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BEGIN:VEVENT
SUMMARY:Ana-Maria Castravet (Université Paris-Saclay\, UVSQ)
DTSTART:20201207T130000Z
DTEND:20201207T140000Z
DTSTAMP:20260404T094702Z
UID:EDGE2020/1
DESCRIPTION:Title: Blown-up toric surfaces with non-polyhedral effective cone\nby
Ana-Maria Castravet (Université Paris-Saclay\, UVSQ) as part of EDGE 202
0 (online)\n\n\nAbstract\nI will report on recent joint work with Antonio
Laface\, Jenia Tevelev and Luca Ugaglia. We construct examples of projecti
ve toric surfaces whose blow-up at a general point has a non-polyhedral ef
fective cone\, both in characteristic 0 and in prime characteristic. As a
consequence\, we prove that the effective cone of the Grothendieck-Knudse
n moduli space of stable\, n-pointed\, rational stable curves\, is not po
lyhedral if n>=10 in characteristic 0 and in positive characteristic for
an infinite set of primes of positive density. In particular\, these modul
i spaces are not Mori dream spaces even in positive characteristic.\n
LOCATION:https://stable.researchseminars.org/talk/EDGE2020/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruadhaí Dervan (University of Cambridge)
DTSTART:20201207T141500Z
DTEND:20201207T151500Z
DTSTAMP:20260404T094702Z
UID:EDGE2020/2
DESCRIPTION:Title: The complex geometry of Bridgeland stability conditions\nby Ru
adhaí Dervan (University of Cambridge) as part of EDGE 2020 (online)\n\n\
nAbstract\nI will discuss geometric partial differential equations on holo
morphic vector bundles that one can associate to Bridgeland stability cond
itions. The setup can be seen as a generalisation of the Hitchin-Kobayashi
correspondence\, which relates slope stability of vector bundles with the
existence of Hermite-Einstein metrics. I will then describe some foundati
onal results concerning these new equations. The algebraic geometry involv
ed will be light on technicalities\; triangulated categories will not appe
ar. This is joint work with John McCarthy and Lars Sektnan.\n
LOCATION:https://stable.researchseminars.org/talk/EDGE2020/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenyang Xu (Princeton University)
DTSTART:20201207T153000Z
DTEND:20201207T163000Z
DTSTAMP:20260404T094702Z
UID:EDGE2020/3
DESCRIPTION:Title: On positivity of the CM line bundle\nby Chenyang Xu (Princeton
University) as part of EDGE 2020 (online)\n\n\nAbstract\n(Joint with Ziqu
an Zhuang) The K-moduli which parametrizes K-polystable Fano varieties is
conjecturally to be projective. In this talk\, I will discuss the result w
e obtained for the positivity of the CM line bundle on the K-moduli. In pa
rticular\, it implies the (proper) component parametrizing smoothable K-po
lystable Fano varieties is projective.\n
LOCATION:https://stable.researchseminars.org/talk/EDGE2020/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nivedita Viswanathan (University of Edinburgh)
DTSTART:20201208T130000Z
DTEND:20201208T140000Z
DTSTAMP:20260404T094702Z
UID:EDGE2020/4
DESCRIPTION:Title: On K-stability of some singular del Pezzo surfaces\nby Nivedit
a Viswanathan (University of Edinburgh) as part of EDGE 2020 (online)\n\n\
nAbstract\nThere has been a lot of development recently in understanding t
he existence of Kahler-Einstein metrics on Fano manifolds due to the Yau-T
ian-Donaldson conjecture\, which gives us a way of looking at this problem
in terms of the notion of K-stability. In particular\, this problem is so
lved in totality for smooth del Pezzo surfaces by Tian. For del Pezzo surf
aces with quotient singularities\, there are partial results. In this talk
\, we will consider singular del Pezzo surfaces which are quasi-smooth\, w
ell-formed hypersurfaces in weighted projective space\, and understand wha
t 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/EDGE2020/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolina Araujo (IMPA)
DTSTART:20201208T141500Z
DTEND:20201208T151500Z
DTSTAMP:20260404T094702Z
UID:EDGE2020/5
DESCRIPTION:Title: Birational geometry of Calabi-Yau pairs and 3-dimensional Cremona
transformations\nby Carolina Araujo (IMPA) as part of EDGE 2020 (onlin
e)\n\n\nAbstract\nRecently\, Oguiso addressed the following question\, att
ributed to Gizatullin: ``Which automorphisms of a smooth quartic K3 surfac
e $D\\subset \\mathbb{P}^3$ are induced by Cremona transformations of the
ambient space $\\mathbb{P}^3$?'' When $D\\subset \\mathbb{P}^3$ is a quar
tic surface\, $(\\mathbb{P}^3\,D)$ is an example of a \\emph{Calabi-Yau pa
ir}\, that is\, a pair $(X\,D)$\, consisting of a normal projective variet
y $X$ and an effective Weil divisor $D$ on $X$ such that $K_X+D\\sim 0$. G
izatullin's question is about birational properties of the Calabi-Yau pair
$(\\mathbb{P}^3\,D)$. In this talk\, I will explain a general framework t
o study the birational geometry of mildly singular Calabi-Yau pairs. Then
I will focus on the case of singular quartic surfaces $D\\subset \\mathbb{
P}^3$. Our results illustrate how the appearance of increasingly worse sin
gularities in $D$ enriches the birational geometry of the pair $(\\mathbb{
P}^3\, D)$\, and lead to interesting subgroups of the Cremona group of $\\
mathbb{P}^3$. This is joint work with Alessio Corti and Alex Massarenti.\n
LOCATION:https://stable.researchseminars.org/talk/EDGE2020/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Constantin Shramov (Higher School of Economics)
DTSTART:20201208T153000Z
DTEND:20201208T163000Z
DTSTAMP:20260404T094702Z
UID:EDGE2020/6
DESCRIPTION:Title: Birational automorphisms of Severi-Brauer surfaces.\nby Consta
ntin Shramov (Higher School of Economics) as part of EDGE 2020 (online)\n\
n\nAbstract\nIn 2009\, I.Dolgachev and V.Iskovskikh classified finite subg
roups of the birational automorphism groups of the projective plane over a
n algebraically closed field of characteristic zero. I will explain an ana
log of their result for birational automorphism groups of Severi-Brauer su
rfaces\, i.e.\, surfaces that become isomorphic to the projective plane af
ter passing to the algebraic closure of the base field. The classification
is obtained by using geometric techniques based on the Minimal Model Prog
ram together with some theory of central simple algebras.\n
LOCATION:https://stable.researchseminars.org/talk/EDGE2020/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Hoskins (Radboud University Nijmegen)
DTSTART:20201209T130000Z
DTEND:20201209T140000Z
DTSTAMP:20260404T094702Z
UID:EDGE2020/7
DESCRIPTION:Title: Constructing new moduli space via non-reductive geometric invarian
t theory\nby Victoria Hoskins (Radboud University Nijmegen) as part of
EDGE 2020 (online)\n\n\nAbstract\nThere are some moduli problems where no
n-reductive groups naturally appear: for example\, moduli of hypersurfaces
in toric varieties\, which may have non-reductive automorphism groups\, a
nd moduli of certain unstable objects\, such as vector bundles of fixed Ha
rder-Narasimhan type\, where there is naturally a parabolic group action.
In this talk\, I will give an introduction to non-reductive GIT and explai
n how to construct quotients when the unipotent radical is 'graded' by a c
opy of the multiplicative group. I will then report on joint work in progr
ess with G. Berczi\, J. Jackson and F. Kirwan on the construction of modul
i spaces of sheaves of fixed Harder-Narasimhan type.\n
LOCATION:https://stable.researchseminars.org/talk/EDGE2020/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gergely Bérczi (Aarhus University)
DTSTART:20201209T153000Z
DTEND:20201209T163000Z
DTSTAMP:20260404T094702Z
UID:EDGE2020/8
DESCRIPTION:Title: Enumerative applications of non-reductive GIT\nby Gergely Bér
czi (Aarhus University) as part of EDGE 2020 (online)\n\n\nAbstract\nPolyn
omial reparametrisation groups form the symmetries of jets of holomorphic
curves in complex manifolds. They play central role in various classical p
roblems in geometry. I report on recent work in two\, seemingly unrelated
questions: (i) degeneracy loci of holomorphic maps between complex manifol
ds and Thom polynomials of singularities and (ii) the Green-Griffiths-Land
and Kobayashi hyperbolicity conjectures. I will explain why moduli of jet
s is a link between the two\, and how recently developed intersection theo
ry of non-reductive GIT quotients led to the proof of the polynomial Kobay
ashi conjecture\, and resulted in new formulas for Thom polynomials.\n
LOCATION:https://stable.researchseminars.org/talk/EDGE2020/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eloise Hamilton (University of Oxford)
DTSTART:20201209T141500Z
DTEND:20201209T151500Z
DTSTAMP:20260404T094702Z
UID:EDGE2020/9
DESCRIPTION:Title: Cohomology of GIT quotients\, reductive and non-reductive\nby
Eloise Hamilton (University of Oxford) as part of EDGE 2020 (online)\n\n\n
Abstract\nGeometric Invariant Theory (GIT) is a powerful tool not only for
constructing quotients in algebraic geometry\, but also for studying the
geometry of these quotients. The aim of this talk is to explain how to cal
culate the (rational) cohomology of quotients constructed on the one hand
using classical GIT\, and on the other using a recent generalisation of GI
T\, called Non-Reductive GIT. As its name suggests\, Non-Reductive GIT ena
bles the construction of quotients by a certain class of non-reductive gro
up actions. After reviewing existing methods for computing the Poincare se
ries of classical GIT quotients when the initial variety is smooth\, we wi
ll show how similar methods can be used to compute the Poincare series of
non-reductive GIT quotients.\n
LOCATION:https://stable.researchseminars.org/talk/EDGE2020/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sébastien Boucksom (École Polytechnique)
DTSTART:20201210T130000Z
DTEND:20201210T140000Z
DTSTAMP:20260404T094702Z
UID:EDGE2020/10
DESCRIPTION:Title: Non-Archimedean pluripotential theory and K-stability\nby Sé
bastien Boucksom (École Polytechnique) as part of EDGE 2020 (online)\n\n\
nAbstract\nNon-Archimedean pluripotential theory interprets test configura
tions as plurisubharmonic functions on a space of valuations\, and provide
s a powerful analytic framework to study and compare various completions o
f the set of test configurations\, phrased in terms of filtrations\, valua
tions\, etc... I will review the main features of this theory\, which is j
oint work with Mattias Jonsson.\n
LOCATION:https://stable.researchseminars.org/talk/EDGE2020/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristiano Spotti (Aarhus University)
DTSTART:20201210T141500Z
DTEND:20201210T151500Z
DTSTAMP:20260404T094702Z
UID:EDGE2020/11
DESCRIPTION:Title: On relations between K-moduli and symplectic geometry\nby Cri
stiano Spotti (Aarhus University) as part of EDGE 2020 (online)\n\n\nAbstr
act\nA natural intriguing question is the following: how much the moduli s
paces of certain polarized varieties know about the symplectic geometry of
the underneath manifold? After giving an overview\, I will discuss joint
work with T. Baier\, G. Granja and R. Sena-Dias where we investigate some
relations between the topology of the moduli spaces of certain varieties\,
of the symplectomorphism group and of the space of compatible integrable
complex structures. In particular\, using results of J. Evans\, we show th
at the space of such complex structures for monotone del Pezzo surfaces of
degree four and five is weakly homotopically contractible.\n
LOCATION:https://stable.researchseminars.org/talk/EDGE2020/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulio Codogni (Università degli Studi Tor Vergata)
DTSTART:20201210T153000Z
DTEND:20201210T163000Z
DTSTAMP:20260404T094702Z
UID:EDGE2020/12
DESCRIPTION:Title: Ample cone of KSB moduli spaces and higher dimensional slope ineq
ualities\nby Giulio Codogni (Università degli Studi Tor Vergata) as p
art of EDGE 2020 (online)\n\n\nAbstract\nI will present some quantitative
results about the ample cone of KSB moduli spaces. These results follow fr
om various higher dimensional generalizations of the Xiao-Cornalba-Harris
slope inequality. Our proofs combine some new Noether inequalities\, and a
careful study of the Harder-Narasimhan filtration of the push-forward of
the log pluri-canonical bundles. The talk is based on a work in progress j
oint with Luca Tasin and Filippo Viviani.\n
LOCATION:https://stable.researchseminars.org/talk/EDGE2020/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milena Hering (University of Edinburgh)
DTSTART:20201211T130000Z
DTEND:20201211T140000Z
DTSTAMP:20260404T094702Z
UID:EDGE2020/13
DESCRIPTION:Title: T-Stability of Toric Tangent bundles\nby Milena Hering (Unive
rsity of Edinburgh) as part of EDGE 2020 (online)\n\n\nAbstract\nIn this t
alk I will give a brief introduction to slope stability and present a comb
inatorial criterion for the tangent bundle on a polarised toric variety t
o be stable in terms of the lattice polytope corresponding to the polarisa
tion. I will then give some applications to toric surfaces and toric varie
ties of Picard rank 2. This is joint work with Benjamin Nill and Hendrik
Süss\n
LOCATION:https://stable.researchseminars.org/talk/EDGE2020/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Petracci (Freie Universität Berlin)
DTSTART:20201211T141500Z
DTEND:20201211T151500Z
DTSTAMP:20260404T094702Z
UID:EDGE2020/14
DESCRIPTION:Title: Toric geometry and singularities on K-moduli\nby Andrea Petra
cci (Freie Universität Berlin) as part of EDGE 2020 (online)\n\n\nAbstrac
t\nAn immediate consequence of Kodaira-Akizuki-Nakano vanishing is that sm
ooth Fano varieties have unobstructed deformations. The same holds for sin
gular Fano varieties with mild singularities and small dimension.\nIn this
talk I will show how to use the combinatorics of lattice polytopes to con
struct examples of K-polystable toric Fano varieties with obstructed defor
mations\, dimension at least 3\, and canonical singularities. This method
produces singularities (even reducible and non-reduced) on K-moduli stacks
and K-moduli spaces of Fano varieties.\nThis is joint work with Anne-Soph
ie Kaloghiros.\n
LOCATION:https://stable.researchseminars.org/talk/EDGE2020/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hendrik Süß (University of Manchester)
DTSTART:20201211T153000Z
DTEND:20201211T163000Z
DTSTAMP:20260404T094702Z
UID:EDGE2020/15
DESCRIPTION:Title: Beta-invariants on T-varieties\nby Hendrik Süß (University
of Manchester) as part of EDGE 2020 (online)\n\n\nAbstract\nIn my talk I a
m presenting previous results on the K-stability of T-varieties in the new
packaging of beta-invariants. The main result will be that for T-varietie
s of complexity 1 Kento Fujita's divisorial polystability is (almost) equi
valent to K-polystability. One practical implication will be that for test
ing K-polystability of such T-varieties it is sufficient to calculate beta
-invariants only for a finite number number of "special" T-invariant prime
divisors on the variety itself.\n
LOCATION:https://stable.researchseminars.org/talk/EDGE2020/15/
END:VEVENT
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