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BEGIN:VEVENT
SUMMARY:Alastair Craw (University of Bath)
DTSTART:20201028T160000Z
DTEND:20201028T173000Z
DTSTAMP:20260404T094939Z
UID:gic-seminar/1
DESCRIPTION:Title: Gale duality and the linearisation map for quiver moduli\nb
y Alastair Craw (University of Bath) as part of GiC (Geometry in Cardiff)
seminar\n\nLecture held in M/2.44a\, 2nd Floor\, School of Mathematics.\n\
nAbstract\nThe goal of the talk is to show you a beautiful matrix and then
to explain its geometric significance. This will enable me to explain why
two rival geometric interpretations of `Reid's recipe' are equivalent. To
begin\, I'll set the scene by discussing the classical McKay corresponden
ce in dimension two and I'll go on to discuss how this extends naturally t
o dimension three. I'll introduce Reid's recipe by studying the cyclic quo
tient singularity of type 1/19(1\,3\,15)\, and this gives me the excuse to
introduce the matrix that I've fallen in love with. I'll reveal the geome
try that this gorgeous matrix encodes\, and as a result\, we'll see that t
wo conjectures for consistent dimer model algebras are equivalent.\n
LOCATION:https://stable.researchseminars.org/talk/gic-seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daria Polyakova (University of Copenhagen)
DTSTART:20201111T160000Z
DTEND:20201111T173000Z
DTSTAMP:20260404T094939Z
UID:gic-seminar/2
DESCRIPTION:Title: Weakly monoidal structure for the DG-category of representation
s up to homotopy\nby Daria Polyakova (University of Copenhagen) as par
t of GiC (Geometry in Cardiff) seminar\n\nLecture held in M/2.44a\, 2nd Fl
oor\, School of Mathematics.\n\nAbstract\nRepresentations up to homotopy o
f a group G were introduced by Abad and Crainic. They form a DG-category R
ep^h(G) whose objects are A-infinity comodules over the coalgebra of funct
ions on G\, and whose morphisms are A-infinity Hom complexes. This categor
y enhances the derived category of ordinary representations. Abad-Crainic-
Dherin proved that the homotopy category of Rep^h(G) is monoidal. They pos
ed a question to define an appropriate homotopy-coherent structure on the
DG-category itself.I will explain how a family of polytopes controls morph
isms of A-infinity (co)modules. Then I will present a new observation that
this family is nothing else but freehedra\, a family constructed earlier
by Saneblidze for entirely different reasons as subdivisions of cubes. Aba
d-Crainic-Dherin monoidal structure appears to follow from Saneblidze’s
diagonal for freehedra. I will extend this diagonal to A-infinity coalgebr
a structure. This is the first ingredient of a “weakly monoidal” struc
ture that I obtain as a DG-lift of Abad-Crainic-Dherin monoidal structure.
\n
LOCATION:https://stable.researchseminars.org/talk/gic-seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agnieszka Bodzenta-Skibinska (Warsaw)
DTSTART:20201125T160000Z
DTEND:20201125T173000Z
DTSTAMP:20260404T094939Z
UID:gic-seminar/3
DESCRIPTION:Title: Exact categories and abelian envelopes\nby Agnieszka Bodzen
ta-Skibinska (Warsaw) as part of GiC (Geometry in Cardiff) seminar\n\nLect
ure held in M/2.44a\, 2nd Floor\, School of Mathematics.\n\nAbstract\nFor
exact categories I will develop a theory parallel to the theory well-known
for triangulated categories\; left and right admissible subcategories\, a
nd (semi-orthogonal) decompositions. In particular\, I will introduce thin
exact categories\, i.e. exact categories will full exceptional collection
s. I will discuss left and right abelian envelopes of an exact category an
d will show that highest weight categories are precisely the abelian envel
opes of thin exact categories. I will also discuss Ringel duality from thi
s point of view. This is joint work with A. Bondal.\n
LOCATION:https://stable.researchseminars.org/talk/gic-seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Thompson (Loughborough)
DTSTART:20201209T160000Z
DTEND:20201209T173000Z
DTSTAMP:20260404T094939Z
UID:gic-seminar/4
DESCRIPTION:Title: Mirror symmetry for fibrations and degenerations\nby Alan T
hompson (Loughborough) as part of GiC (Geometry in Cardiff) seminar\n\nLec
ture held in M/2.44a\, 2nd Floor\, School of Mathematics.\n\nAbstract\nIn
a 2004 paper\, Tyurin briefly hinted at a novel relationship between Calab
i-Yau mirror symmetry and the Fano-LG correspondence. More specifically\,
if one can degenerate a Calabi-Yau manifold to a pair of (quasi-)Fanos\, t
hen one expects to be able to express the mirror Calabi-Yau in terms of th
e corresponding Landau-Ginzburg models. Some details of this correspondenc
e were worked out by C. F. Doran\, A. Harder\, and I in a 2017 paper\, but
much remains mysterious.\n\nIn this talk I will describe recent attempts
to better understand this picture\, and how it hints at a broader mirror s
ymmetric correspondence between degeneration and fibration structures. As
an example of this correspondence\, I will discuss the question of finding
mirrors to certain exact sequences which describe the Hodge theory of deg
enerations.\n\nThe material in this talk is joint work in progress with C.
F. Doran.\n
LOCATION:https://stable.researchseminars.org/talk/gic-seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Will Donovan (Tsinghua)
DTSTART:20210203T160000Z
DTEND:20210203T173000Z
DTSTAMP:20260404T094939Z
UID:gic-seminar/5
DESCRIPTION:Title: Classification of simple flops and variation of GIT\nby Wil
l Donovan (Tsinghua) as part of GiC (Geometry in Cardiff) seminar\n\nLectu
re held in M/2.44a\, 2nd Floor\, School of Mathematics.\n\nAbstract\nThoug
h classification of flops remains very challenging in general\, progress o
n classification of simple flops has been made by D. Li and A. Kanemitsu\,
focusing on their relation with Fano manifolds. Derived equivalence are c
onjectured for all\, and remain open in many cases. I review this\, and di
scuss approaches to proving new equivalences using variation of GIT\, in j
oint work with Weilin Su.\n
LOCATION:https://stable.researchseminars.org/talk/gic-seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yan Soibelman (Kansas State University)
DTSTART:20210303T160000Z
DTEND:20210303T173000Z
DTSTAMP:20260404T094939Z
UID:gic-seminar/6
DESCRIPTION:Title: Algebra of the infrared and Fukaya-Seidel categories with coeff
icients in perverse schobers\nby Yan Soibelman (Kansas State Universit
y) as part of GiC (Geometry in Cardiff) seminar\n\nLecture held in M/2.44a
\, 2nd Floor\, School of Mathematics.\n\nAbstract\nSeveral years ago physi
cists Gaitto\,Moore and Witten discovered a remarkable algebraic structure
underlying all 2d N=(2\,2) QFTs. They call it "the algebra of the infrare
d". Mathematical byproduct of that work was an alternative definition of t
he Fukaya-Seidel category (= Landau-Ginzburg model) of a Kahler manifold.
It is given in terms of the critical points of the superpotential of the L
G-model and gradient trajectories between them.\n\nIn the joint paper with
Kapranov and Kontsevich we interpreted the algebraic structure of Gaiotto
-Moore-Witten in terms of L-infinity and A-infinity algebras associated wi
th the secondary polytope of the convex hull of the set of critical values
of the superpotential.\n\nIn my talk I will explain how our approach can
be generalized to the case of Fukaya-Seidel categories with coefficients w
hich are perverse schobers. The talk is based on the recent work\, joint w
ith Kapranov and Soukhanov.\n
LOCATION:https://stable.researchseminars.org/talk/gic-seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Arkhipov (Aarhus)
DTSTART:20210217T160000Z
DTEND:20210217T173000Z
DTSTAMP:20260404T094939Z
UID:gic-seminar/7
DESCRIPTION:Title: Differential forms with logarithmic singularities and categoric
al braid group actions\nby Sergey Arkhipov (Aarhus) as part of GiC (Ge
ometry in Cardiff) seminar\n\nLecture held in M/2.44a\, 2nd Floor\, School
of Mathematics.\n\nAbstract\nBezrukavnikov and Riche studied the affine H
ecke category - a categorification of the affine braid group. One realizat
ion of this category is via equivariant coherent sheaves on the Steinberg
variety. Braid group generators are provided by explicit coherent sheaves.
However\, braid relations are proved in a rather indirect way - either by
a case by case analysis or by reduction to prime characteristic.\n\nUsing
linear Koszul duality\, we propose another realization of the affine Heck
e category via equivariant Omega-modules on the corresponding simple algeb
raic group G. A study of logarithmic differential forms on Bott-Samelson v
arieties gives a simple and uniform proof of braid relations. The material
of the talk is a joint work in progress with my student Sebastian Orsted.
\n
LOCATION:https://stable.researchseminars.org/talk/gic-seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Favero (Alberta)
DTSTART:20210317T160000Z
DTEND:20210317T173000Z
DTSTAMP:20260404T094939Z
UID:gic-seminar/8
DESCRIPTION:Title: Geometric invariant theory through group compactifications\, de
rived categories\, and derived algebraic geometry\nby David Favero (Al
berta) as part of GiC (Geometry in Cardiff) seminar\n\nLecture held in M/2
.44a\, 2nd Floor\, School of Mathematics.\n\nAbstract\nGiven a group $G$ a
cting on an algebraic variety $X$\, geometric invariant theory tells us ho
w to get a (or several) nice quotient space(s) from this data. Traditional
ly\, this comes from the choice of a $G$-equivariant line bundle on $X$. I
will discuss an alternative approach via partially compactifying the acti
on groupoid. One benefit of this viewpoint is that it produces a natural c
orrespondence between $X$ and itself. This allows us to embedd the derived
category of a given GIT quotient in the derived category of $[X/G]$ and m
ake comparisons (and sometimes deduce equivalences) between derived catego
ries of (the several) GIT quotients. If time permits\, I will also discuss
how to use this approach in the singular setting through the lens of deri
ved algebraic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/gic-seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miles Reid (Warwick)
DTSTART:20210421T150000Z
DTEND:20210421T163000Z
DTSTAMP:20260404T094939Z
UID:gic-seminar/9
DESCRIPTION:Title: The Tate-Oort group TO_p and moduli of Godeaux surfaces\nby
Miles Reid (Warwick) as part of GiC (Geometry in Cardiff) seminar\n\nLect
ure held in M/2.44a\, 2nd Floor\, School of Mathematics.\n\nAbstract\nThe
Tate-Oort group scheme $TO_p$ is\na group scheme of order $p$ defined in\n
mixed characteristic at $p$. It contains\nthe cyclic groups $\\mathbb{Z}/p
$ and $\\mu_p$ in\ncharacteristic $0$\, and the three group\nschemes $\\ma
thbb{Z}/p$\, $\\mu_p$\, and $\\alpha_p$ in\ncharacteristic $p$.\n\nGodeaux
surfaces $X$ in characteristic $5$ with\n$\\mathbb{Z}/5$\, $\\mu_5$\, an
d $\\alpha_5$ in $\\text{Pic} X$ were constructed\nrespectively by Lang\,
Miranda and Liedtke as\nquotients of quintic surfaces $Y_5$ in $\\mathbb{P
}^3$\nequivariant under an action of the dual group\nscheme $\\mu_5$\, $\\
mathbb{Z}/5$\, and $\\alpha_5$. All three of\nthese constructions can be p
ut together in a\nsingle deformation family\, together with the\nclassical
Godeaux surfaces. This is joint work\nwith KIM Soonyoung\, based in part
on her\n2014 Sogang Univ. thesis. See also https://homepages.warwick.ac.uk/~masda/TOp/.\n
LOCATION:https://stable.researchseminars.org/talk/gic-seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clemens Koppensteiner (Oxford)
DTSTART:20210707T150000Z
DTEND:20210707T163000Z
DTSTAMP:20260404T094939Z
UID:gic-seminar/10
DESCRIPTION:Title: The Heisenberg category of a category\, I\nby Clemens Kopp
ensteiner (Oxford) as part of GiC (Geometry in Cardiff) seminar\n\n\nAbstr
act\nIn this series of three talks we will discuss how to associate a Heis
enberg category to any smooth and proper dg category.\n\nIn this first int
roductory talk\, we will consider the geometric motivation for the constru
ction\, review the theory of Heisenberg algebras\, and look at some catego
rifications already in the literature. This is joint work with Ádám Gyen
ge and Timothy Logvinenko.\n
LOCATION:https://stable.researchseminars.org/talk/gic-seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ádám Gyenge (Alfréd Rényi\, Budapest)
DTSTART:20210714T150000Z
DTEND:20210714T163000Z
DTSTAMP:20260404T094939Z
UID:gic-seminar/11
DESCRIPTION:Title: The Heisenberg category of a category\, II\nby Ádám Gyen
ge (Alfréd Rényi\, Budapest) as part of GiC (Geometry in Cardiff) semina
r\n\n\nAbstract\nKhovanov introduced recently a categorification of the in
finite Heisenberg algebra associated\nwith the free boson or\, equivalentl
y\, a rank 1 lattice\, using a graphical construction involving planar dia
grams. We extend Khovanov’s graphical construction to derived categories
of smooth and projective varieties or\, more generally\, to categories ha
ving a Serre functor. In our case the underlying lattice will be the (nume
rical) Grothendieck group of the category. We also obtain a 2-representati
on of our Heisenberg category on a categorical analogue of the Fock space.
Joint work with Clemens Koppensteiner and Timothy Logvinenko.\n
LOCATION:https://stable.researchseminars.org/talk/gic-seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Logvinenko (Cardiff)
DTSTART:20210721T150000Z
DTEND:20210721T163000Z
DTSTAMP:20260404T094939Z
UID:gic-seminar/12
DESCRIPTION:Title: The Heisenberg category of a category\, III\nby Timothy Lo
gvinenko (Cardiff) as part of GiC (Geometry in Cardiff) seminar\n\n\nAbstr
act\nIn this series of three talks we discuss how to associate a Heisenber
g category to any smooth and proper dg category.\n\nIn this final talk\, w
e will present the DG categorical version of our construction\, comparing
it to the additive case construction discussed in the previous talk. The m
ain challenge here is a lack of the genuine Serre functor\, and thus the n
ecessity of working with a homotopy one. We will discuss the unique featur
es of our construction introduced to overcome this and the other challenge
s we encountered. We will also discuss the applications\, as well as the r
easons for working in the DG setting in the first place. This is joint wor
k with Ádám Gyenge and Clemens Koppensteiner.\n
LOCATION:https://stable.researchseminars.org/talk/gic-seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophia Restad (Kansas State University)
DTSTART:20211110T160000Z
DTEND:20211110T173000Z
DTSTAMP:20260404T094939Z
UID:gic-seminar/13
DESCRIPTION:Title: Composing spherical twists\nby Sophia Restad (Kansas State
University) as part of GiC (Geometry in Cardiff) seminar\n\nLecture held
in M/2.44a\, 2nd Floor\, School of Mathematics.\n\nAbstract\nF. Barbacovi
proved that the composition of two spherical twists can itself arise as a
spherical twist\, with a natural choice of a source category. We examine t
his construction further. The construction is based around gluing two dg c
ategories along a certain bimodule. A natural question to ask is whether t
he gluing can be improved\, i.e. if choosing a different bimodule can lead
to a possibly simpler source category. We prove the answer is essentially
no.\n
LOCATION:https://stable.researchseminars.org/talk/gic-seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Barbacovi (UCL)
DTSTART:20211201T160000Z
DTEND:20211201T173000Z
DTSTAMP:20260404T094939Z
UID:gic-seminar/14
DESCRIPTION:Title: Spherical functors and the flop-flop autoequivalence\nby F
ederico Barbacovi (UCL) as part of GiC (Geometry in Cardiff) seminar\n\nLe
cture held in M/2.44a\, 2nd Floor\, School of Mathematics.\n\nAbstract\nBo
ndal—Orlov\, Kawamata conjecture predicts that certain birational transf
ormations called flops should induce derived equivalences. Using such equi
valences we can construct autoequivalences of derived categories which go
under the name of flop-flop autoequivalences. In this talk I will explain
how to realise the flop-flop autoequivalence as (the inverse of) a spheric
al twist around a spherical functor\, thus repackaging the so-called flop-
flop = twist formulas in a single framework. We will also survey some exam
ples of this construction where a splitting of the flop-flop autoequivalen
ce can be read off from the source category of the spherical functor.\n
LOCATION:https://stable.researchseminars.org/talk/gic-seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ed Segal (UCL)
DTSTART:20221215T160000Z
DTEND:20221215T173000Z
DTSTAMP:20260404T094939Z
UID:gic-seminar/15
DESCRIPTION:Title: A survey of hybrid models\nby Ed Segal (UCL) as part of Gi
C (Geometry in Cardiff) seminar\n\nLecture held in M/2.44a\, 2nd Floor\, S
chool of Mathematics.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/gic-seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ed Segal (UCL)
DTSTART:20211215T150000Z
DTEND:20211215T173000Z
DTSTAMP:20260404T094939Z
UID:gic-seminar/16
DESCRIPTION:Title: A survey of hybrid models\nby Ed Segal (UCL) as part of Gi
C (Geometry in Cardiff) seminar\n\nLecture held in M/2.44a\, 2nd Floor\, S
chool of Mathematics.\n\nAbstract\nThe Kuznetsov component of a Fano compl
ete intersection can be realized as a `hybrid model' - a category of matri
x factorizations on a vector bundle over weighted projective space. I'll e
xplain what all this means\, and then discuss some cases where the hybrid
model description can give us some geometric insight into the category.\n
LOCATION:https://stable.researchseminars.org/talk/gic-seminar/16/
END:VEVENT
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