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BEGIN:VEVENT
SUMMARY:Simon K. Donaldson (Imperial / SCGP)
DTSTART:20201123T150000Z
DTEND:20201123T154500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/1
DESCRIPTION:Title: K-stability and scalar curvature\nby Simon K. Donaldson (I
mperial / SCGP) as part of VBAC Webinar Series\n\n\nAbstract\nThis will be
an overview talk about existence results in complex differential geometry
connected to the notion of K-stability. We will explain the analogies wit
h the corresponding results\, going back to Narasimhan and Seshadri\, for
holomorphic vector bundles and outline some strategies of proofs that have
been employed. We will illustrate the general with a discussion of the ca
se of toric manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenyang Xu (Princeton)
DTSTART:20201123T160000Z
DTEND:20201123T164500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/2
DESCRIPTION:Title: An algebraic construction of K-moduli space\nby Chenyang X
u (Princeton) as part of VBAC Webinar Series\n\n\nAbstract\nK-stability of
Fano varieties has become a fast developed topic in algebraic geometry. O
ne major output is the construction of moduli spaces of K-(semi\,poly)-sta
ble Fano varieties\, which resolves a number of pathological issue for fam
ilies of general Fano varieties. The purely algebraic construction is buil
t on a systematical study of K-stability using higher dimensional geometry
\, including a more comprehensive understanding of the notion of K-stabili
ty (for Fano varieties)\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (M.I.T.)
DTSTART:20210118T150000Z
DTEND:20210118T154500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/3
DESCRIPTION:Title: Cohomology of the moduli of Higgs bundles\nby Junliang She
n (M.I.T.) as part of VBAC Webinar Series\n\n\nAbstract\nThe moduli space
of Higgs bundles and Hitchin's integrable system lie at the crossroads of
mathematics physics\, representation theory\, and geometry. In this talk\,
we focus on cohomological structures of these moduli spaces from the aspe
cts of non-abelian Hodge theory\, hyper-kaehler geometry\, and mirror symm
etry. We will discuss recent progress on the P=W conjecture as well as con
nections to some other open conjectures concerning Higgs moduli spaces. Ba
sed on joint work with Mark de Cataldo and Davesh Maulik.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camilla Felisetti (U. Trento)
DTSTART:20210118T160000Z
DTEND:20210118T164500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/4
DESCRIPTION:Title: P=W conjectures for character varieties with a symplectic reso
lution\nby Camilla Felisetti (U. Trento) as part of VBAC Webinar Serie
s\n\n\nAbstract\nCharacter varieties parametrise representations of the fu
ndamental group of a curve. In general these moduli spaces are singular\,
therefore it is customary to slightly change the moduli problem and consid
er smooth analogues\, called twisted character varieties. In this setting\
, the P=W conjecture by de Cataldo\, Hausel\, and Migliorini suggests a su
rprising connection between the topology of Hitchin systems and Hodge theo
ry of character varieties. In joint work with M. Mauri we establish (and i
n some cases formulate) analogous P=W phenomena in the singular case . In
particular we show that the P=W conjecture holds for character varieties w
hich admit a symplectic resolution\, namely in genus 1 and arbitrary rank
and in genus 2 and rank 2.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frances Kirwan (Oxford Univ.)
DTSTART:20210315T150000Z
DTEND:20210315T154500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/5
DESCRIPTION:Title: Non-reductive GIT and HKKP theory\nby Frances Kirwan (Oxfo
rd Univ.) as part of VBAC Webinar Series\n\n\nAbstract\nIn a recent paper
F. Haiden\, L. Katzarkov\, M. Kontsevich and\nP. Pandit study notions of (
semi-)stability and Harder-Narasimhan\nfiltrations in polarised lattices a
nd weight filtations for modular\nlattices\, proving existence and uniquen
ess theorems in these very\ngeneral settings. The aim of this talk is to e
xplore the relationship of\ntheir theory with recent extensions of geometr
ic invariant theory to\nlinear algebraic group actions by non-reductive gr
oups with graded\nunipotent radicals.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eloise Hamilton (IMJ-PRG)
DTSTART:20210315T160000Z
DTEND:20210315T164500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/6
DESCRIPTION:Title: Cohomology of Non-Reductive GIT quotients and unstable Higgs b
undles of rank 2\nby Eloise Hamilton (IMJ-PRG) as part of VBAC Webinar
Series\n\n\nAbstract\nNon-Reductive GIT is a generalisation of GIT which
enables the construction of new moduli spaces. In particular it can be use
d to construct moduli spaces for unstable Higgs/vector bundles on a smooth
projective curve. The aim of this talk is to describe a method for comput
ing the Poincare series of Non-Reductive GIT quotients when the initial va
riety is smooth (analogous to the existing method in classical GIT)\, and
to show how it can be applied in practice in the case of unstable Higgs bu
ndles of rank 2.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kang Zuo (U. Mainz)
DTSTART:20210517T150000Z
DTEND:20210517T154500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/7
DESCRIPTION:Title: Arakelov Inequality for Families of Projective Manifolds\n
by Kang Zuo (U. Mainz) as part of VBAC Webinar Series\n\n\nAbstract\nhe Ar
akelov inequality for families of algebraic curves and abelian varieties g
oes back to the works by Arakelov-Parshin\, Faltings and Deligne (sharp fo
rm)\, and for systems of Hodge bundles is due to the works by Green-Griffi
ths-Kerr\, Jost-Zuo\, Peters\, Viehweg-Zuo. A very recent work by Biquard-
Collier-Garcia-Prada-Toledo is making a further progress on Arakelov-Milno
r inequalities.\n\nIn my talk I shall briefly report on my recent work joi
nt with Xin Lu and Jinbang Yang. We show the Arakelov inequality holds STR
ICTLY for canonical heights of families of n-folds of general type. We als
o show it is asymptotically sharp in a sense. Note that this Arakelov ineq
uality can become actually an equality for families of abelian varieties\,
in which case they are precisely Shimura families.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Collier (U.C. Riverside)
DTSTART:20210517T160000Z
DTEND:20210517T164500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/8
DESCRIPTION:Title: Maximal variations of Hodge structure and sl2-triples\nby
Brian Collier (U.C. Riverside) as part of VBAC Webinar Series\n\n\nAbstrac
t\nIn this talk we will discuss holomorphic maps from the upper half space
into certain homogeneous spaces (period domains) which are equivariant wi
th respect to a representation of the fundamental group of a closed surfac
e. Such maps arise from Higgs bundles on a Riemann surface which are fixed
points of a $\\mathbb C$* action. When the target is a hermitian symmetri
c space\, the Toledo invariant provides an integer invariant which is boun
ded in absolute value. Moreover\, representations which maximize the Toled
o invariant satisfy certain rigidity phenomena and arise from the uniformi
zing representation of the Riemann surface. We will discuss how to general
ize such an invariant for arbitrary period domains\, explain how this inva
riant is bounded and describe how the rigidity phenomena which occur when
the invariant is maximized are related to sl2 triples. This is based on jo
int work with Biquard\, Garcia-Prada and Toledo.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edward Witten (IAS\, Princeton)
DTSTART:20210705T150000Z
DTEND:20210705T160000Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/9
DESCRIPTION:Title: Quantization by Branes and Geometric Langlands\nby Edward
Witten (IAS\, Princeton) as part of VBAC Webinar Series\n\n\nAbstract\nIn
this talk\, which is based on work with D. Gaiotto\, Witten will explain a
quantum field theory perspective on recent developments in the geometric
Langlands program by P. Etinghof\, E. Frenkel and D. Kazhdan (see their pa
per https://arxiv.org/abs/1908.09677)\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Hoskins (Radboud University Nijmegen)
DTSTART:20210705T161500Z
DTEND:20210705T170000Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/10
DESCRIPTION:Title: Motives of moduli spaces of bundles on curves\nby Victori
a Hoskins (Radboud University Nijmegen) as part of VBAC Webinar Series\n\n
\nAbstract\nVarious computations of cohomological invariants of moduli spa
ces of vector bundles and Higgs bundles on curves should be both unified a
nd refined by working with motivic invariants\, which encode finer invaria
nts\, like Hodge structures on cohomology groups and also algebro-geometri
c invariants such as Chow groups. In this talk\, I will present joint work
with Lie Fu and Simon Pepin Lehalleur\, studying the rational Chow motive
s of various moduli spaces of vector bundles on curves with additional str
ucture (such as a Higgs field or parabolic structure). After a short intro
duction to Chow motives\, I will present some results which hold for bundl
es of arbitrary rank. Finally\, I will give some explicit formulas in rank
s 2 and 3.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Mistegaard (IST\, Austria)
DTSTART:20210705T171500Z
DTEND:20210705T180000Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/11
DESCRIPTION:Title: Quantization of moduli spaces and TQFT\nby William Misteg
aard (IST\, Austria) as part of VBAC Webinar Series\n\n\nAbstract\nThe Res
hetikhin-Turaev topological quantum field theory (TQFT) was motivated from
physics by Witten's work on quantum Chern-Simons. In Witten's work quanti
zation of moduli spaces of flat connections and conformal field theory (CF
T) was presented as two equivalent approaches to construct the Hilbert spa
ce associated to an oriented two-manifold. Both approaches depend a priori
on a choice of complex structure on the two-manifold\, although the topol
ogical nature of the theory suggests that the Hilbert space should be inde
pendent of this choice\, and support a projective linear action of the map
ping class group. On the CFT side this topological invariance and the exis
tence of a mapping class group action was proven by Tsuchia\, Ueno and Yam
ada. On the quantization side it was proven for some two-manifolds indepen
dently by Hitchin and Axelrod\, Della Pietra and Witten. Laszlo proved mat
hematically that the CFT approach and the quantization approach of Hitchin
are equivalent. Finally\, Andersen and Ueno have established that the CFT
representations of the mapping class groups are isomorphic to the Resheti
khin-Turaev TQFT mapping class group action. In this talk\, we will\; 1) p
artly review the above story\, 2) review how quantization was used to prov
e important results in quantum topology\, and 3) present work in progress
joint with Andersen\, which constructs the TQFT-representations of the map
ping class groups from the quantization approach in some of the remaining
(parabolic cases)\, not previously dealt with by Hitchin or Axelrod-Della
Pietra and Witten.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Schiffmann (CNRS\, Paris-Sud Orsay)
DTSTART:20210706T150000Z
DTEND:20210706T160000Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/12
DESCRIPTION:Title: Cohomological Hall algebras of curves and surfaces\nby Ol
ivier Schiffmann (CNRS\, Paris-Sud Orsay) as part of VBAC Webinar Series\n
\n\nAbstract\nWe will survey some recent developments on the computations
of various cohomological Hall algebras associated either to (smooth projec
tive) curves\, or to a pair consisting of a curve inside a smooth surface.
The latter case is related to various types of affine yangians. Based on
joint work with E. Diaconescu\, F. Sala and E. Vasserot.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Malusà (University of Toronto)
DTSTART:20210706T161500Z
DTEND:20210706T170000Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/13
DESCRIPTION:Title: A new quantisation scheme for hyperkähler manifolds with Sp(
1) symmetry\nby Alessandro Malusà (University of Toronto) as part of
VBAC Webinar Series\n\n\nAbstract\nIt is often the case\, with many (compl
ex) moduli problems\, that the resulting spaces come with hyperkähler str
uctures and symmetries that act non-trivially on the corresponding familie
s of Kähler forms\, rather than preserving them individually. This makes
it delicate to approach their quantisation\, as a preferred symplectic str
ucture may not be given or the group action to be quantised may not be sym
plectic with respect to it. The U(1)-action on the Hitchin moduli spaces i
s an example of this.\nIn an ongoing joint work with Andersen and Rembado\
, we approach this problem under the assumption that the symmetry group is
an extension of Sp(1) with a transitive action on CP^1\, identified with
the associated space of complex structures. This is the case for known exa
mples such as linear spaces\, the Taub-NUT space\, nilpotent orbits of com
plex Lie groups\, the moduli spaces of framed SU(r)-instantons on R^4\, an
d the Atiyah-Hitchin manifolds of monopoles on R^3. We propose a new hyper
kähler quantisation scheme by assuming given a smooth equivariant family
of pre-quantum line bundles\, and by defining a collection of quantum Hilb
ert spaces parametrised by CP^1. The quantisation of the symmetry group ma
y then be addressed in terms of actions on this family and compatibility w
ith naturally defined connections. These\, however\, turn out to not be fl
at in general\, even projectively\, but we obtain group of representations
on spaces of holomorphic sections of the family of Hilbert spaces\, rathe
r than flat ones\, and we therefore propose this space of holomorphic sect
ions as the relevant quantization of these SP(1)-symmetric Hyper-Kähler m
anifolds.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaime Silva (Inst. Politécnico Lisboa)
DTSTART:20210706T171500Z
DTEND:20210706T180000Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/14
DESCRIPTION:Title: Hodge and motivic structures on abelian character varieties\nby Jaime Silva (Inst. Politécnico Lisboa) as part of VBAC Webinar Ser
ies\n\n\nAbstract\nIn this talk\, I will make an overview about my work on
the mixed Hodge structures and motives of abelian character varieties.\nI
will start by giving a brief account of Hodge structures on character var
ieties\, and how those relate to the topic of non-abelian Hodge theory. Il
lustrating this topic\, I will cover my results on the mixed hodge structu
res of free abelian character varieties and how those illustrate some pred
ictions related to mirror theory.\nAfterwards\, I will talk about more rec
ent results on the motives of character varieties. In this\, I will talk a
bout our attempt to adapt our previous work on Hodge structures of finite
quotients by using a motive that allows for a suitable equivariant version
- the so-called equivariant Chow motives. This is joint work with C. Flor
entino.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (Caltech)
DTSTART:20210707T150000Z
DTEND:20210707T160000Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/15
DESCRIPTION:Title: Brane quantization of SL(2\,C) moduli spaces\nby Sergei G
ukov (Caltech) as part of VBAC Webinar Series\n\n\nAbstract\nThe problem o
f quantization of symplectic manifolds and the Fukaya category side of mir
ror symmetry start with the same input data. Therefore\, it is natural to
wonder whether the answer to the former may be contained in some form of t
he latter. The goal of this talk will be to illustrate how this approach\,
often called "brane quantization\," can help with understanding certain a
spects of the quantization of the moduli space of flat SL(2\,C) connection
s.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriele Rembado (University of Bonn)
DTSTART:20210707T161500Z
DTEND:20210707T170000Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/16
DESCRIPTION:Title: Quantisation of moduli spaces of meromorphic connections\, an
d relations with (irregular) CFT\nby Gabriele Rembado (University of B
onn) as part of VBAC Webinar Series\n\n\nAbstract\nThe geometry and quanti
sation of moduli spaces of unitary flat connections on Riemann surfaces ha
ve been widely studied in the past: as the complex structure on the surfac
e is deformed the moduli spaces assemble into a local system of symplectic
manifolds\, and Kähler quantisation turns it into a projectively flat ve
ctor bundle.\nThe complexified version brings about holomorphic connection
s and hyperkähler manifolds\, requiring new ideas in Kähler quantisation
\; deformation quantisation on the other hand has been carried out in grea
ter generality\, namely for moduli spaces of meromorphic connections with
irregular singularities.\nIn this talk we will briefly review this story a
nd phrase the singular case in the same geometric language of the nonsingu
lar one\, involving flat symplectic fibre bundles: their bases provide an
intrinsic approach to isomonodromic deformations\, and their quantisation
provides a mathematical approach to irregular singularities in the Wess-Zu
mino-Novikov-Witten model.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Du Pei (Harvard University)
DTSTART:20210707T171500Z
DTEND:20210707T180000Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/17
DESCRIPTION:Title: Verlinde Formula for PSL(2\,C) Higgs bundles\nby Du Pei (
Harvard University) as part of VBAC Webinar Series\n\n\nAbstract\nIn this
talk\, I will discuss how to obtain the Verlinde formula for G-Higgs bundl
es when G is not simply connected. I will also mention some of its applica
tions to mirror symmetry and brane quantization.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:János Kollár (Princeton University)
DTSTART:20210913T140000Z
DTEND:20210913T144500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/18
DESCRIPTION:Title: The Zariski topology\, linear systems\, and algebraic varieti
es\, I\nby János Kollár (Princeton University) as part of VBAC Webin
ar Series\n\n\nAbstract\nWe discuss the main steps of the proof that (with
a few exceptions) the Zariski topology determines an algebraic variety. I
n the first talk we explain how to detect linear equivalence using the Zar
iski topology. \n\nThen in the second talk we show that knowing the Zarisk
i topology plus linear equivalence determines the variety. The techniques
of the 2 talks will be mostly independent of each other. (joint work with
Max Lieblich and Will Sawin).\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Olsson (University of California\, Berkeley)
DTSTART:20210913T150000Z
DTEND:20210913T154500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/19
DESCRIPTION:Title: The Zariski topology\, linear systems\, and algebraic varieti
es\, II\nby Martin Olsson (University of California\, Berkeley) as par
t of VBAC Webinar Series\n\n\nAbstract\nWe discuss the main steps of the p
roof that (with a few exceptions) the Zariski topology determines an algeb
raic variety. In the first talk we explain how to detect linear equivalenc
e using the Zariski topology. \n\nThen in the second talk we show that kno
wing the Zariski topology plus linear equivalence determines the variety.
The techniques of the 2 talks will be mostly independent of each other. (j
oint work with Max Lieblich and Will Sawin).\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. Ramanan
DTSTART:20211011T140000Z
DTEND:20211011T143000Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/20
DESCRIPTION:Title: My collaborative work with Narasimhan\nby S. Ramanan as p
art of VBAC Webinar Series\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:T. R. Ramadas
DTSTART:20211011T143000Z
DTEND:20211011T150000Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/21
DESCRIPTION:Title: Narasimhan’s work on conformal blocks\nby T. R. Ramadas
as part of VBAC Webinar Series\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O. Garcia-Prada
DTSTART:20211011T151500Z
DTEND:20211011T154500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/22
DESCRIPTION:Title: The theorem of Narasimhan and Seshadri and generalizations\nby O. Garcia-Prada as part of VBAC Webinar Series\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:G. Harder
DTSTART:20211011T154500Z
DTEND:20211011T161500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/23
DESCRIPTION:Title: Why is the Tamagawa number equal to one?\nby G. Harder as
part of VBAC Webinar Series\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jensen (University of Kentucky)
DTSTART:20220124T143000Z
DTEND:20220124T151500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/24
DESCRIPTION:Title: Non-Abelian Brill-Noether Theory of Genus 13 Curves\nby D
avid Jensen (University of Kentucky) as part of VBAC Webinar Series\n\nAbs
tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Madeline Brandt (Brown University)
DTSTART:20220124T153000Z
DTEND:20220124T161500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/25
DESCRIPTION:Title: Top Weight Cohomology of A_g\nby Madeline Brandt (Brown U
niversity) as part of VBAC Webinar Series\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jochen Heinloth (Universität Duisburg-Essen)
DTSTART:20220328T130000Z
DTEND:20220328T134500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/26
DESCRIPTION:Title: Proper moduli spaces for algebraic stacks\nby Jochen Hein
loth (Universität Duisburg-Essen) as part of VBAC Webinar Series\n\n\nAbs
tract\nAs requested by the organizers\, the main aim of the talk is to set
the stage for the second talk by explaining the notions appearing in the
existence theorem for good (resp. adequate) moduli spaces obtained in join
t work with Jarod Alper and Daniel Halpern-Leistner\, which provide necess
ary and sufficient conditions for a moduli problem to admit a proper modul
i space. I will try to illustrate the notions in examples.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Damiolini (University of Pennsylvania)
DTSTART:20220328T140000Z
DTEND:20220328T144500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/27
DESCRIPTION:Title: Projectivity of moduli spaces of quiver representations\n
by Chiara Damiolini (University of Pennsylvania) as part of VBAC Webinar S
eries\n\n\nAbstract\nIn a recent work of Alper–Belmans–Bragg–Liang
–Tajakka\, the authors explore how the theory of good moduli spaces deve
loped by Alper and Alper–Halpern-Leistner–Heinloth can be used to give
an alternative proof of projectivity of the moduli space of vector bundle
s on a curve. In today's talk\, we will see that a similar approach can be
used to study projectivity of moduli spaces of representations of acyclic
quivers. Analogies and differences with respect to the case of vector bun
dles over curves will be emphasized. This is based on ongoing work with Be
lmans\, Franzen\, Hoskins\, Makarova and Tajakka.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jay Kopper (Penn State University)
DTSTART:20220516T130000Z
DTEND:20220516T134500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/28
DESCRIPTION:Title: Developments in Brill-Noether theory for surfaces\nby Jay
Kopper (Penn State University) as part of VBAC Webinar Series\n\n\nAbstra
ct\nI will discuss recent progress in Brill-Noether theory for vector bund
les on surfaces\, including "weak" Brill-Noether results describing the co
homology of general stable bundles\, positivity results about global gener
ation and ampleness\, and strong Brill-Noether results about Brill-Noether
loci in the moduli space.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Larson (Stanford University and Clay Institute)
DTSTART:20220516T140000Z
DTEND:20220516T144500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/29
DESCRIPTION:Title: Brill-Noether theory over the Hurwitz space\nby Hannah La
rson (Stanford University and Clay Institute) as part of VBAC Webinar Seri
es\n\n\nAbstract\nThe main theorems of Brill-Noether theory describe the m
aps of general curves to projective space. In particular\, for a general c
urve C\, the space of degree d maps C —> P^r is known to be irreducible
when its expected dimension is positive. However\, in nature\, curves C ar
e often encountered already equipped with a map to some projective space\,
which may force them to be special in moduli. The simplest case is when C
is general among curves of fixed gonality. For such curves\, previous wor
k has shown that the space of maps C —> P^r may have multiple components
of varying dimensions (Coppens-Martens\, Pflueger\, Jensen-Ranganathan).
In this talk\, I will discuss joint work with Eric Larson and Isabel Vogt
that explains these multiple components and proves analogs of all of the m
ain theorems of Brill-Noether theory in this setting.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marina Logares (UCM\, Madrid)
DTSTART:20220926T130000Z
DTEND:20220926T134500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/30
DESCRIPTION:Title: From e-polynomials to TQFTs\nby Marina Logares (UCM\, Mad
rid) as part of VBAC Webinar Series\n\n\nAbstract\nMathematics have always
served Physics along history of Science\, not only as a language but as a
source of ideas. The very same is true about Physics as a source of inspi
ration for mathematical discoveries. The aim of this talk is to show how c
ertain algebro-topological invariants\, e-polynomials\, of a G-character v
ariety serve to construct a TQFT and\, moreover\, how this development all
ows to easily explore more general settings for G-character varieties\, su
ch as those related with singular curves.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Azizeh Nozad (IPM\, Tehran)
DTSTART:20220926T140000Z
DTEND:20220926T144500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/31
DESCRIPTION:Title: Mixed Hodge Structures of Character Varieties of Free Groups<
/a>\nby Azizeh Nozad (IPM\, Tehran) as part of VBAC Webinar Series\n\n\nAb
stract\nWith G a complex reductive group\, let $X^rG$ denote the G-charact
er varieties of free group $F_r$ of rank r\, and $X^{irr}G \\subset X^rG$
be the locus of irreducible representation conjugacy classes. Using the st
ratification of $X^rG$ by polystable type coming from affine GIT and the c
ombinatorics of partitions\, we show that the mixed Hodge structures on th
e cohomology groups of $X^rSL_n$ and of $X^rPGL_n$ and on the compactly su
pported cohomology groups of the irreducible loci $X^{irr}SL_n$ and $X^{ir
r}PGL_n$ are isomorphic\, for any $n\,r \\in \\mathbb N$. In particular\,
this would imply their E-polynomials coincide\, settling the question rais
ed by Lawton-Muñoz. This is based on joint work with Carlos Florentino a
nd Alfonso Zamora\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Huybrechts (U. Bonn)
DTSTART:20221121T150000Z
DTEND:20221121T154500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/32
DESCRIPTION:Title: Chow groups of lines on cubic fourfolds\nby Daniel Huybre
chts (U. Bonn) as part of VBAC Webinar Series\n\n\nAbstract\nI will discus
s the Chow group of zero-cycles on the Fano\nvariety of lines in a cubic f
ourfold from the perspective of certain\ndistinguished surfaces contained
in the Fano variety. In particular the\nsurface of lines meeting a fixed l
ine will be discussed in detail. The\nfinal aim is to establish an analogu
e of results of Beauville and Voisin\nfor K3 surfaces. I will give some ba
ckground on Chow groups\, like\nBloch-Beilinson filtration and work of She
n-Vial\, Voisin and others\, and\nstress the geometry of the situation.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valeria Bertini (U. Porto)
DTSTART:20221121T160000Z
DTEND:20221121T164500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/33
DESCRIPTION:Title: Singular symplectic varieties as symplectic quotients of hype
rkähler manifolds\nby Valeria Bertini (U. Porto) as part of VBAC Webi
nar Series\n\n\nAbstract\nOne possible singular analogue of hyperkähler m
anifolds are\nirreducible symplectic varieties\, mainly arising as moduli
spaces of\nsheaves on trivial canonical surfaces and as partial resolution
of\nsymplectic quotients of hyperkähler manifolds. In this talk I will f
ocus\non the second class of examples\, especially in the case of fourfold
s. In\norder to produce new examples\, we will start from the known hyperk
ähler\nfourfolds (Hilbert schemes and generalized Kummer) and act on them
with\nnatural automorphisms\, for which a systematic analysis is possible
. This\nis the content of a work in progress with Armando Capasso\, Annali
sa\nGrossi\, Mirko Mauri and Enrica Mazzon.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolina Araujo (IMPA\, Brazil)
DTSTART:20230123T150000Z
DTEND:20230123T154500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/34
DESCRIPTION:Title: Birational geometry of Calabi-Yau pairs\nby Carolina Arau
jo (IMPA\, Brazil) as part of VBAC Webinar Series\n\n\nAbstract\nConsider
the following problem\, originally posed by Gizatullin: "Which automorphis
ms of a smooth quartic K3 surface in $\\mathbb{P}^3$ are induced by Cremon
a transformations of the ambient space?'' When $S$ is a smooth quartic su
rface in $\\mathbb{P}^3$\, the pair $(\\mathbb{P}^3\,S)$ is an example of
a Calabi-Yau pair\, that is\, a mildly singular pair $(X\,D)$ consisting o
f a normal projective variety X and an effective Weil divisor $D$ on $X$ s
uch that $K_X+D= 0$. In this talk\, I will explain a general framework to
investigate the birational geometry of Calabi-Yau pairs and how this can b
e applied to approach Gizatullin's problem. This is a joint work with Ales
sio Corti and Alex Massarenti.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Abramovich (Brown University)
DTSTART:20230123T160000Z
DTEND:20230123T164500Z
DTSTAMP:20260404T110829Z
UID:VBAC-webinar/35
DESCRIPTION:Title: The Chow ring of a weighted blowup\nby Dan Abramovich (Br
own University) as part of VBAC Webinar Series\n\n\nAbstract\nThis is most
ly a report on work of Brown PhD students Veronica Arena and Stephen Obinn
a.\nThe Chow groups of a blowup of a smooth variety along a smooth subvari
ety is described in Fulton's book using Grothendieck's "key formula"\, inv
olving the Chow groups of the blown up variety\, the center of blowup\, an
d the Chern classes of its normal bundle.\nIf interested in weighted blowu
ps\, one expects everything to generalize directly. This is in hindsight c
orrect\, except that at every turn there is an interesting and delightful
surprise\, shedding light on the original formulas for usual blowups\, esp
ecially when one wants to pin down the integral Chow ring of a stack theor
etic weighted blowup.\nAs an application\, one obtains a quick derivation
of a formula\, due to Di Lorenzo--Pernice--Vistoli and Inchiostro\, of the
Chow ring of the moduli space $\\overline{M}_{1\,2}$.\n
LOCATION:https://stable.researchseminars.org/talk/VBAC-webinar/35/
END:VEVENT
END:VCALENDAR