es in the toric degeneration that have to be resolved.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Nordstrom (Bath)
DTSTART:20210415T120000Z
DTEND:20210415T130000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/53
DESCRIPTION:Title: Extra-twisted connected sum $G_2$-manifolds\nby Johannes Nord
strom (Bath) as part of Online Nottingham algebraic geometry seminar\n\n\n
Abstract\nThe twisted connected sum construction of Kovalev produces many
examples of closed Riemannian $7$-manifolds with holonomy group $G_2$ (a s
pecial class of Ricci-flat manifolds)\, starting from complex algebraic ge
ometry data like Fano $3$-folds. If the pieces admit automorphisms\, then
adding an extra twist to the construction yields examples with a wider var
iety of topological features. I will describe the constructions and outlin
e how one can use them to produce example of e.g. closed $7$-manifolds wit
h disconnected moduli space of holonomy $G_2$ metrics\, or pairs of $G_2$-
manifolds that homeomorphic but not diffeomorphic. This is joint work with
Diarmuid Crowley and Sebastian Goette.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Wormleighton (Washington)
DTSTART:20210422T120000Z
DTEND:20210422T130000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/54
DESCRIPTION:Title: A tale of two widths: lattice and Gromov\nby Ben Wormleighton
(Washington) as part of Online Nottingham algebraic geometry seminar\n\n\
nAbstract\nTo a polytope $P$ whose facet normals are rational one can asso
ciate two geometric objects: a symplectic toric domain $X_P$ and a polaris
ed toric algebraic variety $Y_P$\, which can also be viewed as a potential
ly singular symplectic space. A basic invariant of a symplectic manifold $
X$ is its Gromov width: essentially the size of the largest ball that can
be 'symplectically' embedded in $X$. A conjecture of Averkov-Hofscheier-Ni
ll proposed a combinatorial bound for the Gromov width of $Y_P$\, which I
recently verified in dimension two with Julian Chaidez. I’ll discuss the
proof\, which goes via various symplectic and algebraic invariants with w
insome combinatorial interpretations in the toric case. If there’s time\
, I’ll discuss ongoing work and new challenges for a similar result in h
igher dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wemyss (Glasgow)
DTSTART:20210429T090000Z
DTEND:20210429T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/55
DESCRIPTION:Title: Jacobi algebras on the two-loop quiver and applications\nby M
ichael Wemyss (Glasgow) as part of Online Nottingham algebraic geometry se
minar\n\n\nAbstract\nI will explain recent progress on classifying finite
dimensional Jacobi algebras on the two loop quiver. This is a purely algeb
raic problem\, which at first sight is both seemingly hopeless and seeming
ly detached from any form of reality or wider motivation. There are two su
rprises: first\, the problem is not hopeless\, and parts of the answer are
in fact very beautiful. Second\, this has immediate and surprising conseq
uences to both 3-fold flops and 3-fold divisor-to-curve contractions\, the
ir curve invariants and their conjectural classification. This is joint wo
rk with Gavin Brown.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Travis Mandel (Oklahoma)
DTSTART:20210505T140000Z
DTEND:20210505T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/56
DESCRIPTION:Title: Quantum theta bases for quantum cluster algebras\nby Travis M
andel (Oklahoma) as part of Online Nottingham algebraic geometry seminar\n
\n\nAbstract\nOne of the central goals in the study of cluster algebras is
to better understand various canonical bases and positivity properties of
the cluster algebras and their quantizations. Gross-Hacking-Keel-Kontsevi
ch (GHKK) applied ideas from mirror symmetry to construct so-called "theta
bases" for cluster algebras which satisfy all the desired positivity prop
erties\, thus proving several conjectures regarding cluster algebras. I wi
ll discuss joint work with Ben Davison in which we combine the techniques
used by GHKK with ideas from the DT theory of quiver representations to qu
antize the GHKK construction\, thus producing quantum theta bases and prov
ing the desired quantum positivity properties.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Casals (UC Davis)
DTSTART:20210513T150000Z
DTEND:20210513T160000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/57
DESCRIPTION:Title: Positroid links and braid varieties\nby Roger Casals (UC Davi
s) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\n
I will discuss a class of affine algebraic varieties associated to positiv
e braids\, their relation to open positroid strata in Grassmannians and th
eir cluster structures. First\, I will introduce the objects of interest\,
with the necessary ingredients\, and motivate the problem at hand. Then w
e will discuss in detail how the study of a DG-algebra associated to certa
in links may allow us to better understand the algebraic (and cluster) geo
metry of Richardson and positroid varieties. Explicit examples of this int
erplay between topology and algebraic geometry will be illustrated. At a m
ore conceptual level\, the talk brings to bear insight from symplectic top
ology to better understand positroid varieties. This is joint work with E.
Gorsky\, M. Gorsky and J. Simental.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Markwig (Tübingen)
DTSTART:20210520T090000Z
DTEND:20210520T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/58
DESCRIPTION:Title: Counting bitangents of plane quartics - tropical\, real and arith
metic\nby Hannah Markwig (Tübingen) as part of Online Nottingham alge
braic geometry seminar\n\n\nAbstract\nA smooth plane quartic defined over
the complex numbers has precisely 28 bitangents. This result goes back to
Pluecker. In the tropical world\,the situation is different. One can defin
e equivalence classes of tropical bitangents of which there are 7\, and ea
ch has 4 lifts over the complex numbers. Over the reals\, we can have 4\,
8\, 16 or 28 bitangents. The avoidance locus of a real quartic is the set
in the dual plane consisting of all lines which do not meet the quartic. E
very connected component of the avoidance locus has precisely 4 bitangents
in its closure. For any field k of characteristic not equal to 2 and with
a non-Archimedean valuation which allows us to tropicalize\, we show that
a tropical bitangent class of a quartic either has 0 or 4 lifts over k. T
his way of grouping into sets of 4 which exists tropically and over the re
als is intimately connected: roughly\, tropical bitangent classes can be v
iewed as tropicalizations of closures of connected components of the avoid
ance locus. Arithmetic counts offer a bridge connecting real and complex c
ounts\, and we investigate how tropical geometry can be used to study this
bridge.\n\nThis talk is based on joint work with Maria Angelica Cueto\, a
nd on joint work in progress with Sam Payne and Kristin Shaw.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helge Ruddat (Mainz)
DTSTART:20210527T090000Z
DTEND:20210527T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/59
DESCRIPTION:Title: Polytopes\, periods\, degenerations\nby Helge Ruddat (Mainz)
as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nA l
attice polytope describes a projective toric variety and a regular subdivi
sion of the polytope describes a flat degeneration of the toric variety. I
t is instructive to deform the degenerating family in a way that makes the
geometry non-toric and produces a more interesting real torus fibration o
n the fibres of the degeneration. I am going to explain a simple formula t
hat permits the easy computation of period integrals for the deformed fami
lies. This approach to periods doesn't require any differential equations
and is flexible enough to give proofs for strong results about Gross-Siebe
rt's degenerating families obtained from wall structures. The talk is base
d on joint work with Bernd Siebert.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Ulirsch (Frankfurt)
DTSTART:20210603T120000Z
DTEND:20210603T130000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/60
DESCRIPTION:Title: Parabolic Higgs bundles on toric varieties\nby Martin Ulirsch
(Frankfurt) as part of Online Nottingham algebraic geometry seminar\n\n\n
Abstract\nIn this talk I will explain a version of Simpson’s non-abelian
Hodge correspondence on a toric variety X. There is a natural 1-1 corresp
ondence between stable parabolic Higgs bundles on X and irreducible repres
entations of the fundamental group of the big torus. This correspondence r
educes to a correspondence between toric vector bundles and integral unita
ry representations in a suitable sense. In this story the spherical Tits b
uilding will have a surprise appearance. The main result suggests (at leas
t to me) that there is a yet-to-be-discovered logarithmic incarnation of t
he non-abelian Hodge correspondence.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusuke Nakajima (Kyoto)
DTSTART:20210624T090000Z
DTEND:20210624T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/61
DESCRIPTION:Title: Combinatorial mutations and deformations of dimer models\nby
Yusuke Nakajima (Kyoto) as part of Online Nottingham algebraic geometry se
minar\n\n\nAbstract\nThe combinatorial mutation of a polytope was introduc
ed in the context of the mirror symmetry of Fano manifolds for achieving t
he classification problem. This operation makes a given polytope another o
ne while keeping some properties. In my talk\, I will consider the combina
torial mutation of a polygon associated to a dimer model. A dimer model is
a bipartite graph on the real two-torus\, and the combinatorics of a dime
r model gives rise to a certain lattice polygon. Also\, a dimer model enjo
ys rich information regarding toric geometry associated to that polygon. I
t is known that for any lattice polygon P there is a dimer model whose ass
ociated polygon coincides with P. Thus\, there also exists a dimer model g
iving the lattice polygon obtained as the combinatorial mutation of P. I w
ill observe the relationship between a dimer model giving a lattice polygo
n P and the one giving the combinatorial mutation of P. In particular\, I
introduce the operation which I call the deformation of a dimer model\, an
d show that this operation induces the combinatorial mutation of a polygon
associated to a dimer model. This talk is based on a joint work with A. H
igashitani.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Escobar (Washington)
DTSTART:20210617T120000Z
DTEND:20210617T130000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/62
DESCRIPTION:Title: Wall-crossing phenomenon for Newton-Okounkov bodies\nby Laura
Escobar (Washington) as part of Online Nottingham algebraic geometry semi
nar\n\n\nAbstract\nA Newton-Okounkov body is a convex set associated to a
projective variety\, equipped with a valuation. These bodies generalize th
e theory of Newton polytopes and the correspondence between polytopes and
projective toric varieties. Work of Kaveh-Manon gives an explicit link bet
ween tropical geometry and Newton-Okounkov bodies. We use this link to des
cribe a wall-crossing phenomenon for Newton-Okounkov bodies. As an example
\, we describe wall-crossing formula in the case of the Grassmannian Gr(2\
,m). This is joint work with Megumi Harada.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Lonjou (Paris-Saclay)
DTSTART:20210610T090000Z
DTEND:20210610T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/63
DESCRIPTION:Title: Action of Cremona groups on CAT(0) cube complexes\nby Anne Lo
njou (Paris-Saclay) as part of Online Nottingham algebraic geometry semina
r\n\n\nAbstract\nA key tool to study the plane Cremona group is its action
on a hyperbolic space. Sadly\, in higher rank such an action is not avail
able. Recently\, in geometric group theory\, actions on CAT(0) cube comple
xes turned out to be a powerful tool to study a large class of groups. In
this talk\, based on a common work with Christian Urech\, we will construc
t such complexes on which Cremona groups of rank n act. Then\, we will see
which kind of results on these groups we can obtain.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Montero (Valparaíso)
DTSTART:20210701T130000Z
DTEND:20210701T140000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/64
DESCRIPTION:Title: On the liftability of the automorphism group of smooth hypersurfa
ces of the projective space\nby Pedro Montero (Valparaíso) as part of
Online Nottingham algebraic geometry seminar\n\n\nAbstract\nSmooth hypers
urfaces are classical objects in algebraic geometry since they are the sim
plest varieties one can define as they are given by only one equation. As
such\, they have been intensively studied and their geometry has shaped th
e development of classic and modern algebraic geometry. In this talk\, I w
ill first recall some fundamental results concerning the automorphism grou
p of smooth hypersurfaces of the projective space and then I will present
some new results obtained in a joint work with Victor Gonzalez-Aguilera an
d Alvaro Liendo\, which are inspired by the classification groups which fa
ithfully act on smooth cubic and quintic threefolds by Oguiso\, Wei and Yu
. Finally\, I will discuss some perspectives and open problems that arise
from this.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Galkin (PUC-Rio and HSE)
DTSTART:20210715T120000Z
DTEND:20210715T130000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/65
DESCRIPTION:Title: Graph potentials and combinatorial non-abelian Torelli\nby Se
rgey Galkin (PUC-Rio and HSE) as part of Online Nottingham algebraic geome
try seminar\n\n\nAbstract\nI will introduce graph potentials and discuss s
ome of their combinatorial aspects\, such as small resolution conjecture a
nd combinatorial non-abelian Torelli theorem. The talk is based on the joi
nt works with Pieter Belmans and Swarnava Mukhopadhyay.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ollie Clarke (Ghent and Bristol)
DTSTART:20210812T090000Z
DTEND:20210812T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/66
DESCRIPTION:Title: Combinatorial mutations and block diagonal polytopes\nby Olli
e Clarke (Ghent and Bristol) as part of Online Nottingham algebraic geomet
ry seminar\n\n\nAbstract\nMatching fields were introduced by Sturmfels and
Zelevinsky to study certain Newton polytopes and more recently have been
shown to give rise to toric degenerations of various families of varieties
. Whenever a matching field gives rise to a toric degeneration of the Gras
smannian\, the polytope of the associated toric variety coincides with the
matching field polytope. In this talk I will describe combinatorial mutat
ions of matching field polytopes. We will explore properties of polytopes
which are preserved by mutation\, and we will see that property of giving
rise to a toric degeneration is preserved by mutations. This gives us an e
asy way to generate new families of toric degenerations of the Grassmannia
n from old. This talk is based on joint work with Akihiro Higashitani and
Fatemeh Mohammadi.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:DongSeon Hwang (Ajou)
DTSTART:20210826T090000Z
DTEND:20210826T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/67
DESCRIPTION:Title: Cascades of singular rational surfaces of Picard number one\n
by DongSeon Hwang (Ajou) as part of Online Nottingham algebraic geometry s
eminar\n\n\nAbstract\nI will introduce the notion of cascades of singular
rational surfaces of Picard number one\, which consists of a sequence of s
pecial birational morphisms\, and then discuss some applications in the to
ric case\, Fano case\, and (log) general type case. The latter application
is closely related to algebraic Montgomery-Yang problem\, conjectured by
Kollár.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chengxi Wang (UCLA)
DTSTART:20210708T140000Z
DTEND:20210708T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/68
DESCRIPTION:Title: Varieties of general type with small volume\nby Chengxi Wang
(UCLA) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstra
ct\nBy Hacon-McKernan\, Takayama\, and Tsuji\, there is a constant r_n suc
h that for every r at least r_n\, the r-canonical map of every n-dimension
al variety of general type is birational. In this talk\, we show that r_n
must grow faster than any polynomial in n\, by giving examples of general
type with small volume in high dimensions. In particular\, we construct a
klt n-fold with ample canonical class whose volume is less than 1/2^(2^n).
The klt examples should be close to optimal. This is joint work with Burt
Totaro.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kristin DeVleming (UCSD)
DTSTART:20210722T150000Z
DTEND:20210722T160000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/69
DESCRIPTION:Title: K moduli of quartic K3 surfaces\nby Kristin DeVleming (UCSD)
as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nWe
will discuss a family of compactifications of moduli spaces of log Fano pa
irs coming from K-stability\, and discuss an application to moduli of quar
tic K3 surfaces\, with a focus on the locus of hyperelliptic K3s that aris
e as double covers of $\\mathbb{P}^1\\times\\mathbb{P}^1$ branched over a
$(4\,4)$ curve. We will show that K-stability provides a natural way to i
nterpolate between the GIT moduli space and the Baily-Borel compactificati
on and will relate this interpolation to VGIT wall crossings. This is joi
nt work with Kenny Ascher and Yuchen Liu.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Nickel (Frankfurt)
DTSTART:20210729T130000Z
DTEND:20210729T140000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/70
DESCRIPTION:Title: Local positivity and effective Diophantine approximation\nby
Matthias Nickel (Frankfurt) as part of Online Nottingham algebraic geometr
y seminar\n\n\nAbstract\nIn this talk I will discuss a new approach to pro
ve effective results in Diophantine approximation relying on lower bounds
of Seshadri constants. I will then show how to use it to prove an effectiv
e theorem on the simultaneous approximation of two algebraic numbers satis
fying an algebraic equation.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dhruv Ranganathan (Cambridge)
DTSTART:20210805T120000Z
DTEND:20210805T130000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/71
DESCRIPTION:Title: Toric contact cycles in the moduli space of curves\nby Dhruv
Ranganathan (Cambridge) as part of Online Nottingham algebraic geometry se
minar\n\n\nAbstract\nThe toric contact cycles are loci in the moduli space
of curves that parameterize those curves that admit a morphism to a fixed
toric variety\, with prescribed tangency data with the toric boundary. Th
e cycles are the fundamental building blocks in higher genus logarithmic G
romov-Witten theory and are higher dimensional analogues of the double ram
ification cycles\, which have been studied intensely in the last decade. I
n recent work\, Sam Molcho (ETH) and I proved that these cycles lie in the
tautological part of the Chow ring of the moduli space of curves. A lesso
n I learned from this project\, and earlier work with Navid Nabijou (Cambr
idge)\, is that it can be quite profitable to blend Fulton’s analysis of
blowups and strict transforms with logarithmic Gromov-Witten theory and i
ts virtual class. I’ll try to give a sense of the basic geometric phenom
ena\, and point to some other places where they come up.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Addington (Oregon)
DTSTART:20210923T150000Z
DTEND:20210923T160000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/73
DESCRIPTION:Title: Hodge number are not derived invariants in positive characteristi
c\nby Nicolas Addington (Oregon) as part of Online Nottingham algebrai
c geometry seminar\n\n\nAbstract\nDerived categories of coherent sheaves b
ehave a lot like cohomology\, so it's natural to ask which cohomological i
nvariants are preserved by derived equivalences. After discussing the moti
vation and previous results\, I'll present a derived equivalence between C
alabi-Yau 3-folds in characteristic 3 with different Hodge numbers\; this
couldn't happen in characteristic 0. The project has a substantial compute
r algebra component which I'll spend some time on.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julius Giesler (Tübingen)
DTSTART:20210930T090000Z
DTEND:20210930T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/74
DESCRIPTION:Title: Kanev and Todorov type surfaces in toric 3-folds\nby Julius G
iesler (Tübingen) as part of Online Nottingham algebraic geometry seminar
\n\n\nAbstract\nIn this talk we show at the example of some surfaces of ge
neral type\, so called Kanev and Todorov type surfaces\, how to construct
minimal and canonical models of hypersurfaces in toric varieties. We relat
e the plurigenera and the Kodaira dimension of the hypersurfaces to a spec
ial polytope\, known as the Fine interior. Then we study singularities of
the canonical models of Kanev/Todorov type surfaces via toric geometry\, d
egenerations of these surfaces and investigate some Hodge theoretic conseq
uences.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Sophie Kaloghiros (Brunel)
DTSTART:20211021T090000Z
DTEND:20211021T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/76
DESCRIPTION:Title: The Calabi problem for Fano 3-folds\nby Anne-Sophie Kaloghiro
s (Brunel) as part of Online Nottingham algebraic geometry seminar\n\n\nAb
stract\nI will discuss progress on the Calabi problem for Fano 3-folds. Th
e 105 deformation families of smooth Fano 3-folds\, were classified by Isk
ovskikh\, Mori and Mukai. We determine whether or not the general member o
f each of these 105 families admits a Kähler-Einstein metric. In some cas
es\, it is known that while the general member of the family admits a Käh
ler-Einstein metric\, some other member does not. This leads to the proble
m of determining which members of a deformation family admit a Kähler-Ein
stein metric when the general member does. This is accomplished for most o
f the families\, and I will present a conjectural picture for some of the
remaining families. This is a joint project with Carolina Araujo\, Ana-Mar
ia Castravet\, Ivan Cheltsov\, Kento Fujita\, Jesus Martinez-Garcia\, Cons
tantin Shramov\, Hendrik Süss and Nivedita Viswanathan.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Spink (Stanford)
DTSTART:20210902T150000Z
DTEND:20210902T160000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/77
DESCRIPTION:Title: Log-concavity of matroid h-vectors and mixed Eulerian numbers
\nby Hunter Spink (Stanford) as part of Online Nottingham algebraic geomet
ry seminar\n\n\nAbstract\n(Joint with Andrew Berget and Dennis Tseng) For
any matroid $M$\, we compute the Tutte polynomial using the mixed intersec
tion numbers of certain tautological classes in the combinatorial Chow rin
g arising from Grassmannians. Using mixed Hodge-Riemann relations\, we ded
uce a strengthening of the log-concavity of the h-vector of a matroid comp
lex\, improving on an old conjecture of Dawson that was resolved contempor
aneously by Ardila\, Denham\, and Huh.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Nikolaev (Sheffield)
DTSTART:20210916T130000Z
DTEND:20210916T140000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/78
DESCRIPTION:Title: Abelianisation of Meromorphic Connections\nby Nikita Nikolaev
(Sheffield) as part of Online Nottingham algebraic geometry seminar\n\n\n
Abstract\nThere is a natural 1-1 correspondence between Higgs bundles on a
compact complex curve and line bundles on an appropriate branched cover.
This abelianisation process goes through the direct image functor and it h
as been fruitful in addressing a variety of problems relating to bundles o
n curves. We extend this abelianisation correspondence from Higgs bundles
to flat bundles. This generalisation involves choosing a certain graph whi
ch translates to cohomology as a natural cocycle that exhibits a local def
ormation of the direct image functor. Furthermore\, our abelianisation cor
respondence extends to lambda-connections and recovers the abelianisation
of Higgs bundles as lambda goes to 0. Based in part on joint work in progr
ess with Marco Gualtieri.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Brini (Sheffield)
DTSTART:20211028T090000Z
DTEND:20211028T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/79
DESCRIPTION:Title: Quantum geometry of log-Calabi Yau surfaces\nby Andrea Brini
(Sheffield) as part of Online Nottingham algebraic geometry seminar\n\n\nA
bstract\nA log-Calabi Yau surface with maximal boundary\, or Looijenga pai
r\, is a pair (X\,D) with X a smooth complex projective surface and D a si
ngular anticanonical divisor in X. I will introduce a series of physics-mo
tivated correspondences relating five different classes of enumerative inv
ariants of the pair (X\,D):\n * the log Gromov--Witten theory of (X\,D)\,\
n * the Gromov--Witten theory of X twisted by the sum of the dual line bun
dles to the irreducible components of D\,\n * the open Gromov--Witten theo
ry of special Lagrangians in a toric Calabi--Yau 3-fold determined by (X\,
D)\,\n * the Donaldson--Thomas theory of a symmetric quiver specified by (
X\,D)\, and\n * a class of BPS invariants considered in different contexts
by Klemm--Pandharipande\, Ionel--Parker\, and Labastida--Marino--Ooguri--
Vafa.\nI will also show how the problem of computing all these invariants
is closed-form solvable. Based on joint works with P. Bousseau\, M. van Ga
rrel\, and Y. Schueler.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diana Torres Valencia (University of Pamplona)
DTSTART:20211111T130000Z
DTEND:20211111T140000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/80
DESCRIPTION:Title: CANCELLED - On accumulation points of volumes of stable surfaces
with one cyclic quotient singularity\nby Diana Torres Valencia (Univer
sity of Pamplona) as part of Online Nottingham algebraic geometry seminar\
n\n\nAbstract\nThe set of volumes of stable surfaces does have accumulatio
n points. I will introduce this phenomenon for surfaces with one cyclic qu
otient singularity towards answering the question under which conditions w
e can still have boundedness. Effective bounds allow listing singularities
that might appear on a stable surface after fixing its invariants. I will
show optimal inequalities for stable surfaces with one cyclic quotient si
ngularity\, which can be used to prove boundedness under certain condition
s. I also will introduce the notion of generalized T-singularity\, which i
s a natural generalization of the well-known T-singularities. I will show
how the accumulation points of volumes of stable surfaces with one general
ized T-singularity are formed.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Ros Camacho (Cardiff)
DTSTART:20211125T100000Z
DTEND:20211125T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/81
DESCRIPTION:Title: Computational aspects in orbifold equivalence\nby Ana Ros Cam
acho (Cardiff) as part of Online Nottingham algebraic geometry seminar\n\n
\nAbstract\nLandau-Ginzburg models are a family of physical theories descr
ibed by some polynomial (or "potential") characterized by having an isolat
ed singularity at the origin. Often appearing in mirror-symmetric phenomen
a\, they can be collected in higher categories with nice properties that a
llow direct computations. In this context\, it is possible to introduce an
equivalence relation between two different potentials called "orbifold eq
uivalence". We will present some recent examples of this equivalence\, and
discuss the computational challenges posed by the search of new ones. Joi
nt work with Timo Kluck.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eleonore Faber (Leeds)
DTSTART:20211208T140000Z
DTEND:20211208T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/82
DESCRIPTION:Title: Matrix factorizations for discriminants of pseudo-reflection grou
ps\nby Eleonore Faber (Leeds) as part of Online Nottingham algebraic g
eometry seminar\n\n\nAbstract\nIn this talk we will give an introduction t
o the McKay correspondence for complex reflection groups (joint work with
Ragnar Buchweitz and Colin Ingalls)\, and then show how this allows to ide
ntify certain matrix factorizations of the discriminants of these reflecti
on groups. We will in particular consider the family of pseudo-reflection
groups G(r\,p\,n)\, for which one can explicitly determine matrix factoriz
ations\, using higher Specht polynomials (work in progress with Colin Inga
lls\, Simon May\, and Marco Talarico).\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arina Voorhaar (Geneva)
DTSTART:20220113T130000Z
DTEND:20220113T140000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/83
DESCRIPTION:Title: On the Newton Polytope of the Morse Discriminant\nby Arina Vo
orhaar (Geneva) as part of Online Nottingham algebraic geometry seminar\n\
n\nAbstract\nA famous classical result by Gelfand\, Kapranov and Zelevinsk
y provides a combinatorial description of the vertices of the Newton polyt
ope of the $A$-discriminant (the closure of the set of all non-smooth hype
rsurfaces defined by polynomials with the given support $A$). Namely\, it
gives a surjection from the set of all convex triangulations of the convex
hull of the set $A$ with vertices in $A$ (or\, equivalently\, the set of
all possible combinatorial types of smooth tropical hypersurfaces defined
by tropical polynomials with support $A$) onto the set of vertices of this
Newton polytope. In my talk\, I will discuss a similar problem for the Mo
rse discriminant — the closure of the set of all polynomials with the gi
ven support $A$ which are non-Morse if viewed as polynomial maps. Namely\,
for a $1$-dimensional support set $A$\, there is a surjection from the se
t of all possible combinatorial types of so-called Morse tropical polynomi
als onto the vertices of the Newton polytope of the Morse discriminant.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alastair Craw (Bath)
DTSTART:20211014T100000Z
DTEND:20211014T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/84
DESCRIPTION:Title: Hyperpolygon spaces: beyond the movable cone\nby Alastair Cra
w (Bath) as part of Online Nottingham algebraic geometry seminar\n\n\nAbst
ract\nFor $n\\geq 4$\, the hyperpolygon spaces are a collection of Nakajim
a quiver varieties in dimension $2n-6$ that have been a useful testing gro
und for conjectures on conical symplectic varieties. I'll describe joint w
ork in progress with Gwyn Bellamy\, Steven Rayan\, Travis Schedler and Har
tmut Weiss in which we describe completely the birational geometry of thes
e spaces. The case $n=5$ recovers a well-known finite quotient singularity
in dimension four\, and allows us to provide a uniform construction of al
l 81 projective crepant resolutions studied in previous work of Donten-Bur
y--Wi\\'{s}niewski. I'll also explain the title of the talk by giving a ge
ometric interpretation of the components of the stability parameter even w
hen it doesn't lie in the positive orthant.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Coates (Imperial)
DTSTART:20211007T090000Z
DTEND:20211007T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/85
DESCRIPTION:Title: Rigid maximally mutable Laurent polynomials\nby Tom Coates (I
mperial) as part of Online Nottingham algebraic geometry seminar\n\n\nAbst
ract\nI will describe a class of Laurent polynomials which conjecturally c
orresponds under mirror symmetry to Fano varieties\, in any dimension\, wi
th mild singularities. This is joint work with Alexander Kasprzyk\, Giusep
pe Pitton\, and Ketil Tveiten.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatemeh Mohammadi (Ghent)
DTSTART:20211104T100000Z
DTEND:20211104T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/86
DESCRIPTION:Title: CANCELLED - Matroid stratifications of hypergraph determinantal v
arieties and their realization spaces\nby Fatemeh Mohammadi (Ghent) as
part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nI wil
l provide an introductory talk to hypergraph determinantal varieties from
projective geometry and matroid theory perspectives. I describe their deco
mpositions into matroid varieties. Matroids varieties in general can be re
ducible with arbitrary singularities by the Mnëv-Sturmfels universality t
heorem. Our goal is to provide families of matroids whose corresponding va
rieties are irreducible\, and use them to find minimal irreducible decompo
sitions for hypergraph varieties. The main themes of the talk are:\n1) giv
ing a decomposition for each hypergraph variety\;\n2) identifying each com
ponent in the decomposition as a matroid variety\; and\n3) understanding t
he irreducibility of these matroid varieties and their realizability.\nI w
ill not assume any prior knowledge of algebraic\, polyhedral\, or incidenc
e geometry\, and I will try to make the talk accessible to people with a b
road range of backgrounds. The talk is based on joint work with Oliver Cla
rke\, Kevin Grace\, and Harshit Motwani.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Anderson (Queen Mary)
DTSTART:20211118T130000Z
DTEND:20211118T140000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/87
DESCRIPTION:Title: Paving tropical ideals\nby Nicholas Anderson (Queen Mary) as
part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nTropic
al geometry is a powerful tool in algebraic geometry\, which offers a mult
itude of combinatorial approaches to studying algebraic varieties. This ta
lk will focus on the recent development of tropical commutative algebra by
Diane Maclagan and Felipe Rincon. The central object of study is the “t
ropical Ideal\,” which generalizes the structure of polynomial ideals ov
er fields to be suitable for study in the setting of tropical geometry\, t
hat is\, in polynomial semirings over semifields. All polynomial ideals ov
er a field can be associated to a “realizable” tropical ideal\, and it
is a non-trivial fact that “non-realizable” tropical ideals exist. In
this talk\, I will demonstrate how the combinatorics of matroid theory al
lows us to easily generate a subclass of tropical ideals\, called paving t
ropical ideals\, which in turn allows us to prove that most zero-dimension
al tropical ideals are not realizable.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florin Ambro (Simion Stoilow)
DTSTART:20220127T100000Z
DTEND:20220127T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/88
DESCRIPTION:Title: On Seshadri constants\nby Florin Ambro (Simion Stoilow) as pa
rt of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nThe Sesh
adri constant of a polarized variety $(X\,L)$ at a point $x$ measures how
positive is the polarization $L$ at $x$. If $x$ is very general\, the Sesh
adri constant does not depend on $x$\, and captures global information on
$X$. Inspired by ideas from the Geometry of Numbers\, we introduce in this
talk successive Seshadri minima\, such that the first one is the Seshadri
constant at a point\, and the last one is the width of the polarization a
t the point. Assuming the point is very general\, we obtain two results: a
) the product of the successive Seshadri minima is proportional to the vo
lume of the polarization\; b) if $X$ is toric\, the $i$-th successive Sesh
adri constant is proportional to the $i$-th successive minima of a suitabl
e $0$-symmetric convex body. Based on joint work with Atsushi Ito.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marvin Hahn (Sorbonne)
DTSTART:20220120T100000Z
DTEND:20220120T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/89
DESCRIPTION:Title: The tropical geometry of monotone Hurwitz numbers\nby Marvin
Hahn (Sorbonne) as part of Online Nottingham algebraic geometry seminar\n\
n\nAbstract\nHurwitz numbers are important enumerative invariants in algeb
raic geometry. They count branched maps between Riemann surfaces. Equivale
ntly\, they enumerate factorizations in the symmetric group. Hurwitz numbe
rs were introduced in the 1890s by Adolf Hurwitz and became central object
s of enumerative algebraic geometry in the 1990s through close connections
with the so-called Gromov-Witten theory. This interplay between Hurwitz a
nd Gromov-Witten theory is an active field of research and led to\, among
other things\, the celebrated ELSV formula. In the last decade\, many vari
ants of Hurwitz numbers have been introduced and studied. In particular\,
the question of connections between these variants of Hurwitz numbers and
Gromov-Witten theory is of great interest. So-called monotone Hurwitz numb
ers \, which originate from the theory of random matrices\, are among the
most studied variants of Hurwitz numbers. This talk is a progress report o
f our larger program in which we study the connections between monotone Hu
rwitz numbers and Gromov-Witten theory by combinatorial methods of tropica
l geometry\, and whose long-term goal is a proof of the still open conject
ure of an ELSV - type formula for double monotone Hurwitz numbers. The tal
k is based in part on joint work with Reinier Kramer and Danilo Lewanski.\
n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wendelin Lutz (Imperial)
DTSTART:20220203T100000Z
DTEND:20220203T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/90
DESCRIPTION:Title: A geometric proof of the classification of T-polygons\nby Wen
delin Lutz (Imperial) as part of Online Nottingham algebraic geometry semi
nar\n\n\nAbstract\nOne formulation of mirror symmetry predicts (omitting a
few adjectives) a one-to-one correspondence between equivalence classes o
f lattice polygons and deformation families of del Pezzo surfaces. Lattice
polygons that correspond to smooth Del Pezzo surfaces are called T-polygo
ns and have been classified by Kasprzyk-Nill-Prince using combinatorial me
thods\, thereby verifying the conjecture in the smooth case. I will give a
new geometric proof of their classification result.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qaasim Shafi (Imperial)
DTSTART:20220303T100000Z
DTEND:20220303T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/91
DESCRIPTION:Title: Logarithmic Toric Quasimaps\nby Qaasim Shafi (Imperial) as pa
rt of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nQuasimap
s provide an alternate curve counting system to Gromov-Witten theory\, rel
ated by wall-crossing formulas. Relative (or logarithmic) Gromov-Witten th
eory has proved useful for constructions in mirror symmetry\, as well as f
or determining ordinary Gromov-Witten invariants via the degeneration form
ula. I’ll discuss how to build a theory of logarithmic quasimaps in the
toric case\, some restrictions\, and why one might want to do so.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ananyo Dan (Sheffield)
DTSTART:20220210T100000Z
DTEND:20220210T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/92
DESCRIPTION:Title: McKay correspondence for isolated Gorenstein singularities\nb
y Ananyo Dan (Sheffield) as part of Online Nottingham algebraic geometry s
eminar\n\n\nAbstract\nThe McKay correspondence is a (natural) corresponden
ce between the (non-trivial) irreducible representations of a finite subgr
oup G of SL(2\,C) and the irreducible components of the exceptional diviso
r of a minimal resolution of the associated quotient singularity C^2//G. A
geometric construction for this correspondence was given by González-Spr
inberg and Verdier\, who showed that the two sets also correspond bijectiv
ely to the set of indecomposable reflexive modules on the quotient singula
rity. This was generalised to higher dimensional quotient singularities (i
.e.\, quotient of C^n by a finite subgroup of SL(n\,C)) by Ito-Reid\, wher
e the above sets were substituted by certain smaller subsets. It was furth
er generalised to more general quotient singularities by Bridgeland-King-R
eid\, Iyama-Wemyss and others\, using the language of derived categories.
In this talk\, I will survey past results and discuss what happens for the
isolated Gorenstein singularities case (not necessarily a quotient singul
arity). If time permits\, I will discuss applications to Matrix factorizat
ion. This is joint work in progress with J. F. de Bobadilla and A. Romano-
Velazquez.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jarosław Buczyński (Polish Academy of Sciences)
DTSTART:20220224T100000Z
DTEND:20220224T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/93
DESCRIPTION:Title: Fujita vanishing\, sufficiently ample line bundles\, and cactus v
arieties\nby Jarosław Buczyński (Polish Academy of Sciences) as part
of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nFor a fixe
d projective manifold X\, we say that a property P(L) (where L is a line b
undle on X) is satisfied by sufficiently ample line bundles if there exist
s a line bundle M on X such that P(L) hold for any L with L-M ample. I wil
l discuss which properties of line bundles are satisfied by the sufficient
ly ample line bundles - for example\, can you figure out before the talk\,
whether a sufficiently ample line bundle must be very ample? A basic ingr
edient used to study this concept is Fujita's vanishing theorem\, which is
an analogue of Serre's vanishing for sufficiently ample line bundles. At
the end of the talk I will define cactus varieties (an analogue of secant
varieties) and sketch a proof that cactus varieties to sufficiently ample
embeddings of X are (set-theoretically) defined by minors of matrices with
linear entries. The topic is closely related to conjectures of Eisenbud-K
oh-Stillman (for curves) and Sidman-Smith (for any varieties). The new ing
redients are based on a joint work in preparation with Weronika Buczyńska
and Łucja Farnik.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Borzì (Warwick)
DTSTART:20220317T100000Z
DTEND:20220317T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/94
DESCRIPTION:Title: Weierstrass sets on finite graphs\nby Alessio Borzì (Warwick
) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nW
eiestrass points and Weierstrass semigroups are classical objects of study
in Algebraic Geometry. The problem of determining which semigroups arise
as Weierstrass semigroups of a curve goes back to Hurwitz in 1893. After t
he advent of tropical geometry\, a divisor theory on graphs was developed
by Baker and Norine\, and later extended to metric graphs (namely\, abstra
ct tropical curves) by Gathmann and Kerber\, and Mikhalkin and Zharkov. In
this talk we present two natural tropical analogues of Weierstrass semigr
oups on graphs\, called rank and functional Weierstrass sets\, first appea
red in a work of Kang\, Matthews and Peachey. We present some results on t
hese two objects and their interplay.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Egor Yasinsky (École Polytechnique)
DTSTART:20220324T110000Z
DTEND:20220324T120000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/95
DESCRIPTION:Title: Birational involutions of the projective plane\nby Egor Yasin
sky (École Polytechnique) as part of Online Nottingham algebraic geometry
seminar\n\n\nAbstract\nBirational involutions of the projective plane (or
\, equivalently\, automorphisms of the field of rational functions in two
variables of order 2) were studied already by the Italian school of algebr
aic geometry — Bertini\, Castelnuovo\, and Enriques. However\, their exp
licit and complete description was obtained by Beauville and Bayle only in
2000 and only in the case of a complex projective plane. It turns out tha
t for planes over algebraically non-closed fields the situation is much mo
re complicated. In the first part of the talk\, I will review what is know
n about birational involutions of projective planes over various fields. I
n the second part\, I will talk about the joint work with I. Cheltsov\, F.
Mangolt and S. Zimmerman\, in which we classified birational involutions
of the real projective plane.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franco Rota (Glasgow)
DTSTART:20220331T090000Z
DTEND:20220331T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/96
DESCRIPTION:Title: Full exceptional collection for anticanonical log del Pezzo surfa
ces\nby Franco Rota (Glasgow) as part of Online Nottingham algebraic g
eometry seminar\n\n\nAbstract\nThe homological mirror symmetry conjecture
predicts a correspondence between the derived category of coherent sheaves
of a variety and the symplectic data (packaged in the Fukaya category) of
its mirror object. Motivated by this\, we construct exceptional collectio
ns for (the smooth stacks associated with) a family of log del Pezzo surfa
ces known as the Johnson-Kollar series. These surfaces have quotient\, non
-Gorenstein\, singularities. Thus\, our computation will include on the on
e hand an application of the special McKay correspondence\, and on the oth
er the study of their minimal resolutions\, which are birational to a degr
ee 2 del Pezzo surface. This is all joint work with Giulia Gugiatti.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Hicks (Edinburgh)
DTSTART:20220407T083000Z
DTEND:20220407T090000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/97
DESCRIPTION:Title: Mirror Symmetry and Lagrangian torus fibrations\nby Jeff Hick
s (Edinburgh) as part of Online Nottingham algebraic geometry seminar\n\n\
nAbstract\nMirror symmetry is a predicted equivalence between certain aspe
cts of algebraic geometry and symplectic geometry. The Strominger–Yau–
Zaslow conjecture proposes that this equivalence appears on pairs of algeb
raic and symplectic spaces which have dual torus fibrations. In this preta
lk\, we look at a first example: the complex torus which is fibered by rea
l tori\, and the cotangent bundle of the real torus. We'll see how both ge
ometries can be related to affine geometry on real n-dimensional space.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Hicks (Edinburgh)
DTSTART:20220407T090000Z
DTEND:20220407T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/98
DESCRIPTION:Title: Realizing tropical curves via mirror symmetry\nby Jeff Hicks
(Edinburgh) as part of Online Nottingham algebraic geometry seminar\n\n\nA
bstract\nThe tropicalization map associates to each curve in the algebraic
n-torus a piecewise linear object (tropical curve) in real n-dimensional
space. Given a tropical curve\, a natural question is if it can arise as t
he tropicalization of some algebraic curve. If this is the case we say tha
t the tropical curve is realizable. Determining good realizability criteri
a for tropical curves remains an important part of tropical geometry since
Mikhalkin provided examples of non-realizable tropical curves. We explore
the following strategy for realizing tropical curves:\n(1) Produce a Lagr
angian submanifold of the cotangent bundle of the torus whose moment map p
rojection approximates the tropical curve\;\n(2) Use homological mirror sy
mmetry to obtain a mirror algebraic sheaf\;\n(3) Show that the tropicaliza
tion of the support of this sheaf is the original tropical curve.\nWe will
give full answers to (1) and (3)\, and explain why (2) is fairly subtle.
As applications\, we will obtain some new and known realizability statemen
ts for tropical curves.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nivedita Viswanathan (Loughborough)
DTSTART:20220421T090000Z
DTEND:20220421T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/99
DESCRIPTION:Title: On K-stability of some singular del Pezzo surfaces\nby Nivedi
ta Viswanathan (Loughborough) as part of Online Nottingham algebraic geome
try seminar\n\n\nAbstract\nThere has been a lot of development recently in
understanding the existence of Kahler-Einstein metrics on Fano manifolds
due to the Yau-Tian-Donaldson conjecture\, which gives us a way of looking
at this problem in terms of the notion of K-stability. In particular\, th
is problem is solved in totality for smooth del Pezzo surfaces by Tian. Fo
r del Pezzo surfaces with quotient singularities\, there are partial resul
ts. In this talk\, we will consider singular del Pezzo surfaces of indices
2 and 3\, which are quasi-smooth\, well-formed hypersurfaces in weighted
projective space\, and understand what we can say about their K-stability.
This is joint work with In-Kyun Kim and Joonyeong Won.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zakarias Sjöström Dyrefelt (Aarhus-AIAS)
DTSTART:20220414T090000Z
DTEND:20220414T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/100
DESCRIPTION:Title: Constant scalar curvature and Kähler manifolds with nef canonic
al bundle\nby Zakarias Sjöström Dyrefelt (Aarhus-AIAS) as part of On
line Nottingham algebraic geometry seminar\n\n\nAbstract\nGiven a compact
Kähler manifold it is a classical question\, related to K-stability\, whe
ther it admits a Kähler metric of constant scalar curvature (cscK metric
for short). In this talk we prove that there always exist cscK metrics on
compact Kähler manifolds with nef canonical bundle\, thus on all smooth m
inimal models\, and also on the blowup of any such manifold. This confirms
an expectation of Jian-Shi-Song and extends well-known results of Aubin a
nd Yau to the nef case\, giving a large new class of examples of cscK mani
folds. The tools used are from the variational approach in Kähler geometr
y\, and some related results on stability thresholds and Donaldson's J-equ
ation are discussed along the way.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolaos Tsakanikas (Saarbrücken)
DTSTART:20220428T140000Z
DTEND:20220428T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/101
DESCRIPTION:Title: On the existence of minimal models for generalized pairs\nby
Nikolaos Tsakanikas (Saarbrücken) as part of Online Nottingham algebraic
geometry seminar\n\n\nAbstract\nI will discuss recent progress on the exi
stence of minimal models and Mori fiber spaces for generalized pairs. In p
articular\, I will explain the close relationship between the existence of
minimal models and the existence of weak Zariski decompositions for gener
alized pairs. This is joint work with Vladimir Lazić.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Veronica Fantini (IHES)
DTSTART:20220505T090000Z
DTEND:20220505T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/102
DESCRIPTION:Title: Enumerative geometry in the extended tropical vertex group\n
by Veronica Fantini (IHES) as part of Online Nottingham algebraic geometry
seminar\n\n\nAbstract\nThe extended tropical vertex group is a pro-nilpto
tent Lie group\, which has been introduced in [arxiv:1912.09956] studying
the relationship between scattering diagrams and infinitesimal deformation
s of holomorphic pairs. Scattering diagrams were introduced by Kontsevich
and Soibelman in the context of mirror symmetry. They are defined algebrai
cally\, in terms of pro-nilpotent Lie groups\, but in many applications th
ey have a combinatorial structure which encodes enumerative geometric data
(as Donaldson--Thomas invariants\, Gromov--Witten invariants\,...). In pa
rticular\, Gross\, Pandharipande and Siebert showed how to compute genus z
ero log Gromov--Witten invariants for P^2 via scattering diagrams in the s
o called tropical vertex group. In this talk\, I will discuss a possible g
eneralization regarding how to compute genus zero relative Gromov--Witten
invariants for toric P^2 using scattering diagrams in the extended tropica
l vertex group.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Arbesfeld (Kavli IPMU)
DTSTART:20220512T090000Z
DTEND:20220512T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/103
DESCRIPTION:Title: Descendent series for Hilbert schemes of points on surfaces\
nby Noah Arbesfeld (Kavli IPMU) as part of Online Nottingham algebraic geo
metry seminar\n\n\nAbstract\nStructure often emerges from Hilbert schemes
of points on varieties when the underlying variety is fixed but the number
of points parametrized varies. Some examples of such structure come from
integrals of tautological bundles\, which arise in geometric and physical
computations. When compiled into generating series\, these integrals displ
ay interesting functional properties. I will give an overview of results o
n such series\; the focus will be on K-theoretic descendent series for Hil
bert schemes on surfaces\, certain series formed from holomorphic Euler ch
aracteristics of tautological bundles. In particular\, I will explain how
to see that the K-theoretic descendent series are expansions of rational f
unctions.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiumars Kaveh (Pittsburgh)
DTSTART:20220519T130000Z
DTEND:20220519T140000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/104
DESCRIPTION:Title: Buildings as classifying spaces for toric principal bundles\
nby Kiumars Kaveh (Pittsburgh) as part of Online Nottingham algebraic geom
etry seminar\n\n\nAbstract\nA building is a certain infinite combinatorial
object (abstract simplicial complex) associated to a (semisimple) linear
algebraic group which encodes the relative position of maximal tori and pa
rabolic/parahoric subgroups in it. After an introduction to buildings and
discussing some examples from linear algebra\, I will talk about some rece
nt results on classification of torus equivariant principal G-bundles on t
oric varieties (over a field) and toric schemes (over a discrete valuation
ring). These are extensions of Klyachko's classification of torus equivar
iant vector bundles on toric varieties. For this we introduce the notions
of "piecewise linear map" to the Tits building and "piecewise affine map"
to the Bruhat-Tits building of a linear algebraic group. This is joint wor
k with Chris Manon (Kentucky) and Boris Tsvelikhovsky (Pittsburgh).\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fei Xie (Edinburgh)
DTSTART:20220526T090000Z
DTEND:20220526T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/105
DESCRIPTION:Title: Residual categories of quadric surface bundles\nby Fei Xie (
Edinburgh) as part of Online Nottingham algebraic geometry seminar\n\n\nAb
stract\nThe residual category (or the Kuznetsov component) of a quadric su
rface bundle is the non-trivial component in the derived category. It is e
quivalent to the twisted derived category of a double cover over the base
when the quadric surface bundle has simple degeneration (fibers have coran
k at most 1). I will consider quadric surface bundles with fibers of coran
k at most 2 and describe their residual categories as (twisted) derived ca
tegories of some scheme in two situations: (1) when the bundle has a smoot
h section\; (2) when the total space is smooth and the base is a smooth su
rface. The results can be applied to describe the residual categories of a
(partial) resolution of nodal quintic del Pezzo threefolds\, cubic fourfo
lds containing a plane and certain complete intersections of quadrics.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Bäuerle (Eberhard Karl University of Tübingen)
DTSTART:20220623T090000Z
DTEND:20220623T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/106
DESCRIPTION:Title: Gorenstein Fano 3-folds of Picard number 1 with a 2-torus action
\nby Andreas Bäuerle (Eberhard Karl University of Tübingen) as part
of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nWe classify
the non-toric\, $\\mathbb{Q}$-factorial\, log terminal\, Gorenstein Fano
threefolds of Picard number one that admit an effective action of a two-di
mensional torus.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chen Jiang (Shanghai Center for Mathematical Sciences)
DTSTART:20200630T090000Z
DTEND:20200630T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/107
DESCRIPTION:Title: Explicit boundedness of canonical Fano 3-folds\nby Chen Jian
g (Shanghai Center for Mathematical Sciences) as part of Online Nottingham
algebraic geometry seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chen Jiang (Shanghai Center for Mathematical Sciences)
DTSTART:20220630T090000Z
DTEND:20220630T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/108
DESCRIPTION:Title: RESCHEDULED TO 8 JULY: Explicit boundedness of canonical Fano 3-
folds\nby Chen Jiang (Shanghai Center for Mathematical Sciences) as pa
rt of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nMotivate
d by the classification of canonical Fano 3-folds\, we are interested in b
oundedness results on different kinds of canonical Fano 3-folds\, such as
anticanonical systems\, indices\, degrees\, and so on. I will summarize kn
own results with recent progress\, such as the explicit upper bound of ani
tcanonical volumes and the effective birationality of anticanonical system
s (based on joint works with Yu Zou) and some open problems.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau (ETH Zurich)
DTSTART:20220721T090000Z
DTEND:20220721T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/109
DESCRIPTION:Title: Fock–Goncharov dual cluster varieties and Gross–Siebert mirr
ors\nby Pierrick Bousseau (ETH Zurich) as part of Online Nottingham al
gebraic geometry seminar\n\n\nAbstract\nCluster varieties come in pairs: f
or any X-cluster variety there is an associated Fock–Goncharov dual A-cl
uster variety. On the other hand\, in the context of mirror symmetry\, ass
ociated with any log Calabi–Yau variety is its mirror dual\, which can b
e constructed using the enumerative geometry of rational curves in the fra
mework of the Gross–Siebert program. I will explain how to bridge the th
eory of cluster varieties with the algebro-geometric framework of Gross–
Siebert mirror symmetry\, and show that the mirror to the X-cluster variet
y is a degeneration of the Fock–Goncharov dual A-cluster variety. To do
this\, we investigate how the cluster scattering diagram of Gross–Hackin
g–Keel–Kontsevich compares with the canonical scattering diagram defin
ed by Gross–Siebert to construct mirror duals in arbitrary dimensions. T
his is joint work with Hülya Argüz.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Léonard Pille-Schneider (Paris)
DTSTART:20220714T090000Z
DTEND:20220714T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/110
DESCRIPTION:Title: Degenerations of Calabi-Yau manifolds and integral affine geomet
ry\nby Léonard Pille-Schneider (Paris) as part of Online Nottingham a
lgebraic geometry seminar\n\n\nAbstract\nLet $X\\rightarrow D^*$ be a maxi
mal degeneration of $n$-dimensional Calabi-Yau varieties over the puncture
d disk. The SYZ conjecture\, motivated by mirror symmetry\, predicts that
the general fiber $X_t$ admits a Lagrangian torus fibration $f_t : X_t \\r
ightarrow B$ onto a base $B$ of real dimension $n$\, and that as $t\\right
arrow 0$ the variety $X_t$ endowed with its Ricci-flat Kähler metric coll
apses to the space $B$\, endowed with a $Z$-affine structure. The goal of
this talk is to explain how to construct the space $B$ with its extra stru
ctures using non-archimedean geometry. In particular\, in the case of Ferm
at threefolds in $\\mathbb{P}^4$\, using the toric geometry of the ambient
space\, we are able to construct a non-archimedean SYZ fibration inducing
on $B$ the affine structure naturally induced by the Gromov-Hausdorff con
vergence recently proved by Yang Li. This is based on work joint with Enri
ca Mazzon.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elisa Postinghel (Trento)
DTSTART:20220707T090000Z
DTEND:20220707T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/111
DESCRIPTION:Title: The geometry of Weyl orbits on blow-ups of projective spaces
\nby Elisa Postinghel (Trento) as part of Online Nottingham algebraic geom
etry seminar\n\n\nAbstract\nLinear systems of divisors on blow-ups of proj
ective spaces in points in general positions are connected to certain poly
nomial interpolation problems. While for the case of plane curves and of s
urfaces in 3-space there are conjectures\, although long standing\, formul
ated by M. Nagata\, B. Segre and others\, in the higher dimensional case w
e are in the dark. However\, when the number of points is not too large an
d the blow-ups are Mori dream spaces\, an action of the Weyl group on cycl
es of any codimension governs the birational behaviour of the space on the
one hand\, and the stable base locus of divisors on the other hand\, and
it yields a solution to the interpolation problem. Joint work with C. Bram
billa\, O. Dumitrescu and L. Santana Sánchez.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chen Jiang (Shanghai Center for Mathematical Sciences)
DTSTART:20220708T090000Z
DTEND:20220708T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/112
DESCRIPTION:Title: Explicit boundedness of canonical Fano 3-folds\nby Chen Jian
g (Shanghai Center for Mathematical Sciences) as part of Online Nottingham
algebraic geometry seminar\n\n\nAbstract\nMotivated by the classification
of canonical Fano 3-folds\, we are interested in boundedness results on d
ifferent kinds of canonical Fano 3-folds\, such as anticanonical systems\,
indices\, degrees\, and so on. I will summarize known results with recent
progress\, such as the explicit upper bound of anitcanonical volumes and
the effective birationality of anticanonical systems (based on joint works
with Yu Zou) and some open problems.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Schaffler (Roma Tre University)
DTSTART:20220728T090000Z
DTEND:20220728T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/113
DESCRIPTION:Title: Boundary divisors in the compactification by stable surfaces of
moduli of Horikawa surfaces\nby Luca Schaffler (Roma Tre University) a
s part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nSmoo
th minimal surfaces of general type with $K^2=1$\, $p_g=2$\, and $q=0$ con
stitute a fundamental example in the geography of algebraic surfaces\, and
the 28-dimensional moduli space $\\mathbf{M}$ of their canonical models a
dmits a modular compactification $\\overline{\\mathbf{M}}$ via the minimal
model program. We describe eight new irreducible boundary divisors in su
ch compactification parametrizing reducible stable surfaces. Additionally\
, we study the relation with the GIT compactification of $\\mathbf{M}$ and
the Hodge theory of the degenerate surfaces that the eight divisors param
etrize. This is joint work in progress with Patricio Gallardo\, Gregory Pe
arlstein\, and Zheng Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felipe Espreafico (IMPA)
DTSTART:20220811T130000Z
DTEND:20220811T140000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/114
DESCRIPTION:Title: Gauss-Manin Connection in Disguise and Mirror Symmetry\nby F
elipe Espreafico (IMPA) as part of Online Nottingham algebraic geometry se
minar\n\n\nAbstract\nIn this talk\, we aim to explain what the Gauss-Manin
Connection in Disguise program is and why it is important. The idea is to
construct objects which behave similarly to modular forms using the Gauss
-Manin connection associated to a family of varieties with fixed topologic
al data. We focus on the applications to Mirror Symmetry\, especially the
relations with Gromov-Witten invariants and the periods of the mirror quin
tic family. Among them\, I will explain my results for the open string Mir
ror Symmetry and open Gromov-Witten invariants.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Hübsch (Howard University)
DTSTART:20220825T090000Z
DTEND:20220825T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/115
DESCRIPTION:Title: Laurent Smoothing\, Turin Degenerations and Mirror Symmetry\
nby Tristan Hübsch (Howard University) as part of Online Nottingham algeb
raic geometry seminar\n\n\nAbstract\nCalabi-Yau hypersurfaces in toric spa
ces of general type (encoded by certain non-convex polytopes) are degenera
te but may be smoothed by rational anticanonical sections. Nevertheless\,
gauged linear sigma model phases and an increasing number of their classic
al and quantum data are just as computable as for their siblings encoded b
y reflexive polytopes\, and they all have transposition mirrors. Showcasin
g Calabi-Yau hypersurfaces in Hirzebruch scrolls shows this class of const
ructions to be infinitely vast\, yet amenable to several well-founded alge
bro-geometric methods of analysis. This talk will include joint work with
Per Berglund\, as reported in part: arXiv:1606.07420\, arXiv:1611.10300 a
nd arXiv:2205.12827.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swarnava Mukhopadhyay (Tata Institute)
DTSTART:20220804T090000Z
DTEND:20220804T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/116
DESCRIPTION:Title: Graph potentials and mirrors of moduli of rank two bundles on cu
rves\nby Swarnava Mukhopadhyay (Tata Institute) as part of Online Nott
ingham algebraic geometry seminar\n\n\nAbstract\nGraph potentials are Laur
ent polynomials associated to (colored) trivalent graphs that were introdu
ced in a joint work with Belmans and Galkin. They naturally appear as Newt
on polynomials of natural toric degenerations of the moduli space of rank
two bundles. In this talk we will first discuss how graph potentials compu
te quantum periods of the moduli space $M$ of rank two bundles with fixed
odd degree determinant and hence can be regarded as a partial mirror to $M
$. From the view point of mirror symmetry\, we will show how the critical
value decomposition of graph potentials provides evidence for the conjectu
ral semiorthogonal decomposition of $D^bCoh(M)$. If time permits we will a
lso discuss a formula to efficiently compute the periods of graph potentia
l via a TQFT. This is a joint work with Pieter Belmans and Sergey Galkin.\
n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfredo Nájera Chávez (UNAM)
DTSTART:20220901T130000Z
DTEND:20220901T140000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/117
DESCRIPTION:Title: Newton–Okounkov bodies and minimal models of cluster varieties
\nby Alfredo Nájera Chávez (UNAM) as part of Online Nottingham algeb
raic geometry seminar\n\n\nAbstract\nI will explain a general procedure to
construct Newton–Okounkov bodies for a certain class of (partial) compa
ctifications of cluster varieties. This class consists of the (partial) mi
nimal models of cluster varieties with enough theta functions. This constr
uction applies for example to Grassmannians and Flag varieties\, among oth
ers. Our construction depends on a choice of torus in the atlas of the clu
ster variety and the associated Newton–Okounkov body lives inside a real
vector space. Time permitting\, I will explain how to compare the Newton
–Okounkov bodies associated with different tori and elaborate on the "in
trinsic Newton–Okounkov body"\, which is an object that does not depend
on the choice of torus and lives inside the real tropicalization of the mi
rror cluster variety. This is based on upcoming work with Lara Bossinger\,
Man-Wai Cheung and Timothy Magee.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianluca Occhetta (Trento)
DTSTART:20220922T090000Z
DTEND:20220922T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/118
DESCRIPTION:Title: Maximal disjoint Schubert cycles in Rational Homogeneous spaces<
/a>\nby Gianluca Occhetta (Trento) as part of Online Nottingham algebraic
geometry seminar\n\n\nAbstract\nIn 1974 Tango proved that there are no non
-constant morphisms from $lmathbb{P}^n$ to the Grassmannian $G(l\,m)$ if $
n > m$\; similar results were later obtained for morphisms from other Fano
manifolds to Grassmannians. In this talk I will present the following gen
eralization of these results: if $X$ and $Y$ are rational homogeneous mani
fold obtained as quotients of classical groups $G_X$ and $G_Y$ of the same
type and $rk(G_X) > rk(G_Y)$ then there are no non-constant morphisms fro
m $X$ to $Y$. The key ingredient of the proof is the determination of the
effective good divisibility of rational homogeneous manifolds of classical
type\, that is\, the greatest integer $s$ such that two effective cycles
in the Chow ring whose sum of codimensions is $s$ have nonzero intersectio
n. This talk is based on a joint work with R. Muñoz and L.E. Solá Conde.
\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Reading (North Carolina)
DTSTART:20220915T140000Z
DTEND:20220915T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/119
DESCRIPTION:Title: Scatter\, cluster\, scatter\, model\nby Nathan Reading (Nort
h Carolina) as part of Online Nottingham algebraic geometry seminar\n\n\nA
bstract\nCluster algebras were invented/discovered in order to understand
total positivity. But almost immediately\, mathematicians (and later physi
cists) started finding connections between the combinatorics/geometry/alge
bra of cluster algebras and other areas of mathematics and physics. Most r
elevant for this talk are two connections: In one direction\, the theory o
f scattering diagrams (mirror symmetry/Donaldson-Thomas theory/integrable
systems) has been applied to prove key structural results about cluster al
gebras. In the other direction\, certain cluster algebras seem to be relev
ant to the computation of scattering amplitudes in physics. The title of t
his talk is also an outline. I will introduce scattering diagrams\, then i
ntroduce cluster algebras\, and connect the two. Then I will give a brief\
, naïve summary of the observed connections between cluster algebras and
scattering amplitudes\, to motivate the idea that a physicist might be int
erested in combinatorial models for cluster algebras/scattering diagrams.
I will conclude with a survey of the state of research on these combinator
ial models\, focusing on the models that I have worked most closely with.\
n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Tasin (Milano)
DTSTART:20220929T090000Z
DTEND:20220929T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/120
DESCRIPTION:Title: Sasaki-Einstein metrics on spheres\nby Luca Tasin (Milano) a
s part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nIt i
s a classical problem in geometry to construct new metrics on spheres. I w
ill report on a joint work with Yuchen Liu and Taro Sano in which we const
ruct infinitely many families of Sasaki-Einstein metrics on odd-dimensiona
l spheres that bound parallelizable manifolds\, proving in this way conjec
tures of Boyer-Galicki-Kollár and Collins-Székelyhidi. The construction
is based on showing the K-stability of certain Fano weighted orbifold hype
rsurfaces.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Ugaglia (Palermo)
DTSTART:20221013T083000Z
DTEND:20221013T093000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/121
DESCRIPTION:Title: Seshadri constants of toric surfaces\nby Luca Ugaglia (Paler
mo) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\
nIn this talk\, after introducing Seshadri constants of projective surface
s and some known results\, I will focus on the case of toric projective su
rfaces associated to lattice polygons. I will prove some relations between
the rationality of Seshadri constants and the geometry of the polygon\, a
nd I will present some possible applications to the case of weighted proje
ctive planes. This is based on a joint work with Antonio Laface.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aimeric Malter (Birmingham)
DTSTART:20221006T090000Z
DTEND:20221006T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/122
DESCRIPTION:Title: A derived equivalence of the Libgober-Teitelbaum and Batyrev-Bor
isov mirror constructions\nby Aimeric Malter (Birmingham) as part of O
nline Nottingham algebraic geometry seminar\n\n\nAbstract\nIn this talk I
will demonstrate how Variations of Geometric Invariant Theory can be used
to provide a derived equivalence between complete intersections in toric v
arieties. I will illustrate this by proving the derived equivalence of two
mirror constructions\, due to Libgober-Teitelbaum and Batyrev-Borisov.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Schneider (EPFL)
DTSTART:20221103T100000Z
DTEND:20221103T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/123
DESCRIPTION:Title: Birational maps of Severi-Brauer surfaces\, with applications to
Cremona groups of higher rank\nby Julia Schneider (EPFL) as part of O
nline Nottingham algebraic geometry seminar\n\n\nAbstract\nCremona groups
are groups of birational transformations of a projective space. Their stru
cture depends on the dimension and the field. In this talk\, however\, we
will first focus on birational transformations of (non-trivial) Severi-Bra
uer surfaces\, that is\, surfaces that become isomorphic to the projective
plane over the algebraic closure of K. Such surfaces do not contain any K
-rational point. We will prove that if such a surface contains a point of
degree 6\, then its group of birational transformations is not generated b
y elements of finite order as it admits a surjective group homomorphism to
the integers. As an application\, we use this result to study Mori fiber
spaces over the field of complex numbers\, for which the generic fiber is
a non-trivial Severi-Brauer surface. We prove that any group of cardinalit
y at most the one of the complex numbers is a quotient of the Cremona grou
p of rank 4 (and higher). This is joint work with Jérémy Blanc and Egor
Yasinsky.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Abreu (Fluminense Federal University)
DTSTART:20221020T090000Z
DTEND:20221020T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/124
DESCRIPTION:Title: Wall-crossing of Brill-Noether cycles in compactified Jacobians<
/a>\nby Alex Abreu (Fluminense Federal University) as part of Online Notti
ngham algebraic geometry seminar\n\n\nAbstract\nWe will discuss an explici
t graph formula\, in terms of boundary strata classes\, for the wall-cross
ing of universal (over the moduli space of curves) Brill-Noether classes.
More precisely\, fix two stability conditions for universal compactified J
acobians that are on different sides of a wall in the stability space. The
n we can compare the two universal Brill-Noether classes on the two compac
tified Jacobians by pulling one of them back along the (rational) identity
map. The calculation involves constructing a resolution by means of subse
quent blow-ups. This is joint with Nicola Pagani.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joey Palmer (Illinois)
DTSTART:20221110T150000Z
DTEND:20221110T160000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/125
DESCRIPTION:Title: Integrable systems with S^1-actions and the associated polygons<
/a>\nby Joey Palmer (Illinois) as part of Online Nottingham algebraic geom
etry seminar\n\n\nAbstract\nSemitoric systems are a type of four-dimension
al integrable system which admit a global $S^1$-action\; these systems wer
e classified by Pelayo and Vu Ngoc in 2011\, generalizing the classificati
on of toric integrable systems and making use of an invariant called a `se
mitoric polygon'. I will present some results about bifurcations of such s
ystems\, and show how this can be used to construct explicit examples of s
uch systems associated to certain given semitoric polygon. Time permitting
\, I will also discuss how hypersemitoric systems\, a generalization of se
mitoric systems\, appear in this context. Some of the results I will prese
nt are joint with Yohann Le Floch and Sonja Hohloch.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasiliki Petrotou (Hebrew University of Jerusalem)
DTSTART:20221117T100000Z
DTEND:20221117T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/126
DESCRIPTION:Title: Tom & Jerry triples and the 4-intersection unprojection formats<
/a>\nby Vasiliki Petrotou (Hebrew University of Jerusalem) as part of Onli
ne Nottingham algebraic geometry seminar\n\n\nAbstract\nUnprojection is a
theory in Commutative Algebra due to Miles Reid which constructs and analy
ses more complicated rings from simpler ones. The talk will be about two n
ew formats of unprojection which we call Tom & Jerry triples and 4-interse
ction format respectively. The motivation is to construct codimension 6 Go
renstein rings starting from codimensions 3 and 2 respectively. As an appl
ication we will construct three families of codimension 6 Fano 3-folds in
weighted projective space which appear in the Graded Ring Database.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Silversmith (Warwick)
DTSTART:20221128T100000Z
DTEND:20221128T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/127
DESCRIPTION:Title: Cross-ratios and perfect matchings\nby Rob Silversmith (Warw
ick) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract
\nGiven a bipartite graph G (subject to a constraint)\, the "cross-ratio d
egree" of G is a non-negative integer invariant of G\, defined via a simpl
e counting problem in algebraic geometry. I will discuss some natural cont
exts in which cross-ratio degrees arise. I will then present a perhaps-sur
prising upper bound on cross-ratio degrees in terms of counting perfect ma
tchings. Finally\, time permitting\, I may discuss the tropical side of th
e story.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tiago Duarte Guerreiro (Essex)
DTSTART:20221208T100000Z
DTEND:20221208T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/128
DESCRIPTION:Title: On toric Sarkisov Links from P^4\nby Tiago Duarte Guerreiro
(Essex) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstr
act\nAccording to the Sarkisov Program\, a birational map between a Fano v
ariety of Picard rank one and a Mori fibre space can be decomposed as a fi
nite sequence of Elementary Sarkisov Links starting with the blowup of a c
entre. Hence\, it is natural to try to understand the latter maps explicit
ly. In this talk we explain how to describe all possible toric Elementary
Sarkisov Links starting with the blowup of a point in $\\mathbb{P}^4$.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucie Devey (Frankfurt and Grenoble)
DTSTART:20230126T100000Z
DTEND:20230126T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/129
DESCRIPTION:Title: Stability of toric vector bundles in terms of parliaments of pol
ytopes\nby Lucie Devey (Frankfurt and Grenoble) as part of Online Nott
ingham algebraic geometry seminar\n\n\nAbstract\nGiven any toric vector bu
ndle\, we may construct its parliament of polytopes. This is a generalizat
ion of the Newton polytope (or moment polytope) of a toric line bundle. Th
is object contains a huge amount of information about the original bundle:
notably on its global sections and its positivity. We can also easily kno
w if the toric bundle is (semi-/poly-)stable with respect to any polarisat
ion. I will give a combinatorial visualisation of stability of toric vecto
r bundles.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yaoxiong Wen (KIAS)
DTSTART:20230202T100000Z
DTEND:20230202T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/130
DESCRIPTION:Title: Mirror symmetry for the parabolic G-Higgs bundle\, from local to
global\nby Yaoxiong Wen (KIAS) as part of Online Nottingham algebraic
geometry seminar\n\n\nAbstract\nMotivated by geometric Langlands\, we ini
tiate a program to study the mirror symmetry for the moduli space of parab
olic G-Higgs bundles. This talk will focus on $G=\\textrm{Sp}_{2n}$ and it
s Langlands dual $\\textrm{SO}_{2n+1}$. Our goal is to prove the SYZ mirro
r symmetry and topological mirror symmetry (TMS). The parabolic structure
of the parabolic Higgs bundle is related to the nilpotent orbit closure. S
o we need to first figure out the mirror pair for nilpotent orbits. Classi
cally\, there is a famous Springer duality between special orbits. Therefo
re\, it is natural to speculate that the mirror symmetry we seek may coinc
ide with Springer duality in the context of special orbits. Unfortunately\
, such a naive statement fails. To remedy the situation\, together with Pr
of. Ruan and Prof. Fu (arXiv:2207.10533)\, we propose a conjecture which a
sserts the mirror symmetry for certain parabolic/induced covers of special
orbits. Then\, we prove the conjecture for Richardson orbits and obtain c
ertain partial results in general. After understanding the mirror paraboli
c structures\, together with W. He\, X. Su\, B. Wang\, X. Wen\, we are wor
king in progress to prove the SYZ and TMS for the moduli space of paraboli
c $\\textrm{Sp}_{2n}/\\textrm{SO}_{2n+1}$-Higgs bundles with dual paraboli
c structures.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fenglong You (ETH-Zurich)
DTSTART:20230222T100000Z
DTEND:20230222T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/131
DESCRIPTION:Title: Relative quantum cohomology under birational transformations
\nby Fenglong You (ETH-Zurich) as part of Online Nottingham algebraic geom
etry seminar\n\n\nAbstract\nI will talk about how relative quantum cohomol
ogy\, defined by Tseng--You and Fan--Wu--You\, varies under birational tra
nsformations. Relation with FJRW theory and extremal transitions of absolu
te Gromov--Witten theory will also be discussed.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Ducat (Durham)
DTSTART:20230309T100000Z
DTEND:20230309T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/132
DESCRIPTION:Title: Quartic surfaces up to volume preserving equivalence\nby Tom
Ducat (Durham) as part of Online Nottingham algebraic geometry seminar\n\
n\nAbstract\nWe consider log Calabi-Yau pairs of the form $(\\mathbb{P}^3\
, D)$\, where $D$ is a quartic surface\, up to volume-preserving equivalen
ce. The coregularity of the pair $(\\mathbb{P}^3\, D)$ is a discrete volum
e-preserving invariant $c=0\,1$ or $2$\, and which depends on the nature o
f the singularities of $D$. We classify all pairs $(\\mathbb{P}^3\,D)$ of
coregularity $c=0$ or $1$ up to volume preserving equivalence. In particul
ar\, if $c=0$ then we show that $(\\mathbb{P}^3\, D)$ admits a volume pres
erving birational map onto a toric pair.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iacopo Brivio (NCTS)
DTSTART:20230209T100000Z
DTEND:20230209T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/133
DESCRIPTION:Title: Invariance of plurigenera and KSBA moduli in positive and mixed
characteristic\nby Iacopo Brivio (NCTS) as part of Online Nottingham a
lgebraic geometry seminar\n\n\nAbstract\nA famous theorem by Siu states th
at plurigenera are invariant under smooth deformations for complex project
ive manifolds\, a result which is a cornerstone of higher dimensional modu
li theory. In this talk we will explore some examples showing that Siu's t
heorem fails in positive and mixed characteristic\, then discuss the impli
cations at the level of moduli theory\, as well as some related questions.
\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duc-Khanh Nguyen (Albany)
DTSTART:20230216T140000Z
DTEND:20230216T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/134
DESCRIPTION:Title: A generalization of the Murnaghan-Nakayama rule for $K$-$k$-Schu
r and $k$-Schur functions\nby Duc-Khanh Nguyen (Albany) as part of Onl
ine Nottingham algebraic geometry seminar\n\n\nAbstract\nWe introduce a ge
neralization of $K$-$k$-Schur functions and $k$-Schur functions via the Pi
eri rule. Then we obtain the Murnaghan-Nakayama rule for the generalized f
unctions. The rule are described explicitly in the cases of $K$-$k$-Schur
functions and $k$-Schur functions\, with concrete descriptions and algorit
hms for coefficients. Our work recovers the result of Bandlow\, Schilling\
, and Zabrocki for $k$-Schur functions\, and explains it as a degeneration
of the rule for $K$-$k$-Schur functions. In particular\, many other speci
al cases promise to be detailed in the future.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ayush Kumar Tewari (Ghent)
DTSTART:20230302T100000Z
DTEND:20230302T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/135
DESCRIPTION:Title: Forbidden patterns in tropical planar curves and panoptigons
\nby Ayush Kumar Tewari (Ghent) as part of Online Nottingham algebraic geo
metry seminar\n\n\nAbstract\nTropical curves in $\\mathbb{R}^2$ correspond
to metric planar graphs but not all planar graphs arise in this way. We d
escribe several new classes of graphs that cannot occur. For instance\, th
is yields a full combinatorial characterization of the tropically planar g
raphs of genus at most six. We also define a special family of lattice pol
ytopes namely panoptigons and enumerate all possible panoptigons under mil
d lattice width constraints and show how they can be used to find a forbid
den pattern in tropical planar curves. We also will discuss some possible
applications of the classification of panoptigons and ongoing work on suit
able generalizations. This talk is based on work in Tewari (2022) and join
t work with Michael Joswig (2020) and Ralph Morrison (2021).\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Zaffalon (KU Leuven)
DTSTART:20230323T100000Z
DTEND:20230323T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/136
DESCRIPTION:Title: Toric degenerations of partial flag varieties via matching field
s and combinatorial mutations\nby Francesca Zaffalon (KU Leuven) as pa
rt of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nToric de
generations are an important tool that can be used to analyze algebraic va
rieties as they allow us to understand a general variety via the geometry
of their associated toric varieties. In this talk\, I will show how to pro
duce a new large family of toric degenerations of Grassmannians and (parti
al) flag varieties\, whose combinatorics is governed by matching fields. M
oreover\, I will study the relations between polytopes associated to diffe
rent toric degenerations of the same variety. This is done using the tool
of combinatorial mutations\, particular piecewise linear functions on poly
topes. Finally\, I will show how our methods can be used to compute new fa
milies of toric degenerations of small Grassmannians and flag varieties. T
his talk is based on joint work with Oliver Clarke and Fatemeh Mohammadi.\
n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Urbinati (Udine)
DTSTART:20230316T150000Z
DTEND:20230316T160000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/137
DESCRIPTION:Title: Mori Dream Pairs and C^*-actions\nby Stefano Urbinati (Udine
) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nT
he idea of the talk is that of giving a connection between 'local' Mori th
eory and $C^*$-actions. In particular\, we construct and characterize a co
rrespondence between Mori dream regions arising from small modifications o
f normal projective varieties and $C^*$-actions on polarized pairs which a
re bordisms. This is joint work with Lorenzo Barban\, Eleonora A. Romano a
nd Luis E. Solá Conde.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernd Siebert (Texas)
DTSTART:20230317T100000Z
DTEND:20230317T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/138
DESCRIPTION:Title: Toward the logarithmic Hilbert scheme\nby Bernd Siebert (Tex
as) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\
nLogarithmic geometry provides tools to work relative a normal crossings d
ivisor\, including normal crossings degenerations. I will report on work i
n progress with Mattia Talpo and Richard Thomas to define a natural logari
thmic analogue of the ordinary Hilbert scheme. Immediate applications incl
ude induced good degenerations of Hilbert schemes of points. Our point of
view also suggests a definition of tropical Hilbert schemes. One larger ai
m is to develop robust logarithmic methods to deal with coherent sheaves i
n maximal degenerations as they appear in mirror symmetry.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chuyu Zhou (EPFL)
DTSTART:20230504T090000Z
DTEND:20230504T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/139
DESCRIPTION:Title: On wall crossing for K-stability with multiple boundaries\nb
y Chuyu Zhou (EPFL) as part of Online Nottingham algebraic geometry semina
r\n\n\nAbstract\nIn this talk\, we will focus on a wall-crossing theory fo
r log Fano pairs with multiple boundaries. As a key ingredient\, we will p
resent that the K-semistable domains are polytopes. This is based on a rec
ent work https://arxiv.org/abs/2302.13503.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukas Braun (Freiburg)
DTSTART:20230420T090000Z
DTEND:20230420T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/140
DESCRIPTION:Title: Reductive quotients of klt varieties\nby Lukas Braun (Freibu
rg) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\
nIn this talk\, I will explain the proof of a recent result\, obtained tog
ether with Daniel Greb\, Kevin Langlois\, and Joaquin Moraga\, that reduct
ive quotients of klt type varieties are of klt type. This generalizes and
extends a classical result by Boutot\, stating that these kinds of quotien
ts preserve rational singularities. The statement was also well known in t
he case of finite groups. If time permits\, I will also discuss several ap
plications of our result\, e.g. on quotients of Fano type varieties\, good
moduli spaces\, and collapsing of homogeneous bundles.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Gioia Cifani (Roma Tre)
DTSTART:20230412T090000Z
DTEND:20230412T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/141
DESCRIPTION:Title: Reconstructing curves from their Hodge classes\nby Maria Gio
ia Cifani (Roma Tre) as part of Online Nottingham algebraic geometry semin
ar\n\n\nAbstract\nRecently\, Movasati and Sertöz pose several interesting
questions about the reconstruction of a variety from its Hodge class. In
particular they give the notion of a perfect class: the Hodge class of a v
ariety $X$ is perfect if its annihilator is a sum of ideals of varieties w
hose Hodge class is a nonzero rational multiple of that of $X$. I will rep
ort on a joint work with Gian Pietro Pirola and Enrico Schlensiger\, in wh
ich we give an answer to some of these questions for curves: in particular
\, we show that the Hodge class of a smooth rational quartic on a surface
of degree 4 is not perfect\, and that the Hodge class of an arithmetically
Cohen-Macaulay curve is always perfect. Moreover\, I will give some resul
ts on the problem in higher dimension.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Esser (UCLA)
DTSTART:20230413T140000Z
DTEND:20230413T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/142
DESCRIPTION:Title: Automorphisms of weighted projective hypersurfaces\nby Louis
Esser (UCLA) as part of Online Nottingham algebraic geometry seminar\n\n\
nAbstract\nAutomorphism groups of smooth hypersurfaces in projective space
are well studied in algebraic geometry. In this talk\, I'll work in the
more general setting of automorphism groups of quasismooth hypersurfaces i
n weighted projective space and consider the following questions: when are
these groups linear? When are they finite\, and if finite\, how large ca
n they get? What does the automorphism group of a very general hypersurfa
ce with given weights and degree look like? In each case\, I'll generaliz
e analogous results for ordinary projective hypersurfaces and explain how
unexpected behavior appears in the weighted setting.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aline Zanardini (Leiden)
DTSTART:20230427T090000Z
DTEND:20230427T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/143
DESCRIPTION:Title: Pencils of plane cubics revisited\nby Aline Zanardini (Leide
n) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\n
In recent joint work with M. Hattori we have considered the problem of cla
ssifying linear systems of hypersurfaces (of a fixed degree) in some proje
ctive space up to projective equivalence via geometric invariant theory (G
IT). And we have obtained a complete and explicit stability criterion. In
this talk I will explain how this criterion can be used to recover Miranda
’s description of the GIT stability of pencils of plane cubics.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Bates (US Naval Academy)
DTSTART:20230511T140000Z
DTEND:20230511T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/144
DESCRIPTION:Title: Numerical methods for working with polynomial systems\nby Da
niel Bates (US Naval Academy) as part of Online Nottingham algebraic geome
try seminar\n\n\nAbstract\nWhether testing conjectures in algebraic geomet
ry or trying to solve polynomial systems for some application\, numerical
methods are sometimes a useful alternative to well-known symbolic algorith
ms. This talk is intended to introduce some of the main tools of the field
of numerical algebraic geometry\, including homotopy continuation and the
numerical irreducible decomposition. In particular\, given a polynomial s
ystem\, we will see how numerical methods can provide floating point appro
ximations to points on each irreducible component of the corresponding com
plex variety. We will also visit a few recent uses of these methods and co
nsider the benefits and drawbacks compared to exact\, symbolic methods.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Trusiani (Toulouse)
DTSTART:20230518T090000Z
DTEND:20230518T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/145
DESCRIPTION:Title: A relative Yau-Tian-Donaldson conjecture and stability threshold
s\nby Antonio Trusiani (Toulouse) as part of Online Nottingham algebra
ic geometry seminar\n\n\nAbstract\nOn a Fano variety\, the Yau–Tian–Do
naldson correspondence connects the existence of Kähler–Einstein metric
s to an algebro-geometric notion called $K$-stability. In the last decade\
, the latter has proved to be very valuable in Algebraic Geometry: for ins
tance\, it is used for the construction of moduli spaces. In the first par
t of the talk\, partly motivated by the study of Kähler–Einstein metric
s with prescribed singularities\, a new relative $K$-stability notion will
be introduced for a fixed smooth Fano variety. A particular focus will be
given to motivations and intuitions\, making a comparison with the log $K
$-stability/log Kähler–Einstein metrics. The relative $K$-stability and
the Kähler–Einstein metrics with prescribed singularities will then be
related to each other through a Yau–Tian–Donaldson correspondence\, w
hich will be the core of the talk. An important role will be played by alg
ebro-geometric valuative criteria\, which will be also used to link the re
lative $K$-stability to the genuine $K$-stability.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fei Si (BICMR)
DTSTART:20230601T090000Z
DTEND:20230601T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/146
DESCRIPTION:Title: K-moduli space of del Pezzo surface pairs\nby Fei Si (BICMR)
as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nA
K3 surfaces with anti-symplectic involution can be identified with a pair
$(X\,C)$ consisting of a del Pezzo surface $X$ with a curve $C \\sim −2K
_X$. Their moduli space has many compactifications from various perspectiv
es. In this talk\, we will discuss the compactifications from $K$-moduli t
heoretic side and its relation to Baily-Borel compactification from Hodge
theoretic side. In particular\, we will give an explicit description of $K
$-moduli space $P_c^K$ parametrizing $K$-polystable del Pezzo pairs $(X\,c
C)$ under the framework of wall-crossing for $K$-moduli space due to Asche
r-DeVleming-Liu. Moreover\, we will show the $K$-moduli space $P_c^K$ is i
somorphic to certain log canonical model on Baily-Borel compactification o
f the moduli space of K3 surfaces with anti-symplectic involution. This ca
n be viewed as another example of Hassett-Keel-Looijenga program proposed
by Laza-O'Grady. This is based on joint work with Long Pan and Haoyu Wu.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kelly Jabbusch (Michigan)
DTSTART:20230525T140000Z
DTEND:20230525T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/147
DESCRIPTION:Title: The minimal projective bundle dimension and toric 2-Fano manifol
ds\nby Kelly Jabbusch (Michigan) as part of Online Nottingham algebrai
c geometry seminar\n\n\nAbstract\nIn this talk we will discuss higher Fano
manifolds\, which are Fano manifolds with positive higher Chern character
s. In particular we will focus on toric 2-Fano manifolds. Motivated by the
problem of classifying toric 2-Fano manifolds\, we will introduce a new i
nvariant for smooth projective toric varieties\, the minimal projective bu
ndle dimension\, $m(X)$. This invariant $m(X)$ captures the minimal degree
of a dominating family of rational curves on $X$ or\, equivalently\, the
minimal length of a centrally symmetric primitive relation for the fan of
$X$. We'll present a classification of smooth projective toric varieties w
ith $m(X) \\ge \\dim(X)-2$\, and show that projective spaces are the only
2-Fano manifolds among smooth projective toric varieties with $m(X)$ equal
to $1$\, $\\dim(X)-2$\, $\\dim(X)-1$\, or $\\dim(X)$. This is joint work
with Carolina Araujo\, Roya Beheshti\, Ana-Maria Castravet\, Svetlana Maka
rova\, Enrica Mazzon\, and Nivedita Viswanathan.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yalong Cao (RIKEN)
DTSTART:20230831T100000Z
DTEND:20230831T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/148
DESCRIPTION:Title: From curve counting on Calabi-Yau 4-folds to quasimaps for quive
rs with potentials\nby Yalong Cao (RIKEN) as part of Online Nottingham
algebraic geometry seminar\n\n\nAbstract\nI will start by reviewing an ol
d joint work with Davesh Maulik and Yukinobu Toda on relating Gromov-Witte
n\, Gopakumar-Vafa (in the sense of Klemm-Pandharipande) and stable pair i
nvariants on compact Calabi-Yau 4-folds. For non-compact CY4 like local cu
rves\, similar invariants can be studied via the perspective of quasimaps
to quivers with potentials. In a recent joint work with Gufang Zhao\, we d
efine a virtual count for such quasimaps and prove a gluing formula. Compu
tations of examples will also be discussed.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Esterov (LIMS)
DTSTART:20230622T090000Z
DTEND:20230622T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/149
DESCRIPTION:Title: Bernstein-Kouchnirenko-Khovanskii with a symmetry\nby Alexan
der Esterov (LIMS) as part of Online Nottingham algebraic geometry seminar
\n\n\nAbstract\nA generic polynomial $f(x\,y\,z)$ with a prescribed Newton
polytope defines a symmetric spatial curve $f(x\,y\,z)=f(y\,x\,z)=0$. We
shall study its geometry\, and classify the Newton polytopes for which thi
s geometry is exceptional. As a motivating application\, we shall classify
generic one-parameter families of complex univariate polynomials\, whose
Galois group differs from the complete symmetric group. We shall see how s
ome of these results conjecturally extend to higher dimensions and more co
mplicated symmetries. This is based on joint work with Lionel Lang.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junyan Zhao (Illinois)
DTSTART:20230713T140000Z
DTEND:20230713T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/150
DESCRIPTION:Title: Moduli of curves of genus 6 and K-stability\nby Junyan Zhao
(Illinois) as part of Online Nottingham algebraic geometry seminar\n\n\nAb
stract\nIn this talk\, I will describe a way to study moduli of curves of
small genus (eg. $g=3\,4\,6$) via $K$-stability. For instance\, a general
curve $C$ of genus $6$ can be embedded into the unique quintic del Pezzo
surface $X_5$ as a divisor of class $-2K_{X_5}$. Thus the $K$-moduli space
s of the pair $(X_5\, cC)$ are birational to the moduli of DM-stable curve
s $\\bar{M}_6$. On the other hand\, $X_5$ can be embedded in $\\mathbb{P}^
1 \\times\\mathbb{P}^2$ as a divisor of class $\\mathcal{O}(1\,2)$\, under
which $-2K_X$ is linearly equivalent to $\\mathcal{O}_X(2\,2)$. One can s
tudy the VGIT-moduli spaces in this setting. In this talk\, I will compar
e these various compactifications of moduli spaces.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Suzuki (São Paulo)
DTSTART:20230706T140000Z
DTEND:20230706T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/151
DESCRIPTION:Title: Birationally equivalent Landau-Ginzburg models on cotangent bund
les and adjoint orbits\nby Bruno Suzuki (São Paulo) as part of Online
Nottingham algebraic geometry seminar\n\n\nAbstract\nWe show that the Lie
potential on the minimal semisimple adjoint orbit of $\\mathfrak{sl}(n+1\
,\\mathbb{C})$ coincides with toric potential on the cotangent bundle of $
\\mathbb{P}^{n}$. We then study the corresponding Landau-Ginzburg models i
n deformation families and give some examples of how the deformations aff
ect the mirrors.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Massarenti (Ferrara)
DTSTART:20230803T140000Z
DTEND:20230803T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/152
DESCRIPTION:Title: On the (uni)rationality problem for quadric bundles and hypersur
faces\nby Alex Massarenti (Ferrara) as part of Online Nottingham algeb
raic geometry seminar\n\n\nAbstract\nA variety $X$ over a field is unirati
onal if there is a dominant rational map from a projective space to $X$. W
e will discuss the unirationality problem for quartic hypersurfaces and qu
adric bundles over a arbitrary field in the the perspective of the relatio
n between unirationality and rational connectedness. We will prove unirati
onality of quadric bundles under certain positivity assumptions on their a
nti-canonical divisor. As a consequence we will get the unirationality of
any smooth 4-fold quadric bundle over the projective plane\, over an algeb
raically closed field\, and with discriminant of degree at most 12.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nawaz Sultani (Michigan)
DTSTART:20230810T090000Z
DTEND:20230810T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/153
DESCRIPTION:Title: Gromov-Witten theory of Non-Convex Complete Intersections\nb
y Nawaz Sultani (Michigan) as part of Online Nottingham algebraic geometry
seminar\n\n\nAbstract\nFor a convex complete intersection $X$\, the Quant
um Lefshetz Hyperplane theorem (QLHT) relates the Gromov-Witten (GW) invar
iants of $X$ to those of the ambient space. This is most notably used in t
he proof of genus 0 mirror symmetry for complete intersections in toric va
rieties\, since the invariants of the ambient toric variety are easier to
compute. However\, orbifold complete intersections are rarely convex\, hen
ce QLHT often fails even in genus 0. In this talk\, I will showcase a meth
od to compute the genus 0 GW invariants for orbifold complete intersection
s in stack quotients of the form $[V /\\!\\!/ G]$\, regardless of convexit
y conditions. The invariants computed by this method include all the invar
iants one expects of QLHT\, even when QLHT fails. This talk will include r
esults from joint works with Felix Janda (Notre Dame) and Yang Zhou (Fudan
)\, and with Rachel Webb (Berkeley).\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Livia Campo (KIAS)
DTSTART:20230824T090000Z
DTEND:20230824T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/154
DESCRIPTION:Title: Flags on Fano 3-fold hypersurfaces\nby Livia Campo (KIAS) as
part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nThe e
xistence of Kaehler-Einstein metrics on Fano 3-folds can be determined by
studying some positive numbers called stability thresholds. K-stability is
ensured if appropriate bounds can be found for these thresholds. An effec
tive way to verify such bounds is to construct flags of point-curve-surfac
e inside the Fano 3-folds. This approach was initiated by Abban-Zhuang\, a
nd allows us to restrict the computation of bounds for stability threshold
s only on flags. We employ this machinery to prove K-stability of terminal
quasi-smooth Fano 3-fold hypersurfaces. Many of these varieties had been
attacked by Kim-Okada-Won using log canonical thresholds. In this talk I w
ill tackle the remaining Fano hypersurfaces via Abban-Zhuang Theory.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/154/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andres Fernandez Herrero (Columbia)
DTSTART:20230727T090000Z
DTEND:20230727T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/155
DESCRIPTION:Title: Harder-Narasimhan theory for gauged maps\nby Andres Fernande
z Herrero (Columbia) as part of Online Nottingham algebraic geometry semin
ar\n\n\nAbstract\nIn this talk\, I will discuss recent techniques develope
d to construct moduli spaces of decorated principal bundles on a fixed com
pact Riemann surface. Using these techniques\, we construct a Harder-Naras
imhan stratification\, which can be used to obtain a generalization of the
Verlinde formula in the context of decorated principal bundles. This talk
is based on joint work with Daniel Halpern-Leistner.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/155/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mauro Porta (Strasbourg)
DTSTART:20230907T090000Z
DTEND:20230907T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/156
DESCRIPTION:Title: Categorified Beauville-Laszlo theorem (and related problems)
\nby Mauro Porta (Strasbourg) as part of Online Nottingham algebraic geome
try seminar\n\n\nAbstract\nSheaves of Azumaya algebras were introduced by
Grothendieck to represent classes in the cohomological Brauer group of sch
emes\, i.e. $Br(X) := H^2_{\\text{\\'et}}(X\;G_m)$\, along the same lines
every class in $H^1_{\\text{\\'et}}(X\;G_m)$ is representable by a line bu
ndle on $X$. However\, it turns out that not every class in $Br(X)$ can be
represented by a sheaf of Azumaya algebras\, as shown in the case of Mumf
ord's normal surface. In much more recent times\, Toën introduced the not
ion of sheaf of derived Azumaya algebra\, and proved that these objects re
present even non-torsion classes in $Br(X)$. In collaboration with Federic
o Binda we studied two problems related to derived Azumaya algebras: the G
rothendieck existence and the Beauville-Laszlo theorems. In this talk\, I
will survey both questions and explain how our categorified approach allow
s to go beyond a classical injectivity result of Grothendieck. I will fini
sh with a brief discussion of the consequences of categorified Beauville-L
aszlo that will be the object of a future work.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/156/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sokratis Zikas (Poitiers)
DTSTART:20230720T090000Z
DTEND:20230720T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/157
DESCRIPTION:Title: On connected algebraic subgroups of groups of birational transfo
rmations\nby Sokratis Zikas (Poitiers) as part of Online Nottingham al
gebraic geometry seminar\n\n\nAbstract\nThe problem of understanding the s
tructure of the group of birational transformations $\\mathrm{Bir}(X)$ of
a projective variety $X$ is an old one\, with early results dating all the
way back to the 19th century. In general $\\mathrm{Bir}(X)$ does not admi
t the structure of an algebraic group\; however one may study algebraic su
bgroups of it and how they relate to one another. In the last decade there
has been a resurgence of results in this area\, mainly due to the use of
the modern machinery of the Minimal Model Program and the Sarkisov Program
. In this talk I will present this modern framework as well as various res
ults around the study of algebraic subgroups of $\\mathrm{Bir}(X)$ for a M
ori fiber space $X$.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/157/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Ovcharenko (Steklov)
DTSTART:20230928T140000Z
DTEND:20230928T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/158
DESCRIPTION:Title: Modularity of Landau-Ginzburg models\nby Mikhail Ovcharenko
(Steklov) as part of Online Nottingham algebraic geometry seminar\n\n\nAbs
tract\nIn the past decades\, there were proposed many different inter-rela
ted approaches to Mirror Symmetry for Fano varieties. The goal of this tal
k is to show that in the case of Fano threefolds these approaches are in h
armony with each other. General anticanonical sections of a Fano threefold
and general fibres of its Landau-Ginbzurg model are K3 surfaces\, so it i
s natural to consider Mirror Symmetry for K3 surfaces as well. One of its
most interesting forms is so called Dolgachev-Nikulin duality: for a latti
ce $L$ it corresponds to a complete family of $L$-polarized K3 surfaces a
complete family of $L^*$-polarized K3 surfaces\, where $L^*$ is a dual lat
tice. For any smooth Fano threefold $X$ we show that the polarization of i
ts general anticanonical section by $\\mathrm{Pic}(X)$ is Dolgachev-Nikuli
n dual to the polarization of a general fibre $F$ of its tame compactified
toric Landau-Ginzburg model $Z\\rightarrow\\mathbb{P}^1$ by the (explicit
ly constructed) lattice of monodromy invariants. Moreover\, if the antican
onical class of $X$ is very ample\, we prove that the deformation space of
pairs $(Z\, F)$ form a complete family of $\\mathrm{Pic}(X)^*$-polarized
K3 surfaces. As a consequence\, we obtain that for any such Fano threefold
$X$ the corresponding moduli space of $\\mathrm{Pic}(X)^*$-polarized K3 s
urfaces is uniruled. This is a joint work with Charles Doran\, Andrew Hard
er\, Ludmil Katzarkov\, and Victor Przyjalkowski.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/158/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deniz Genlik (Ohio)
DTSTART:20230914T140000Z
DTEND:20230914T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/159
DESCRIPTION:Title: Higher genus Gromov-Witten theory of C^n/Z_n: Holomorphic anomal
y equations and crepant resolution\nby Deniz Genlik (Ohio) as part of
Online Nottingham algebraic geometry seminar\n\n\nAbstract\nIn this talk\,
we present certain results regarding the higher genus Gromov-Witten theor
y of $\\mathbb{C}^n/\\mathbb{Z}_n$ obtained by studying its cohomological
field theory structure in detail. Holomorphic anomaly equations are certai
n recursive partial differential equations predicted by physicists for the
Gromov-Witten potential of a Calabi-Yau threefold. We prove holomorphic a
nomaly equations for $\\mathbb{C}^n/\\mathbb{Z}_n$ for any $n\\ge3$. In ot
her words\, we present a phenomenon of holomorphic anomaly equations in ar
bitrary dimensions\, a result beyond the consideration of physicists. The
proof of this fact relies on showing that the Gromov-Witten potential of $
\\mathbb{C}^n/\\mathbb{Z}_n$ lies in a certain polynomial ring. Moreover\,
we prove an arbitrary genera crepant resolution correspondence for $\\mat
hbb{C}^n/\\mathbb{Z}_n$ by showing that its cohomological field theory mat
ches with that of $K\\mathbb{P}^{n-1}$\, where $K\\mathbb{P}^{n-1}$ is the
total space of the canonical bundle of $\\mathbb{P}^{n-1}$. More precisel
y\, we show that the Gromov-Witten potential of $K\\mathbb{P}^{n-1}$ also
lies in a similar polynomial ring\, and we show that it matches with the G
romov-Witten potential of $\\mathbb{C}^n/\\mathbb{Z}_n$ under an isomorphi
sm of these polynomial rings. This talk is based on the joint works arXiv:
2301.08389 and arXiv:2308.00780 with Hsian-Hua Tseng.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/159/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nawaz Sultani (Michigan)
DTSTART:20231005T140000Z
DTEND:20231005T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/160
DESCRIPTION:Title: Gromov-Witten theory of non-convex complete intersections\nb
y Nawaz Sultani (Michigan) as part of Online Nottingham algebraic geometry
seminar\n\n\nAbstract\nFor a convex complete intersection $X$\, the Quant
um Lefshetz Hyperplane theorem (QLHT) relates the Gromov-Witten (GW) invar
iants of $X$ to those of the ambient space. This is most notably used in t
he proof of genus $0$ mirror symmetry for complete intersections in toric
varieties\, since the invariants of the ambient toric variety are easier t
o compute. However\, orbifold complete intersections are rarely convex\, h
ence QLHT often fails even in genus $0$. In this talk\, I will showcase a
method to compute the genus $0$ GW invariants for orbifold complete inters
ections in stack quotients of the form $[V/\\!\\!/G]$\, regardless of conv
exity conditions. The invariants computed by this method include all the i
nvariants one expects of QLHT\, even when QLHT fails. This talk will inclu
de results from joint works with Felix Janda (Notre Dame) and Yang Zhou (F
udan)\, and with Rachel Webb (Berkeley).\n\n(Note: This is a repeat of Naw
az's talk on 10 August\, which had to be abandoned part-way through due to
severe weather causing technical issues.)\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/160/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lena Ji (Michigan)
DTSTART:20231110T150000Z
DTEND:20231110T160000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/161
DESCRIPTION:Title: Symmetries of Fano varieties\nby Lena Ji (Michigan) as part
of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nProkhorov a
nd Shramov showed that the BAB conjecture (later proven by Birkar) implies
the Jordan property for automorphism groups of complex Fano varieties. Th
is property in particular gives an upper bound on the size of semisimple g
roups acting faithfully on $n$-dimensional complex Fano varieties\, and th
is bound only depends on $n$. We investigate the geometric consequences of
an action by a large semisimple group - in particular the symmetric group
. We give an effective upper bound on the size of these symmetric group ac
tions\, and we obtain optimal bounds for certain classes of varieties (tor
ic varieties and Fano weighted complete intersections). Finally\, we draw
a connection between large symmetric actions and boundedness of varieties\
, by showing that the maximally symmetric Fano fourfolds form a bounded fa
mily. This work is joint with Louis Esser and Joaquín Moraga.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/161/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodoros Papazachariou (Glasgow)
DTSTART:20230921T090000Z
DTEND:20230921T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/162
DESCRIPTION:Title: On divisorial stability of finite covers\nby Theodoros Papaz
achariou (Glasgow) as part of Online Nottingham algebraic geometry seminar
\n\n\nAbstract\nDivisorial stability of a polarised variety is a stronger
- but conjecturally equivalent - variant of uniform K-stability introduced
by Boucksom-Jonsson. Whereas uniform K-stability is defined in terms of t
est configurations\, divisorial stability is defined in terms of convex co
mbinations of divisorial valuations on the variety. In this talk\, I will
give a quick account on divisorial stability\, and then I will describe th
e behaviour of divisorial stability under finite group actions. In particu
lar\, I will show that equivariant divisorial stability of a polarised var
iety is equivalent to log divisorial stability of its quotient. I will the
n use this result to give a general construction of equivariantly divisori
ally stable polarised varieties. This is joint work with R. Dervan.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/162/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuchen Liu (Courant Institute)
DTSTART:20231012T140000Z
DTEND:20231012T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/163
DESCRIPTION:Title: Moduli of boundary polarized Calabi-Yau pairs\nby Yuchen Liu
(Courant Institute) as part of Online Nottingham algebraic geometry semin
ar\n\n\nAbstract\nWhile the theories of KSBA stability and K-stability hav
e been successful in constructing compact moduli spaces of canonically pol
arized varieties and Fano varieties\, respectively\, the case of Calabi-Ya
u varieties remains less well understood. I will discuss a new approach to
this problem in the case of boundary polarized Calabi-Yau pairs $(X\,D)$\
, i.e. $X$ is a Fano variety and $D$ is an anticanonical $\\mathbb{Q}$-div
isor\, in which we consider all semi-log-canonical degenerations. One chal
lenge of this approach is that the moduli stack can be unbounded. Neverthe
less\, if we consider boundary polarized Calabi-Yau pairs as degenerations
of $\\mathbb{P}^2$ with plane curves\, we show that there exists a projec
tive good moduli space despite the unboundedness. This is joint work with
K. Ascher\, D. Bejleri\, H. Blum\, K. DeVleming\, G. Inchiostro\, and X. W
ang.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/163/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Lian (Tufts)
DTSTART:20231019T140000Z
DTEND:20231019T150000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/164
DESCRIPTION:Title: Counting curves on P^r\nby Carl Lian (Tufts) as part of Onli
ne Nottingham algebraic geometry seminar\n\n\nAbstract\nWe will explain a
complete solution to the following problem. If $(C\,p_1\,\\ldots\,p_n)$ is
a general curve of genus $g$ and $x_1\,\\ldots\,x_n$ are general points o
n $\\mathbb{P}^r$\, then how many degree $d$ maps $f:C\\to\\mathbb{P}^r$ a
re there with $f(p_i)=x_i$? These are the "Tevelev degrees" of projective
space\, which were previously known only when $r=1$\, when $d$ is large co
mpared to $g$\, or virtually in Gromov-Witten theory. Time-permitting\, we
will also discuss some partial results when the conditions $f(p_i)=x_i$ a
re replaced by conditions $f(p_i) \\in X_i$\, where the $X_i$ are linear s
paces of any dimension.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/164/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathlén Kohn (KTH)
DTSTART:20231026T090000Z
DTEND:20231026T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/165
DESCRIPTION:Title: Rolling-shutter cameras & Kummer's classification of order-one l
ine congruences\nby Kathlén Kohn (KTH) as part of Online Nottingham a
lgebraic geometry seminar\n\n\nAbstract\nIn this talk\, we explain how alg
ebraic geometry can be used to model and understand rolling-shutter camera
s. Most consumer cameras today (e.g. in smartphones) use rolling shutters
that do not capture an image at the same time but rather scan rapidly acro
ss the scene to be captured. When such a camera moves and rotates\, the re
sulting picture can show the same 3D point several times\, and straight li
nes in 3-space become higher-degree curves on the image. The set of light
rays through such a camera form an algebraic surface in the Grassmannian o
f lines in projective 3-space. Kummer classified such surfaces (classicall
y called line congruence) of order-one in 1866. We explain how Kummer's cl
assification essentially characterizes all rolling-shutter cameras that se
e a generic 3D point exactly once. When such a camera takes a picture of a
line in 3-space\, the image is a high-degree curve. We compute that degre
e D in terms of the movement and rotation of the camera\, and show that th
e image curve has multiplicity D-1 at one special point on the image plane
. This talk is based on ongoing work with Marvin Hahn\, Orlando Marigliano
\, and Tomas Pajdla.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/165/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haidong Liu (Sun Yat-sen)
DTSTART:20231207T100000Z
DTEND:20231207T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/166
DESCRIPTION:Title: On Miyaoka type and Kawamata-Miyaoka type inequalities\nby H
aidong Liu (Sun Yat-sen) as part of Online Nottingham algebraic geometry s
eminar\n\n\nAbstract\nIn the classification theory of varieties with nef a
nti-canonical divisors\, Miyaoka type and Kawamata-Miyaoka type inequaliti
es which concern about the relations between the first and second Chern cl
asses play an important role. In this talk\, I will show some recent progr
ess on these inequalities and their application on the classification of 3
-folds with nef anti-canonical divisors. Part of these works is jointed wi
th Masataka Iwai and Chen Jiang\, and part is jointed with Jie Liu.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/166/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chengxi Wang (UCLA)
DTSTART:20231116T160000Z
DTEND:20231116T170000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/167
DESCRIPTION:Title: Fano varieties with extreme behavior\nby Chengxi Wang (UCLA)
as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nIt
is attractive to classify Fano varieties with various types of singularit
ies that originated from the minimal model program. For a Fano variety\, t
he Fano index is the largest integer $m$ such that the anti-canonical divi
sor is $\\mathbb{Q}$-linearly equivalent to m times some Weil divisor. For
Fano varieties of various singularities\, I show the Fano indexes can gro
w double exponentially with respect to the dimension. Those examples are a
lso conjecturally optimal and have a close connection with Calabi-Yau vari
eties of extreme behavior.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/167/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thibaut Delcroix (Montpellier)
DTSTART:20231123T150000Z
DTEND:20231123T160000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/168
DESCRIPTION:Title: Fano spherical varieties of small dimension and rank\nby Thi
baut Delcroix (Montpellier) as part of Online Nottingham algebraic geometr
y seminar\n\n\nAbstract\nA spherical variety $(X\,G)$ is a normal complex
algebraic variety $X$ equipped with the action of a connected complex redu
ctive group $G$ such that a Borel subgroup $B$ of $G$ acts with an open de
nse orbit. The rank of $(X\,G)$ is the rank of the lattice of $B$-eigenval
ues in the $B$-module of rational functions on $X$. I will present the cla
ssification of the 260 locally factorial Fano spherical varieties $(X\,G)$
of dimension four and of rank two or less\, obtained in a joint work with
Pierre-Louis Montagard. Those spherical varieties are described via combi
natorial data\, from which it is easy to read off geometric properties of
the underlying variety $X$\, such as the Picard rank\, anticanonical degre
e\, K-stability\, etc.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/168/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Li (Princeton)
DTSTART:20231130T150000Z
DTEND:20231130T160000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/169
DESCRIPTION:Title: On the cone conjecture for log Calabi-Yau mirrors of Fano 3-fold
s\nby Jennifer Li (Princeton) as part of Online Nottingham algebraic g
eometry seminar\n\n\nAbstract\nLet $Y$ be a smooth projective 3-fold admit
ting a K3 fibration $f: Y \\rightarrow \\mathbb{P}^{1}$ with $-K_{Y} = f^{
\\ast} \\mathcal{O}(1)$. We show that the pseudoautomorphism group of $Y$
acts with finitely many orbits on the codimension one faces of the movable
cone if $H^{3}(Y\, \\mathbb{C}) = 0$\, confirming a special case of the K
awamata-Morrison-Totaro cone conjecture. In Coates-Corti-Galkin-Kasprzyk 2
016\, Przyjalkowski 2018\, and Cheltsov-Przyjalkowski 2018\, the authors c
onstruct log Calabi-Yau 3-folds with K3 fibrations satisfying the hypothes
es of our theorem as the mirrors of Fano 3-folds.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/169/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kimoi Kemboi (Cornell)
DTSTART:20231214T160000Z
DTEND:20231214T170000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/170
DESCRIPTION:Title: Exceptional collections and window categories\nby Kimoi Kemb
oi (Cornell) as part of Online Nottingham algebraic geometry seminar\n\n\n
Abstract\nThe derived category of a variety is a crucial algebraic invaria
nt with several profound implications on the geometry of the underlying va
riety. This talk will focus on a particular structure of derived categorie
s called a full exceptional collection. We will discuss the landscape of f
ull exceptional collections and its connections to geometry\, then explore
how to produce them for linear GIT quotients using ideas from "window" ca
tegories and equivariant geometry. As an example\, we will consider a larg
e class of linear GIT quotients by a reductive group of rank two\, where t
his machinery produces full exceptional collections consisting of tautolog
ical vector bundles. This talk is based on joint work with Daniel Halpern-
Leistner.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/170/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swaraj Sridhar Parde (Michigan)
DTSTART:20240118T160000Z
DTEND:20240118T170000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/171
DESCRIPTION:Title: A Frobenius version of Tian's alpha invariant\, and the F-signat
ure of Fano varieties\nby Swaraj Sridhar Parde (Michigan) as part of O
nline Nottingham algebraic geometry seminar\n\n\nAbstract\nThe Alpha invar
iant of a complex Fano manifold was introduced by Tian to detect its $K$-s
tability\, an algebraic condition that implies the existence of a Kähler
–Einstein metric. Demailly later reinterpreted the Alpha invariant algeb
raically in terms of a singularity invariant called the log canonical thre
shold. In this talk\, we will present an analog of the Alpha invariant for
Fano varieties in positive characteristics\, called the Frobenius-Alpha i
nvariant. This analog is obtained by replacing "log canonical threshold" w
ith "$F$-pure threshold"\, a singularity invariant defined using the Frobe
nius map. We will review the definition of these invariants and the relati
ons between them. The main theorem proves some interesting properties of t
he Frobenius-Alpha invariant\; namely\, we will show that its value is alw
ays at most $1/2$ and make connections to a version of local volume called
the $F$-signature. Time permitting\, we will also discuss the semicontinu
ity properties of the Frobenius-Alpha invariant.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/171/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Calla Tschanz (Jagiellonian)
DTSTART:20240125T100000Z
DTEND:20240125T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/172
DESCRIPTION:Title: Expansions for Hilbert schemes of points on semistable degenerat
ions\nby Calla Tschanz (Jagiellonian) as part of Online Nottingham alg
ebraic geometry seminar\n\n\nAbstract\nLet $X\\rightarrow C$ be a projecti
ve family of surfaces over a curve with smooth general fibres and simple n
ormal crossing singularity in the special fibre $X_0$. We construct a good
compactification of the moduli space of relative length $n$ zero-dimensio
nal subschemes on $X\\setminus X_0$ over $C\\setminus\\{0\\}$. In order to
produce this compactification we study expansions of the special fibre $X
_0$ together with various GIT stability conditions\, generalising the work
of Gulbrandsen-Halle-Hulek who use GIT to offer an alternative approach t
o the work of Li-Wu for Hilbert schemes of points on simple degenerations.
We construct stacks which we prove to be equivalent to the underlying sta
ck of some choices of logarithmic Hilbert schemes produced by Maulik-Ranga
nathan.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/172/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annamaria Ortu (Gothenburg)
DTSTART:20240201T100000Z
DTEND:20240201T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/173
DESCRIPTION:Title: Moduli of stable fibrations\nby Annamaria Ortu (Gothenburg)
as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nSmo
oth fibrations between projective varieties can be thought of as both a ge
neralisation of vector bundles and as a way of studying the behaviour of p
rojective varieties in families. On holomorphic vector bundles\, the Hitch
in-Kobayashi correspondence establishes an equivalence between slope-stabi
lity and the existence of canonical connections\, called Hermite-Einstein
connections. A foundational result in the theory of vector bundles is the
construction of a moduli space of stable vector bundles\; such a moduli sp
ace can also be constructed analytically through the Hitchin-Kobayashi cor
respondence. On smooth fibrations we will define an analytic stability con
dition which we use to construct a moduli space of analytically stable smo
oth fibrations.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/173/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Marquand (Courant Institute)
DTSTART:20240229T150000Z
DTEND:20240229T160000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/174
DESCRIPTION:Title: The defect of a cubic threefold\nby Lisa Marquand (Courant I
nstitute) as part of Online Nottingham algebraic geometry seminar\n\n\nAbs
tract\nThe defect of a cubic threefold with isolated singularities is a me
asure of the failure of Poincare duality\, and also the failure to be $\\m
athbb{Q}$-factorial. From the work of Cheltsov\, a cubic threefold with on
ly nodal singularities is $\\mathbb{Q}$-factorial if and only if there are
at most 5 nodes. We investigate the defect of cubic threefolds with worse
than nodal isolated singularities\, and provide a geometric method to com
pute this global invariant. One can then compute the Mixed Hodge structure
on the middle cohomology of the cubic threefold\, in terms of the defect
(a global invariant) and local invariants (Du Bois and Link invariants) de
termined by the singularity types. We then relate the defect to geometric
properties of the cubic threefold\, showing it is positive if and only if
the cubic contains a plane or a rational normal cubic scroll. The focus of
this work is to provide more insight into the existence of reducible fibe
rs for compactified intermediate jacobian fibrations associated to a smoot
h (not necessarily general) cubic fourfold. This is joint work with Sasha
Viktorova.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/174/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo da Silva (Universite Paris Saclay)
DTSTART:20240328T100000Z
DTEND:20240328T110000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/175
DESCRIPTION:Title: Log Calabi-Yau geometry and Cremona maps\nby Eduardo da Silv
a (Universite Paris Saclay) as part of Online Nottingham algebraic geometr
y seminar\n\n\nAbstract\nIn the context of algebraic geometry\, decomposit
ion and inertia groups are special subgroups of the Cremona group which pr
eserve a certain subvariety of $\\mathbb{P}^n$ as a set and pointwise\, re
spectively. These groups were and still are classic objects of study in th
e area\, with explicit descriptions in several instances. In the particula
r case where this fixed subvariety is a hypersurface of degree $n+1$\, we
have the notion of Calabi-Yau pair which allows us to use new tools to dea
l with the study of these groups and one of them is the so-called volume p
reserving Sarkisov Program. Using this approach we prove that an appropria
te algorithm of the Sarkisov Program in dimension 2 applied to an element
of the decomposition group of a nonsingular plane cubic is automatically v
olume preserving. From this\, we deduce some properties of the (volume pre
serving) Sarkisov factorization of its elements. Regarding now a 3-dimensi
onal context\, we give a description of which toric weighted blowups of a
point are volume preserving and among them\, which ones will initiate a vo
lume preserving Sarkisov link from a Calabi-Yau pair $(\\mathbb{P}^3\,D)$
of coregularity 2. In this case\, $D$ is necessarily an irreducible normal
quartic surface having canonical singularities. This last result enhances
and extends the recent works of Guerreiro and Araujo\, Corti and Massaren
ti in a log Calabi-Yau geometrical perspective\, and it is a possible star
ting point to study the decomposition group of such quartics.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/175/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Denisova (Edinburgh)
DTSTART:20240404T090000Z
DTEND:20240404T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/176
DESCRIPTION:Title: Family 3-5 and $\\delta$-invariant of polarized del Pezzo surfac
es\nby Elena Denisova (Edinburgh) as part of Online Nottingham algebra
ic geometry seminar\n\n\nAbstract\nIt is known that a smooth Fano variety
admits a Kahler Einstein metric if and only if it is K-polystable. For two
-dimensional Fano varieties (del Pezzo surfaces) Tian and Yau proved that
a smooth del Pezzo surface is K-polystable if and only if it is not a blow
up of $\\mathbb{P}^2$ in one or two points. A lot of research was done fo
r threefolds however\, not everything is known and often the problem can b
e reduced to computing $\\delta$-invariant of (possibly singular) del Pezz
o surfaces. In my talk\, I will present an explicit example of such comput
ation.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/176/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Jaramillo Puentes (Duisburg-Essen)
DTSTART:20240418T090000Z
DTEND:20240418T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/177
DESCRIPTION:Title: Examples of Enumerative Problems for Arbitrary Fields\nby An
drés Jaramillo Puentes (Duisburg-Essen) as part of Online Nottingham alge
braic geometry seminar\n\n\nAbstract\nOver the complex numbers the solutio
ns to enumerative problems are invariant: the number of solutions of a pol
ynomial equation or polynomial system\, the number of lines or curves in a
surface\, etc. Over the real numbers such invariance fails. However\, the
signed count of solutions may lead to numerical invariants: Descartes' ru
le of signs\, Poincaré-Hopf theorem\, real curve-counting invariants.\n\n
Since many of these problems have a geometric nature\, one may ask the sam
e problems for arbitrary fields. Motivic homotopy theory allows to do enum
erative geometry over an arbitrary base\, leading to additional arithmetic
and geometric information.\n\nThe goal of this talk is to illustrate a ge
neralized notion of sign that allows us to state a motivic version of clas
sical problems: the number of lines on cubic surfaces\, the Bézout theore
m\, and the curve-counting invariants.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/177/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mingchen Xia (IMJ-PRG)
DTSTART:20240509T090000Z
DTEND:20240509T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/178
DESCRIPTION:Title: Partial Okounkov bodies and toric geometry\nby Mingchen Xia
(IMJ-PRG) as part of Online Nottingham algebraic geometry seminar\n\n\nAbs
tract\nGiven a big line bundle $L$ on a projective manifold\, Lazarsfeld
–Mustată and Kaveh–Khovanskii introduced method of constructing conve
x bodies associated with $L$. These convex bodies are known as Okounkov bo
dies. When $L$ is endowed with a singular positive Hermitian metric $h$\,
I will explain how to construct smaller convex bodies from the data $(L\,h
)$. These convex bodies play important roles in the study of the singulari
ties of $h$. As an application\, I will explain a non-trivial application
in toric geometry due to Yi Yao.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/178/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inder Kaur (Glasgow)
DTSTART:20240523T090000Z
DTEND:20240523T100000Z
DTSTAMP:20260404T111244Z
UID:notts_ag/179
DESCRIPTION:Title: Examples of varieties satisfying multiplicative Chow-Kunneth dec
omposition\nby Inder Kaur (Glasgow) as part of Online Nottingham algeb
raic geometry seminar\n\n\nAbstract\nThe Chow ring of a variety encodes a
lot of information about its geometry and is the subject of many interesti
ng conjectures. A conjecture of Shen-Vial predicts that the Chow ring of a
ny hyperkaehler variety admits a multiplicative Chow-Kunneth decomposition
. I will begin by recalling some of the basic properties of the Chow ring\
, the origins of the conjecture and then discuss some of the known cases.
I will discuss in detail the case of Hilbert schemes of points on a K3 sur
face. This is joint work in progress with R. Laterveer.\n
LOCATION:https://stable.researchseminars.org/talk/notts_ag/179/
END:VEVENT
END:VCALENDAR