BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Simon K. Donaldson (Imperial / SCGP)
DTSTART:20201123T150000Z
DTEND:20201123T154500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/1
DESCRIPTION:Title: K-stability and scalar curvature\nby Simon K. Donaldson (Imperial
/ SCGP) as part of VBAC Webinar Series\n\n\nAbstract\nThis will be an ove
rview talk about existence results in complex differential geometry connec
ted to the notion of K-stability. We will explain the analogies with the c
orresponding results\, going back to Narasimhan and Seshadri\, for holomor
phic vector bundles and outline some strategies of proofs that have been e
mployed. We will illustrate the general with a discussion of the case of t
oric manifolds.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenyang Xu (Princeton)
DTSTART:20201123T160000Z
DTEND:20201123T164500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/2
DESCRIPTION:Title: An algebraic construction of K-moduli space\nby Chenyang Xu (Prin
ceton) as part of VBAC Webinar Series\n\n\nAbstract\nK-stability of Fano v
arieties has become a fast developed topic in algebraic geometry. One majo
r output is the construction of moduli spaces of K-(semi\,poly)-stable Fan
o varieties\, which resolves a number of pathological issue for families o
f general Fano varieties. The purely algebraic construction is built on a
systematical study of K-stability using higher dimensional geometry\, incl
uding a more comprehensive understanding of the notion of K-stability (for
Fano varieties)\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (M.I.T.)
DTSTART:20210118T150000Z
DTEND:20210118T154500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/3
DESCRIPTION:Title: Cohomology of the moduli of Higgs bundles\nby Junliang Shen (M.I.
T.) as part of VBAC Webinar Series\n\n\nAbstract\nThe moduli space of Higg
s bundles and Hitchin's integrable system lie at the crossroads of mathema
tics physics\, representation theory\, and geometry. In this talk\, we foc
us on cohomological structures of these moduli spaces from the aspects of
non-abelian Hodge theory\, hyper-kaehler geometry\, and mirror symmetry. W
e will discuss recent progress on the P=W conjecture as well as connection
s to some other open conjectures concerning Higgs moduli spaces. Based on
joint work with Mark de Cataldo and Davesh Maulik.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camilla Felisetti (U. Trento)
DTSTART:20210118T160000Z
DTEND:20210118T164500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/4
DESCRIPTION:Title: P=W conjectures for character varieties with a symplectic resolution<
/a>\nby Camilla Felisetti (U. Trento) as part of VBAC Webinar Series\n\n\n
Abstract\nCharacter varieties parametrise representations of the fundament
al group of a curve. In general these moduli spaces are singular\, therefo
re it is customary to slightly change the moduli problem and consider smoo
th analogues\, called twisted character varieties. In this setting\, the P
=W conjecture by de Cataldo\, Hausel\, and Migliorini suggests a surprisin
g connection between the topology of Hitchin systems and Hodge theory of c
haracter varieties. In joint work with M. Mauri we establish (and in some
cases formulate) analogous P=W phenomena in the singular case . In particu
lar we show that the P=W conjecture holds for character varieties which ad
mit a symplectic resolution\, namely in genus 1 and arbitrary rank and in
genus 2 and rank 2.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frances Kirwan (Oxford Univ.)
DTSTART:20210315T150000Z
DTEND:20210315T154500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/5
DESCRIPTION:Title: Non-reductive GIT and HKKP theory\nby Frances Kirwan (Oxford Univ
.) as part of VBAC Webinar Series\n\n\nAbstract\nIn a recent paper F. Haid
en\, L. Katzarkov\, M. Kontsevich and\nP. Pandit study notions of (semi-)s
tability and Harder-Narasimhan\nfiltrations in polarised lattices and weig
ht filtations for modular\nlattices\, proving existence and uniqueness the
orems in these very\ngeneral settings. The aim of this talk is to explore
the relationship of\ntheir theory with recent extensions of geometric inva
riant theory to\nlinear algebraic group actions by non-reductive groups wi
th graded\nunipotent radicals.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eloise Hamilton (IMJ-PRG)
DTSTART:20210315T160000Z
DTEND:20210315T164500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/6
DESCRIPTION:Title: Cohomology of Non-Reductive GIT quotients and unstable Higgs bundles
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 used to co
nstruct moduli spaces for unstable Higgs/vector bundles on a smooth projec
tive curve. The aim of this talk is to describe a method for computing the
Poincare series of Non-Reductive GIT quotients when the initial variety i
s 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 bundles o
f rank 2.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kang Zuo (U. Mainz)
DTSTART:20210517T150000Z
DTEND:20210517T154500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/7
DESCRIPTION:Title: Arakelov Inequality for Families of Projective Manifolds\nby Kang
Zuo (U. Mainz) as part of VBAC Webinar Series\n\n\nAbstract\nhe Arakelov
inequality for families of algebraic curves and abelian varieties goes bac
k to the works by Arakelov-Parshin\, Faltings and Deligne (sharp form)\, a
nd for systems of Hodge bundles is due to the works by Green-Griffiths-Ker
r\, Jost-Zuo\, Peters\, Viehweg-Zuo. A very recent work by Biquard-Collier
-Garcia-Prada-Toledo is making a further progress on Arakelov-Milnor inequ
alities.\n\nIn my talk I shall briefly report on my recent work joint with
Xin Lu and Jinbang Yang. We show the Arakelov inequality holds STRICTLY f
or canonical heights of families of n-folds of general type. We also show
it is asymptotically sharp in a sense. Note that this Arakelov inequality
can become actually an equality for families of abelian varieties\, in whi
ch case they are precisely Shimura families.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Collier (U.C. Riverside)
DTSTART:20210517T160000Z
DTEND:20210517T164500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/8
DESCRIPTION:Title: Maximal variations of Hodge structure and sl2-triples\nby Brian C
ollier (U.C. Riverside) as part of VBAC Webinar Series\n\n\nAbstract\nIn t
his talk we will discuss holomorphic maps from the upper half space into c
ertain homogeneous spaces (period domains) which are equivariant with resp
ect to a representation of the fundamental group of a closed surface. 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 symmetric space
\, the Toledo invariant provides an integer invariant which is bounded in
absolute value. Moreover\, representations which maximize the Toledo invar
iant satisfy certain rigidity phenomena and arise from the uniformizing re
presentation of the Riemann surface. We will discuss how to generalize suc
h an invariant for arbitrary period domains\, explain how this invariant i
s bounded and describe how the rigidity phenomena which occur when the inv
ariant is maximized are related to sl2 triples. This is based on joint wor
k with Biquard\, Garcia-Prada and Toledo.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edward Witten (IAS\, Princeton)
DTSTART:20210705T150000Z
DTEND:20210705T160000Z
DTSTAMP:20260422T225759Z
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 ta
lk\, which is based on work with D. Gaiotto\, Witten will explain a quantu
m field theory perspective on recent developments in the geometric Langlan
ds program by P. Etinghof\, E. Frenkel and D. Kazhdan (see their paper htt
ps://arxiv.org/abs/1908.09677)\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Hoskins (Radboud University Nijmegen)
DTSTART:20210705T161500Z
DTEND:20210705T170000Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/10
DESCRIPTION:Title: Motives of moduli spaces of bundles on curves\nby Victoria Hoski
ns (Radboud University Nijmegen) as part of VBAC Webinar Series\n\n\nAbstr
act\nVarious computations of cohomological invariants of moduli spaces of
vector bundles and Higgs bundles on curves should be both unified and refi
ned by working with motivic invariants\, which encode finer invariants\, l
ike Hodge structures on cohomology groups and also algebro-geometric invar
iants such as Chow groups. In this talk\, I will present joint work with L
ie Fu and Simon Pepin Lehalleur\, studying the rational Chow motives of va
rious moduli spaces of vector bundles on curves with additional structure
(such as a Higgs field or parabolic structure). After a short introduction
to Chow motives\, I will present some results which hold for bundles of a
rbitrary rank. Finally\, I will give some explicit formulas in ranks 2 and
3.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Mistegaard (IST\, Austria)
DTSTART:20210705T171500Z
DTEND:20210705T180000Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/11
DESCRIPTION:Title: Quantization of moduli spaces and TQFT\nby William Mistegaard (I
ST\, Austria) as part of VBAC Webinar Series\n\n\nAbstract\nThe Reshetikhi
n-Turaev topological quantum field theory (TQFT) was motivated from physic
s by Witten's work on quantum Chern-Simons. In Witten's work quantization
of moduli spaces of flat connections and conformal field theory (CFT) was
presented as two equivalent approaches to construct the Hilbert space asso
ciated to an oriented two-manifold. Both approaches depend a priori on a c
hoice of complex structure on the two-manifold\, although the topological
nature of the theory suggests that the Hilbert space should be independent
of this choice\, and support a projective linear action of the mapping cl
ass group. On the CFT side this topological invariance and the existence o
f a mapping class group action was proven by Tsuchia\, Ueno and Yamada. On
the quantization side it was proven for some two-manifolds independently
by Hitchin and Axelrod\, Della Pietra and Witten. Laszlo proved mathematic
ally that the CFT approach and the quantization approach of Hitchin are eq
uivalent. Finally\, Andersen and Ueno have established that the CFT repres
entations of the mapping class groups are isomorphic to the Reshetikhin-Tu
raev TQFT mapping class group action. In this talk\, we will\; 1) partly r
eview the above story\, 2) review how quantization was used to prove impor
tant results in quantum topology\, and 3) present work in progress joint w
ith Andersen\, which constructs the TQFT-representations of the mapping cl
ass groups from the quantization approach in some of the remaining (parabo
lic cases)\, not previously dealt with by Hitchin or Axelrod-Della Pietra
and Witten.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Schiffmann (CNRS\, Paris-Sud Orsay)
DTSTART:20210706T150000Z
DTEND:20210706T160000Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/12
DESCRIPTION:Title: Cohomological Hall algebras of curves and surfaces\nby Olivier S
chiffmann (CNRS\, Paris-Sud Orsay) as part of VBAC Webinar Series\n\n\nAbs
tract\nWe will survey some recent developments on the computations of vari
ous cohomological Hall algebras associated either to (smooth projective) c
urves\, or to a pair consisting of a curve inside a smooth surface. The la
tter case is related to various types of affine yangians. Based on joint w
ork with E. Diaconescu\, F. Sala and E. Vasserot.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Malusà (University of Toronto)
DTSTART:20210706T161500Z
DTEND:20210706T170000Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/13
DESCRIPTION:Title: A new quantisation scheme for hyperkähler manifolds with Sp(1) symm
etry\nby Alessandro Malusà (University of Toronto) as part of VBAC We
binar Series\n\n\nAbstract\nIt is often the case\, with many (complex) mod
uli problems\, that the resulting spaces come with hyperkähler structures
and symmetries that act non-trivially on the corresponding families of K
ähler forms\, rather than preserving them individually. This makes it del
icate to approach their quantisation\, as a preferred symplectic structure
may not be given or the group action to be quantised may not be symplecti
c with respect to it. The U(1)-action on the Hitchin moduli spaces is an e
xample of this.\nIn an ongoing joint work with Andersen and Rembado\, we a
pproach this problem under the assumption that the symmetry group is an ex
tension of Sp(1) with a transitive action on CP^1\, identified with the as
sociated space of complex structures. This is the case for known examples
such as linear spaces\, the Taub-NUT space\, nilpotent orbits of complex L
ie groups\, the moduli spaces of framed SU(r)-instantons on R^4\, and the
Atiyah-Hitchin manifolds of monopoles on R^3. We propose a new hyperkähle
r quantisation scheme by assuming given a smooth equivariant family of pre
-quantum line bundles\, and by defining a collection of quantum Hilbert sp
aces parametrised by CP^1. The quantisation of the symmetry group may then
be addressed in terms of actions on this family and compatibility with na
turally defined connections. These\, however\, turn out to not be flat in
general\, even projectively\, but we obtain group of representations on sp
aces of holomorphic sections of the family of Hilbert spaces\, rather than
flat ones\, and we therefore propose this space of holomorphic sections a
s the relevant quantization of these SP(1)-symmetric Hyper-Kähler manifol
ds.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaime Silva (Inst. Politécnico Lisboa)
DTSTART:20210706T171500Z
DTEND:20210706T180000Z
DTSTAMP:20260422T225759Z
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 Series\n\n
\nAbstract\nIn this talk\, I will make an overview about my work on the mi
xed Hodge structures and motives of abelian character varieties.\nI will s
tart by giving a brief account of Hodge structures on character varieties\
, and how those relate to the topic of non-abelian Hodge theory. Illustrat
ing this topic\, I will cover my results on the mixed hodge structures of
free abelian character varieties and how those illustrate some predictions
related to mirror theory.\nAfterwards\, I will talk about more recent res
ults on the motives of character varieties. In this\, I will talk about ou
r attempt to adapt our previous work on Hodge structures of finite quotien
ts by using a motive that allows for a suitable equivariant version - the
so-called equivariant Chow motives. This is joint work with C. Florentino.
\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (Caltech)
DTSTART:20210707T150000Z
DTEND:20210707T160000Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/15
DESCRIPTION:Title: Brane quantization of SL(2\,C) moduli spaces\nby Sergei Gukov (C
altech) as part of VBAC Webinar Series\n\n\nAbstract\nThe problem of quant
ization of symplectic manifolds and the Fukaya category side of mirror sym
metry 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 the latt
er. The goal of this talk will be to illustrate how this approach\, often
called "brane quantization\," can help with understanding certain aspects
of the quantization of the moduli space of flat SL(2\,C) connections.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriele Rembado (University of Bonn)
DTSTART:20210707T161500Z
DTEND:20210707T170000Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/16
DESCRIPTION:Title: Quantisation of moduli spaces of meromorphic connections\, and relat
ions with (irregular) CFT\nby Gabriele Rembado (University of Bonn) as
part of VBAC Webinar Series\n\n\nAbstract\nThe geometry and quantisation
of moduli spaces of unitary flat connections on Riemann surfaces have been
widely studied in the past: as the complex structure on the surface is de
formed the moduli spaces assemble into a local system of symplectic manifo
lds\, and Kähler quantisation turns it into a projectively flat vector bu
ndle.\nThe complexified version brings about holomorphic connections and h
yperkähler manifolds\, requiring new ideas in Kähler quantisation\; defo
rmation quantisation on the other hand has been carried out in greater gen
erality\, namely for moduli spaces of meromorphic connections with irregul
ar singularities.\nIn this talk we will briefly review this story and phra
se the singular case in the same geometric language of the nonsingular one
\, involving flat symplectic fibre bundles: their bases provide an intrins
ic approach to isomonodromic deformations\, and their quantisation provide
s a mathematical approach to irregular singularities in the Wess-Zumino-No
vikov-Witten model.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Du Pei (Harvard University)
DTSTART:20210707T171500Z
DTEND:20210707T180000Z
DTSTAMP:20260422T225759Z
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 bundles when
G is not simply connected. I will also mention some of its applications t
o mirror symmetry and brane quantization.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:János Kollár (Princeton University)
DTSTART:20210913T140000Z
DTEND:20210913T144500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/18
DESCRIPTION:Title: The Zariski topology\, linear systems\, and algebraic varieties\, I<
/a>\nby János Kollár (Princeton University) as part of VBAC Webinar Seri
es\n\n\nAbstract\nWe discuss the main steps of the proof that (with a few
exceptions) the Zariski topology determines an algebraic variety. In the f
irst talk we explain how to detect linear equivalence using the Zariski to
pology. \n\nThen in the second talk we show that knowing the Zariski topol
ogy plus linear equivalence determines the variety. The techniques of the
2 talks will be mostly independent of each other. (joint work with Max Lie
blich and Will Sawin).\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Olsson (University of California\, Berkeley)
DTSTART:20210913T150000Z
DTEND:20210913T154500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/19
DESCRIPTION:Title: The Zariski topology\, linear systems\, and algebraic varieties\, II
\nby Martin Olsson (University of California\, Berkeley) as part of VB
AC Webinar Series\n\n\nAbstract\nWe discuss the main steps of the proof th
at (with a few exceptions) the Zariski topology determines an algebraic va
riety. In the first talk we explain how to detect linear equivalence using
the Zariski topology. \n\nThen in the second talk we show that knowing th
e Zariski topology plus linear equivalence determines the variety. The tec
hniques of the 2 talks will be mostly independent of each other. (joint wo
rk with Max Lieblich and Will Sawin).\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. Ramanan
DTSTART:20211011T140000Z
DTEND:20211011T143000Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/20
DESCRIPTION:Title: My collaborative work with Narasimhan\nby S. Ramanan as part of
VBAC Webinar Series\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:T. R. Ramadas
DTSTART:20211011T143000Z
DTEND:20211011T150000Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/21
DESCRIPTION:Title: Narasimhan’s work on conformal blocks\nby T. R. Ramadas as par
t of VBAC Webinar Series\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O. Garcia-Prada
DTSTART:20211011T151500Z
DTEND:20211011T154500Z
DTSTAMP:20260422T225759Z
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://researchseminars.org/talk/VBAC-webinar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:G. Harder
DTSTART:20211011T154500Z
DTEND:20211011T161500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/23
DESCRIPTION:Title: Why is the Tamagawa number equal to one?\nby G. Harder as part o
f VBAC Webinar Series\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jensen (University of Kentucky)
DTSTART:20220124T143000Z
DTEND:20220124T151500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/24
DESCRIPTION:Title: Non-Abelian Brill-Noether Theory of Genus 13 Curves\nby David Je
nsen (University of Kentucky) as part of VBAC Webinar Series\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Madeline Brandt (Brown University)
DTSTART:20220124T153000Z
DTEND:20220124T161500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/25
DESCRIPTION:Title: Top Weight Cohomology of A_g\nby Madeline Brandt (Brown Universi
ty) as part of VBAC Webinar Series\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jochen Heinloth (Universität Duisburg-Essen)
DTSTART:20220328T130000Z
DTEND:20220328T134500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/26
DESCRIPTION:Title: Proper moduli spaces for algebraic stacks\nby Jochen Heinloth (U
niversität Duisburg-Essen) as part of VBAC Webinar Series\n\n\nAbstract\n
As requested by the organizers\, the main aim of the talk is to set the st
age for the second talk by explaining the notions appearing in the existen
ce theorem for good (resp. adequate) moduli spaces obtained in joint work
with Jarod Alper and Daniel Halpern-Leistner\, which provide necessary and
sufficient conditions for a moduli problem to admit a proper moduli space
. I will try to illustrate the notions in examples.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Damiolini (University of Pennsylvania)
DTSTART:20220328T140000Z
DTEND:20220328T144500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/27
DESCRIPTION:Title: Projectivity of moduli spaces of quiver representations\nby Chia
ra Damiolini (University of Pennsylvania) as part of VBAC Webinar Series\n
\n\nAbstract\nIn a recent work of Alper–Belmans–Bragg–Liang–Tajakk
a\, the authors explore how the theory of good moduli spaces developed by
Alper and Alper–Halpern-Leistner–Heinloth can be used to give an alter
native proof of projectivity of the moduli space of vector bundles on a cu
rve. 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 bundles over
curves will be emphasized. This is based on ongoing work with Belmans\, F
ranzen\, Hoskins\, Makarova and Tajakka.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jay Kopper (Penn State University)
DTSTART:20220516T130000Z
DTEND:20220516T134500Z
DTSTAMP:20260422T225759Z
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\nAbstract\nI w
ill discuss recent progress in Brill-Noether theory for vector bundles on
surfaces\, including "weak" Brill-Noether results describing the cohomolog
y of general stable bundles\, positivity results about global generation a
nd ampleness\, and strong Brill-Noether results about Brill-Noether loci i
n the moduli space.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Larson (Stanford University and Clay Institute)
DTSTART:20220516T140000Z
DTEND:20220516T144500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/29
DESCRIPTION:Title: Brill-Noether theory over the Hurwitz space\nby Hannah Larson (S
tanford University and Clay Institute) as part of VBAC Webinar Series\n\n\
nAbstract\nThe main theorems of Brill-Noether theory describe the maps of
general curves to projective space. In particular\, for a general curve C\
, the space of degree d maps C —> P^r is known to be irreducible when it
s expected dimension is positive. However\, in nature\, curves C are 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 gen
eral among curves of fixed gonality. For such curves\, previous work has s
hown that the space of maps C —> P^r may have multiple components of var
ying dimensions (Coppens-Martens\, Pflueger\, Jensen-Ranganathan). In this
talk\, I will discuss joint work with Eric Larson and Isabel Vogt that ex
plains these multiple components and proves analogs of all of the main the
orems of Brill-Noether theory in this setting.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marina Logares (UCM\, Madrid)
DTSTART:20220926T130000Z
DTEND:20220926T134500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/30
DESCRIPTION:Title: From e-polynomials to TQFTs\nby Marina Logares (UCM\, Madrid) 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 inspiration
for mathematical discoveries. The aim of this talk is to show how certain
algebro-topological invariants\, e-polynomials\, of a G-character variety
serve to construct a TQFT and\, moreover\, how this development allows to
easily explore more general settings for G-character varieties\, such as t
hose related with singular curves.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Azizeh Nozad (IPM\, Tehran)
DTSTART:20220926T140000Z
DTEND:20220926T144500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/31
DESCRIPTION:Title: Mixed Hodge Structures of Character Varieties of Free Groups\nby
Azizeh Nozad (IPM\, Tehran) as part of VBAC Webinar Series\n\n\nAbstract\
nWith G a complex reductive group\, let $X^rG$ denote the G-character vari
eties 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 stratific
ation of $X^rG$ by polystable type coming from affine GIT and the combinat
orics of partitions\, we show that the mixed Hodge structures on the cohom
ology groups of $X^rSL_n$ and of $X^rPGL_n$ and on the compactly supported
cohomology groups of the irreducible loci $X^{irr}SL_n$ and $X^{irr}PGL_n
$ are isomorphic\, for any $n\,r \\in \\mathbb N$. In particular\, this wo
uld imply their E-polynomials coincide\, settling the question raised by L
awton-Muñoz. This is based on joint work with Carlos Florentino and Alfo
nso Zamora\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Huybrechts (U. Bonn)
DTSTART:20221121T150000Z
DTEND:20221121T154500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/32
DESCRIPTION:Title: Chow groups of lines on cubic fourfolds\nby Daniel Huybrechts (U
. Bonn) as part of VBAC Webinar Series\n\n\nAbstract\nI will discuss the C
how group of zero-cycles on the Fano\nvariety of lines in a cubic fourfold
from the perspective of certain\ndistinguished surfaces contained in the
Fano variety. In particular the\nsurface of lines meeting a fixed line wil
l be discussed in detail. The\nfinal aim is to establish an analogue of re
sults of Beauville and Voisin\nfor K3 surfaces. I will give some backgroun
d on Chow groups\, like\nBloch-Beilinson filtration and work of Shen-Vial\
, Voisin and others\, and\nstress the geometry of the situation.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valeria Bertini (U. Porto)
DTSTART:20221121T160000Z
DTEND:20221121T164500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/33
DESCRIPTION:Title: Singular symplectic varieties as symplectic quotients of hyperkähle
r manifolds\nby Valeria Bertini (U. Porto) as part of VBAC Webinar Ser
ies\n\n\nAbstract\nOne possible singular analogue of hyperkähler manifold
s are\nirreducible symplectic varieties\, mainly arising as moduli spaces
of\nsheaves on trivial canonical surfaces and as partial resolution of\nsy
mplectic quotients of hyperkähler manifolds. In this talk I will focus\no
n the second class of examples\, especially in the case of fourfolds. In\n
order to produce new examples\, we will start from the known hyperkähler\
nfourfolds (Hilbert schemes and generalized Kummer) and act on them with\n
natural automorphisms\, for which a systematic analysis is possible. This\
nis the content of a work in progress with Armando Capasso\, Annalisa\nGro
ssi\, Mirko Mauri and Enrica Mazzon.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolina Araujo (IMPA\, Brazil)
DTSTART:20230123T150000Z
DTEND:20230123T154500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/34
DESCRIPTION:Title: Birational geometry of Calabi-Yau pairs\nby Carolina Araujo (IMP
A\, Brazil) as part of VBAC Webinar Series\n\n\nAbstract\nConsider the fol
lowing problem\, originally posed by Gizatullin: "Which automorphisms of a
smooth quartic K3 surface in $\\mathbb{P}^3$ are induced by Cremona trans
formations of the ambient space?'' When $S$ is a smooth quartic surface i
n $\\mathbb{P}^3$\, the pair $(\\mathbb{P}^3\,S)$ is an example of a Calab
i-Yau pair\, that is\, a mildly singular pair $(X\,D)$ consisting of a nor
mal projective variety X and an effective Weil divisor $D$ on $X$ such tha
t $K_X+D= 0$. In this talk\, I will explain a general framework to investi
gate the birational geometry of Calabi-Yau pairs and how this can be appli
ed to approach Gizatullin's problem. This is a joint work with Alessio Cor
ti and Alex Massarenti.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Abramovich (Brown University)
DTSTART:20230123T160000Z
DTEND:20230123T164500Z
DTSTAMP:20260422T225759Z
UID:VBAC-webinar/35
DESCRIPTION:Title: The Chow ring of a weighted blowup\nby Dan Abramovich (Brown Uni
versity) as part of VBAC Webinar Series\n\n\nAbstract\nThis is mostly a re
port on work of Brown PhD students Veronica Arena and Stephen Obinna.\nThe
Chow groups of a blowup of a smooth variety along a smooth subvariety is
described in Fulton's book using Grothendieck's "key formula"\, involving
the Chow groups of the blown up variety\, the center of blowup\, and the C
hern classes of its normal bundle.\nIf interested in weighted blowups\, on
e expects everything to generalize directly. This is in hindsight correct\
, except that at every turn there is an interesting and delightful surpris
e\, shedding light on the original formulas for usual blowups\, especially
when one wants to pin down the integral Chow ring of a stack theoretic we
ighted blowup.\nAs an application\, one obtains a quick derivation of a fo
rmula\, due to Di Lorenzo--Pernice--Vistoli and Inchiostro\, of the Chow r
ing of the moduli space $\\overline{M}_{1\,2}$.\n
LOCATION:https://researchseminars.org/talk/VBAC-webinar/35/
END:VEVENT
END:VCALENDAR