BEGIN:VCALENDAR
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PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Chenyang Xu (MIT)
DTSTART:20200414T150000Z
DTEND:20200414T160000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/1
DESCRIPTION:Title: K-moduli of Fano varieties\nby Chenyang Xu (MIT) as part of Hod
ge Seminar\n\nLecture held in Bayes Centre (5th floor\, room 5.10).\n\nAbs
tract\nOne main theme of the algebraic K-stability theory of Fano varietie
s is to use it to construct moduli spaces of K-(semi\,polystable) Fano var
ieties. Several main ingredients have been established\, based on the rece
nt development of our understanding of K-stability theory and other inputs
. In this talk\, we will discuss the current status of the construction.\n
\nConference ID: 699 366 190\nPassword: 030418\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregory Sankaran (University of Bath)
DTSTART:20200421T143000Z
DTEND:20200421T153000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/2
DESCRIPTION:Title: Blowups with log canonical singularities\nby Gregory Sankaran (
University of Bath) as part of Hodge Seminar\n\nLecture held in Bayes Cent
re (5th floor\, room 5.10).\n\nAbstract\nWe show that the minimum weight o
f a weighted blow-up of ${\\mathbb A}^d$\nwith $\\varepsilon$-log canonica
l singularities is bounded by a constant\ndependin only on $\\varepsilon$
and $d$. This was conjectured by Birkar.\nUsing the recent classification
of 4-dimensional empty simplices by\nIglesias-Vali\\~no and Santos\, we wo
rk out an explicit bound for blowups of\n${\\mathbb A}^4$ with terminal si
ngularities: the smallest weight is always at\nmost 32\, and at most 6 in
all but finitely many cases.\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Hoskins (Radboud University Nijmegen)
DTSTART:20200428T143000Z
DTEND:20200428T153000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/3
DESCRIPTION:Title: Motives of moduli spaces of bundles over a curve\nby Victoria H
oskins (Radboud University Nijmegen) as part of Hodge Seminar\n\nLecture h
eld in Bayes Centre (5th floor\, room 5.10).\n\nAbstract\nFollowing Grothe
ndieck’s vision that a motive of an algebraic variety should capture man
y of its cohomological invariants\, Voevodsky introduced a triangulated ca
tegory of motives which partially realises this idea. After describing som
e properties of this category\, I will explain how to define the motive of
certain algebraic stacks. I will then state and sketch a proof for a form
ula the motive of the moduli stack of vector bundles on a smooth projectiv
e curve\; this formula is compatible with classical computations of invari
ants of this stack due to Harder\, Atiyah--Bott and Behrend--Dhillon. The
proof involves rigidifying this stack using Quot and Flag-Quot schemes par
ametrising Hecke modifications as well as a motivic version of an argument
of Laumon and Heinloth on the cohomology of small maps. If there is time\
, I will discuss how this can be used to study motives of other related mo
duli spaces such as the moduli space of Higgs bundles. This is joint work
with Simon Pepin Lehalleur.\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau (ETH Zurich)
DTSTART:20200512T143000Z
DTEND:20200512T153000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/4
DESCRIPTION:Title: Quasimodular forms from Betti numbers\nby Pierrick Bousseau (ET
H Zurich) as part of Hodge Seminar\n\nLecture held in Bayes Centre (5th fl
oor\, room 5.10).\n\nAbstract\nThis talk will be about refined curve count
ing on local P^2\, the noncompact Calabi-Yau 3-fold total space of the can
onical line bundle of the projective plane. I will explain how to construc
t quasimodular forms starting from Betti numbers of moduli spaces of one-d
imensional coherent sheaves on P^2. This gives a proof of some stringy pre
dictions about the refined topological string theory of local P^2 in the N
ekrasov-Shatashvili limit. This work is in part joint with Honglu Fan\, Sh
uai Guo\, and Longting Wu.\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Nicaise (Imperial College London)
DTSTART:20200602T143000Z
DTEND:20200602T153000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/5
DESCRIPTION:Title: Stable rationality of complete intersections\nby Johannes Nicai
se (Imperial College London) as part of Hodge Seminar\n\nLecture held in B
ayes Centre (5th floor\, room 5.10).\n\nAbstract\nI will explain an ongoin
g project with John Christian Ottem to establish several new classes of st
ably irrational complete intersections. Our results are based on degenerat
ion techniques and a birational version of the nearby cycles functor that
was developed in collaboration with Evgeny Shinder.\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swarnava Mukhopadhyay (TIFR Mumbai)
DTSTART:20200604T143000Z
DTEND:20200604T153000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/6
DESCRIPTION:Title: Graph potentials and the moduli space of vector bundles of rank two
on a curve\nby Swarnava Mukhopadhyay (TIFR Mumbai) as part of Hodge S
eminar\n\nLecture held in Bayes Centre (5th floor\, room 5.10).\n\nAbstrac
t\nIn this talk\, we will discuss a conjectural decomposition of the deriv
ed category of the moduli space $M$ of stable vector bundles rank two bund
les and fixed determinant on a smooth algebraic curve $\\Sigma$ into deriv
ed categories of symmetric products of the original curve. We will also co
nsider natural potentials $W$ associated with a decomposition of a surface
$\\Sigma$ into pairs of pants. Using TQFT gluing axioms\, we will show h
ow to compute the respective periods of $W$ very fast and simultaneously f
or all genera.\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Dancer (Oxford)
DTSTART:20200616T143000Z
DTEND:20200616T153000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/7
DESCRIPTION:Title: Symplectic duality and implosion\nby Andrew Dancer (Oxford) as
part of Hodge Seminar\n\nLecture held in Bayes Centre (5th floor\, room 5.
10).\n\nAbstract\nWe discuss hyperkahler implosion spaces. their relevance
to group actions\, and why they should fit into the symplectic duality pi
cture. For certain groups we present candidates for the symplectic duals o
f the associated implosion spaces and provide computational evidence. This
is joint work with Amihay Hanany and Frances Kirwan.\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucien Hennecart (University of Edinburgh)
DTSTART:20211007T120000Z
DTEND:20211007T130000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/8
DESCRIPTION:Title: The number of isoclasses of absolutely indecomposable representatio
ns of the modular group is a polynomial\nby Lucien Hennecart (Universi
ty of Edinburgh) as part of Hodge Seminar\n\nLecture held in Bayes Centre
(5th floor\, room 5.10).\n\nAbstract\nWe will explain how to prove that th
e number of isomorphism classes of absolutely indecomposable representatio
ns of the modular group over a finite field is a polynomial (with integer
coefficients) in the cardinality of the finite field. For this\, we consid
er the stack of representations\, its inertia stack and the nilpotent vers
ion of the inertia stack. By standard techniques\, we reduce the question
to the calculation of the number of points of the nilpotent inertia stack.
This is done using a Jordan stratification and favourable homological pro
perties. We will sketch the ideas to prove the positivity of the coeffici
ents of the counting polynomial\, which include a purity property of the r
epresentation stack. This is ongoing joint work with Fabian Korthauer.\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sasha Minets (University of Edinburgh)
DTSTART:20211021T120000Z
DTEND:20211021T130000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/9
DESCRIPTION:Title: KLR algebras in positive characteristic and their stratifications\nby Sasha Minets (University of Edinburgh) as part of Hodge Seminar\n\n
Lecture held in Bayes Centre (5th floor\, room 5.10).\n\nAbstract\nFor a g
iven quiver\, modules over KLR algebras are used to categorify the corresp
onding quantum group. While for Dynkin quivers representation theory of KL
R algebras is fairly well understood\, it becomes much more intricate for
affine quivers\, especially in positive characteristic. In this talk\, I w
ill explain how to obtain some structural results in this case by studying
analogues of KLR algebras associated to curves and surfaces. This is base
d on ongoing work with Ruslan Maksimau.\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franco Rota (University of Glasgow)
DTSTART:20211027T124500Z
DTEND:20211027T134500Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/12
DESCRIPTION:by Franco Rota (University of Glasgow) as part of Hodge Semina
r\n\nLecture held in Bayes Centre (5th floor\, room 5.10).\nAbstract: TBA\
n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dougal Davis (University of Edinburgh)
DTSTART:20211027T140000Z
DTEND:20211027T150000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/13
DESCRIPTION:Title: Mixed Hodge modules\, Lusztig-Vogan polynomials\, and unitary repr
esentations of real reductive groups\nby Dougal Davis (University of E
dinburgh) as part of Hodge Seminar\n\nLecture held in Bayes Centre (5th fl
oor\, room 5.10).\n\nAbstract\nLet (G\, K) be the symmetric pair associate
d with a real reductive group G_R. In this talk\, I will explain joint wor
k in progress with Kari Vilonen concerning K-equivariant twisted mixed Hod
ge modules on the flag variety of G\, and an application to the representa
tion theory of G_R. The Grothendieck group of mixed Hodge modules\, which
enhances the Grothendieck group of G_R-modules\, has two bases consisting
of standard and irreducible objects. At the level of weights\, the change
of basis matrix was computed algorithmically by Kazhdan-Lusztig and Luszti
g-Vogan in terms of Hecke algebra combinatorics. Our first main theorem up
grades this to the full Grothendieck group by adding an extra Hodge parame
ter to the Lusztig-Vogan polynomials. Our second main theorem is a "polari
sed" version of the Jantzen conjecture\; following ideas of Schmid and Vil
onen\, it allows the signature multiplicity polynomial of Adams-van Leeuwe
n-Trapa-Vogan to be read off from our Hodge polynomial. These two results
combined recover a key formula in the ALTV algorithm for identifying the u
nitary representations of G_R.\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (Yale University)
DTSTART:20211124T130000Z
DTEND:20211124T140000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/16
DESCRIPTION:Title: Cohomology of the moduli of Higgs bundles via positive characteris
tic\nby Junliang Shen (Yale University) as part of Hodge Seminar\n\nLe
cture held in Bayes Centre (5th floor\, room 5.10).\n\nAbstract\nIn this t
alk\, I will explain how techniques arising from the non-abelian Hodge the
ory in positive characteristic provide "consistency checks" of the P=W con
jecture\, where the latter concerns the cohomological aspect of the non-ab
elian Hodge theory over the complex numbers. We will focus on two aspects:
(1) the Galois conjugation\, and (2) the Hodge-Tate decomposition. Based
on joint work with Mark de Cataldo\, Davesh Maulik\, and Siqing Zhang.\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Orsola Capovilla-Searle (UC Davis)
DTSTART:20211124T150000Z
DTEND:20211124T160000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/17
DESCRIPTION:Title: Infinitely many Lagrangian Tori in Milnor fibers constructed via L
agrangian Fillings of Legendrian links\nby Orsola Capovilla-Searle (UC
Davis) as part of Hodge Seminar\n\nLecture held in Bayes Centre (5th floo
r\, room 5.10).\n\nAbstract\nOne approach to studying symplectic manifolds
with contact boundary is to consider Lagrangian submanifolds with Legendr
ian boundary\; in particular\, one can study exact Lagrangian fillings of
Legendrian links. There are still many open questions on the spaces of exa
ct Lagrangian fillings of Legendrian links in the standard contact 3-spher
e\, and one can use Floer theoretic invariants to study such fillings. We
show that a family of oriented Legendrian links has infinitely many distin
ct exact orientable Lagrangian fillings up to Hamiltonian isotopy. Within
this family\, we provide some of the first examples of a Legendrian link t
hat admits infinitely many planar exact Lagrangian fillings. Weinstein dom
ains are examples of symplectic manifolds with contact boundary that have
a handle decomposition compatible with the symplectic structure of the man
ifold. Weinstein handlebody diagrams are given by projections of Legendria
n submanifolds. We provide Weinstein handlebody diagrams of the 4-dimensio
nal Milnor fibers of T_{p\,q\,r} singularities\, which we then use to cons
truct infinitely many Lagrangian tori and spheres in these spaces\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Pressland (University of Leeds)
DTSTART:20211208T134500Z
DTEND:20211208T144500Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/18
DESCRIPTION:Title: Categorification of positroids and positroid varieties\nby Mat
thew Pressland (University of Leeds) as part of Hodge Seminar\n\nLecture h
eld in Bayes Centre (5th floor\, room 5.10).\n\nAbstract\nThe Grassmannian
and its totally positive part have a very rich combinatorial structure\,
studied by many people. In particular\, Postnikov has shown how the totall
y positive Grassmannian is stratified by positroid varieties. Recent work
of Galashin and Lam shows that the coordinate ring of each (open) positroi
d stratum is a cluster algebra\, with this structure determined by a combi
natorial object called a Postnikov diagram. In this talk\, I will explain
how the same diagram also gives rise to representation theoretic objects w
hich can be used to (additively) categorify this cluster algebra. This is
partly joint work with İlke Çanakçı and Alastair King.\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hongdi Huang (Rice University)
DTSTART:20211208T150000Z
DTEND:20211208T160000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/19
DESCRIPTION:Title: Twisting of graded quantum groups and solutions to the quantum Yan
g-Baxter equation\nby Hongdi Huang (Rice University) as part of Hodge
Seminar\n\nLecture held in Bayes Centre (5th floor\, room 5.10).\n\nAbstra
ct\nLet $H$ be a Hopf algebra over a field $k$ such that $H$ is $\\mathbb
Z$-graded as an algebra. In this talk\, we introduce the notion of a twist
ing pair for $H$ and show that the Zhang twist of $H$ by such a pair can b
e realized as a 2-cocycle twist. As an application of twisting pairs\, we
discuss an algorithm to produce a family of solutions to the quantum Yang-
Baxter equation from a given solution via the Faddeev-Reshetikhin-Takhtaja
n construction.\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vyjayanthi Chari (UC Riverside)
DTSTART:20211118T134500Z
DTEND:20211118T144500Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/21
DESCRIPTION:by Vyjayanthi Chari (UC Riverside) as part of Hodge Seminar\n\
nLecture held in Bayes Centre (5th floor\, room 5.10).\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sukjoo Lee (University of Edinburgh)
DTSTART:20211202T130000Z
DTEND:20211202T140000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/22
DESCRIPTION:by Sukjoo Lee (University of Edinburgh) as part of Hodge Semin
ar\n\nLecture held in Bayes Centre (5th floor\, room 5.10).\nAbstract: TBA
\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART:20211216T130000Z
DTEND:20211216T140000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/23
DESCRIPTION:by TBA as part of Hodge Seminar\n\nLecture held in Bayes Centr
e (5th floor\, room 5.10).\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kostya Tolmachov (University of Edinburgh)
DTSTART:20210929T124500Z
DTEND:20210929T134500Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/24
DESCRIPTION:Title: Monodromic model for Khovanov-Rozansky homology\nby Kostya Tol
machov (University of Edinburgh) as part of Hodge Seminar\n\nLecture held
in Bayes Centre (5th floor\, room 5.10).\n\nAbstract\nKhovanov-Rozansky ho
mology is a link invariant which\, by a result of Khovanov\, can be comput
ed as the Hochschild cohomology functor applied to complexes of Soergel bi
modules. I will describe a new geometric model for the Hochschild cohomolo
gy of Soergel bimodules\, living in the monodromic Hecke category. I will
also explain how it allows to identify objects representing individual Hoc
hsсhild cohomology groups as imagesof explicit character sheaves. Based o
n a joint work with Roman Bezrukavnikov.\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Léa Bittmann (University of Edinburgh)
DTSTART:20210929T140000Z
DTEND:20210929T150000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/25
DESCRIPTION:Title: A Schur-Weyl duality between Double Afffine Hecke Algebras and qua
ntum groups\nby Léa Bittmann (University of Edinburgh) as part of Hod
ge Seminar\n\nLecture held in Bayes Centre (5th floor\, room 5.10).\n\nAbs
tract\nSchur-Weyl duality is often used to relate type A Lie groups (or qu
antum groups) to symmetric groups (or Hecke algebras). In this talk\, I wi
ll describe an instance of this Schur-Weyl duality\, between representatio
ns of the type A quantum group at roots of unity and representations of th
e Double Affine Hecke Algebra. The construction uses ribbon calculus and n
ews combinatorial objects called "doubly periodic tableaux". This is based
on joint work with A. Chandler\, A. Mellit and C. Novarini.\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shengxuan Liu (University of Warwick)
DTSTART:20211013T124500Z
DTEND:20211013T134500Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/26
DESCRIPTION:Title: Stability condition on Calabi-Yau threefold of complete intersecti
on of quadratic and quartic hypersurfaces\nby Shengxuan Liu (Universit
y of Warwick) as part of Hodge Seminar\n\nLecture held in Bayes Centre (5t
h floor\, room 5.10).\n\nAbstract\nIn this talk\, I will first introduce t
he background of Bridgeland stability condition. Then I will mention some
existence result of Bridgeland stability. Next I will prove the Bogomolov-
Gieseker type inequality of X_(2\,4)\, Calabi-Yau threefold of complete in
tersection of quadratic and quartic hypersufaces\, by proving the Clifford
type inequality of the curve X_(2\,2\,2\,4). Then this will provide the e
xistence of Bridgeland stability condition of X_(2\,4).\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wahei Hara (University of Glasgow)
DTSTART:20211013T140000Z
DTEND:20211013T150000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/27
DESCRIPTION:Title: Global generation of instanton bundles of charge 3 on del Pezzo th
reefolds of degree 4\nby Wahei Hara (University of Glasgow) as part of
Hodge Seminar\n\nLecture held in Bayes Centre (5th floor\, room 5.10).\n\
nAbstract\nWe show that any del Pezzo threefold of degree 4 admits an inst
anton bundle E of charge 3 such that E(1) is globally generated. This ques
tion is the most important part in our classification of weak Fano bundles
on del Pezzo threefolds of degree 4. We study elliptic curves of degree 7
and show that any del Pezzo threefold of degree 4 contains such curves th
at are generated by quadratic equations using the deformation theory\, and
then we construct the desired instanton bundles by Hartshorne-Serre corre
spondence. This talk depends on a joint works with T. Fukuoka and D. Ishik
awa.\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umut Varolgunes (University of Edinburgh)
DTSTART:20211104T130000Z
DTEND:20211104T140000Z
DTSTAMP:20260422T212902Z
UID:Edinburgh_Geom/29
DESCRIPTION:Title: Trying to quantify Gromov's non-squeezing theorem\nby Umut Var
olgunes (University of Edinburgh) as part of Hodge Seminar\n\nLecture held
in Bayes Centre (5th floor\, room 5.10).\n\nAbstract\nGromov's celebrated
result says (colloquially) that one cannot symplectically embed a ball of
radius 1.1 into a cylinder of radius 1. I will show that in 4d if one rem
oves from this ball a Lagrangian plane passing through the origin\, then s
uch an embedding becomes possible. I will also show that this gives the sm
allest Minkowski dimension of a closed subset with this property. I will e
nd with many questions. This is based on joint work with K. Sackel\, A. So
ng and J. Zhu.\n
LOCATION:https://researchseminars.org/talk/Edinburgh_Geom/29/
END:VEVENT
END:VCALENDAR