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BEGIN:VEVENT
SUMMARY:Alastair Craw (University of Bath)
DTSTART:20201028T160000Z
DTEND:20201028T173000Z
DTSTAMP:20260422T225922Z
UID:gic-seminar/1
DESCRIPTION:Title: Gale duality and the linearisation map for quiver moduli\nby Alast
air 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\nAbstra
ct\nThe goal of the talk is to show you a beautiful matrix and then to exp
lain its geometric significance. This will enable me to explain why two ri
val geometric interpretations of `Reid's recipe' are equivalent. To begin\
, I'll set the scene by discussing the classical McKay correspondence in d
imension two and I'll go on to discuss how this extends naturally to dimen
sion three. I'll introduce Reid's recipe by studying the cyclic quotient s
ingularity of type 1/19(1\,3\,15)\, and this gives me the excuse to introd
uce the matrix that I've fallen in love with. I'll reveal the geometry tha
t this gorgeous matrix encodes\, and as a result\, we'll see that two conj
ectures for consistent dimer model algebras are equivalent.\n
LOCATION:https://researchseminars.org/talk/gic-seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daria Polyakova (University of Copenhagen)
DTSTART:20201111T160000Z
DTEND:20201111T173000Z
DTSTAMP:20260422T225922Z
UID:gic-seminar/2
DESCRIPTION:Title: Weakly monoidal structure for the DG-category of representations up to
homotopy\nby Daria Polyakova (University of Copenhagen) as part of Gi
C (Geometry in Cardiff) seminar\n\nLecture held in M/2.44a\, 2nd Floor\, S
chool of Mathematics.\n\nAbstract\nRepresentations up to homotopy of a gro
up G were introduced by Abad and Crainic. They form a DG-category Rep^h(G)
whose objects are A-infinity comodules over the coalgebra of functions on
G\, and whose morphisms are A-infinity Hom complexes. This category enhan
ces the derived category of ordinary representations. Abad-Crainic-Dherin
proved that the homotopy category of Rep^h(G) is monoidal. They posed a qu
estion to define an appropriate homotopy-coherent structure on the DG-cate
gory itself.I will explain how a family of polytopes controls morphisms of
A-infinity (co)modules. Then I will present a new observation that this f
amily is nothing else but freehedra\, a family constructed earlier by Sane
blidze for entirely different reasons as subdivisions of cubes. Abad-Crain
ic-Dherin monoidal structure appears to follow from Saneblidze’s diagona
l for freehedra. I will extend this diagonal to A-infinity coalgebra struc
ture. This is the first ingredient of a “weakly monoidal” structure th
at I obtain as a DG-lift of Abad-Crainic-Dherin monoidal structure.\n
LOCATION:https://researchseminars.org/talk/gic-seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agnieszka Bodzenta-Skibinska (Warsaw)
DTSTART:20201125T160000Z
DTEND:20201125T173000Z
DTSTAMP:20260422T225922Z
UID:gic-seminar/3
DESCRIPTION:Title: Exact categories and abelian envelopes\nby Agnieszka Bodzenta-Skib
inska (Warsaw) as part of GiC (Geometry in Cardiff) seminar\n\nLecture hel
d in M/2.44a\, 2nd Floor\, School of Mathematics.\n\nAbstract\nFor exact c
ategories I will develop a theory parallel to the theory well-known for tr
iangulated categories\; left and right admissible subcategories\, and (sem
i-orthogonal) decompositions. In particular\, I will introduce thin exact
categories\, i.e. exact categories will full exceptional collections. I wi
ll discuss left and right abelian envelopes of an exact category and will
show that highest weight categories are precisely the abelian envelopes of
thin exact categories. I will also discuss Ringel duality from this point
of view. This is joint work with A. Bondal.\n
LOCATION:https://researchseminars.org/talk/gic-seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Thompson (Loughborough)
DTSTART:20201209T160000Z
DTEND:20201209T173000Z
DTSTAMP:20260422T225922Z
UID:gic-seminar/4
DESCRIPTION:Title: Mirror symmetry for fibrations and degenerations\nby Alan Thompson
(Loughborough) as part of GiC (Geometry in Cardiff) seminar\n\nLecture he
ld in M/2.44a\, 2nd Floor\, School of Mathematics.\n\nAbstract\nIn a 2004
paper\, Tyurin briefly hinted at a novel relationship between Calabi-Yau m
irror symmetry and the Fano-LG correspondence. More specifically\, if one
can degenerate a Calabi-Yau manifold to a pair of (quasi-)Fanos\, then one
expects to be able to express the mirror Calabi-Yau in terms of the corre
sponding Landau-Ginzburg models. Some details of this correspondence were
worked out by C. F. Doran\, A. Harder\, and I in a 2017 paper\, but much r
emains mysterious.\n\nIn this talk I will describe recent attempts to bett
er understand this picture\, and how it hints at a broader mirror symmetri
c correspondence between degeneration and fibration structures. As an exam
ple of this correspondence\, I will discuss the question of finding mirror
s to certain exact sequences which describe the Hodge theory of degenerati
ons.\n\nThe material in this talk is joint work in progress with C. F. Dor
an.\n
LOCATION:https://researchseminars.org/talk/gic-seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Will Donovan (Tsinghua)
DTSTART:20210203T160000Z
DTEND:20210203T173000Z
DTSTAMP:20260422T225922Z
UID:gic-seminar/5
DESCRIPTION:Title: Classification of simple flops and variation of GIT\nby Will Donov
an (Tsinghua) as part of GiC (Geometry in Cardiff) seminar\n\nLecture held
in M/2.44a\, 2nd Floor\, School of Mathematics.\n\nAbstract\nThough class
ification of flops remains very challenging in general\, progress on class
ification of simple flops has been made by D. Li and A. Kanemitsu\, focusi
ng on their relation with Fano manifolds. Derived equivalence are conjectu
red for all\, and remain open in many cases. I review this\, and discuss a
pproaches to proving new equivalences using variation of GIT\, in joint wo
rk with Weilin Su.\n
LOCATION:https://researchseminars.org/talk/gic-seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yan Soibelman (Kansas State University)
DTSTART:20210303T160000Z
DTEND:20210303T173000Z
DTSTAMP:20260422T225922Z
UID:gic-seminar/6
DESCRIPTION:Title: Algebra of the infrared and Fukaya-Seidel categories with coefficients
in perverse schobers\nby Yan Soibelman (Kansas State University) as p
art of GiC (Geometry in Cardiff) seminar\n\nLecture held in M/2.44a\, 2nd
Floor\, School of Mathematics.\n\nAbstract\nSeveral years ago physicists G
aitto\,Moore and Witten discovered a remarkable algebraic structure underl
ying all 2d N=(2\,2) QFTs. They call it "the algebra of the infrared". Mat
hematical byproduct of that work was an alternative definition of the Fuka
ya-Seidel category (= Landau-Ginzburg model) of a Kahler manifold. It is g
iven in terms of the critical points of the superpotential of the LG-model
and gradient trajectories between them.\n\nIn the joint paper with Kapran
ov and Kontsevich we interpreted the algebraic structure of Gaiotto-Moore-
Witten in terms of L-infinity and A-infinity algebras associated with 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 gene
ralized to the case of Fukaya-Seidel categories with coefficients which ar
e perverse schobers. The talk is based on the recent work\, joint with Kap
ranov and Soukhanov.\n
LOCATION:https://researchseminars.org/talk/gic-seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Arkhipov (Aarhus)
DTSTART:20210217T160000Z
DTEND:20210217T173000Z
DTSTAMP:20260422T225922Z
UID:gic-seminar/7
DESCRIPTION:Title: Differential forms with logarithmic singularities and categorical brai
d group actions\nby Sergey Arkhipov (Aarhus) as part of GiC (Geometry
in Cardiff) seminar\n\nLecture held in M/2.44a\, 2nd Floor\, School of Mat
hematics.\n\nAbstract\nBezrukavnikov and Riche studied the affine Hecke ca
tegory - a categorification of the affine braid group. One realization of
this category is via equivariant coherent sheaves on the Steinberg variety
. Braid group generators are provided by explicit coherent sheaves. Howeve
r\, 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 Hecke categ
ory via equivariant Omega-modules on the corresponding simple algebraic gr
oup G. A study of logarithmic differential forms on Bott-Samelson varietie
s 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://researchseminars.org/talk/gic-seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Favero (Alberta)
DTSTART:20210317T160000Z
DTEND:20210317T173000Z
DTSTAMP:20260422T225922Z
UID:gic-seminar/8
DESCRIPTION:Title: Geometric invariant theory through group compactifications\, derived c
ategories\, and derived algebraic geometry\nby David Favero (Alberta)
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 $G$ acting o
n an algebraic variety $X$\, geometric invariant theory tells us how to ge
t a (or several) nice quotient space(s) from this data. Traditionally\, th
is comes from the choice of a $G$-equivariant line bundle on $X$. I will d
iscuss an alternative approach via partially compactifying the action grou
poid. One benefit of this viewpoint is that it produces a natural correspo
ndence between $X$ and itself. This allows us to embedd the derived catego
ry of a given GIT quotient in the derived category of $[X/G]$ and make com
parisons (and sometimes deduce equivalences) between derived categories 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 derived alg
ebraic geometry.\n
LOCATION:https://researchseminars.org/talk/gic-seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miles Reid (Warwick)
DTSTART:20210421T150000Z
DTEND:20210421T163000Z
DTSTAMP:20260422T225922Z
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\nLecture hel
d in M/2.44a\, 2nd Floor\, School of Mathematics.\n\nAbstract\nThe Tate-Oo
rt group scheme $TO_p$ is\na group scheme of order $p$ defined in\nmixed c
haracteristic at $p$. It contains\nthe cyclic groups $\\mathbb{Z}/p$ and $
\\mu_p$ in\ncharacteristic $0$\, and the three group\nschemes $\\mathbb{Z}
/p$\, $\\mu_p$\, and $\\alpha_p$ in\ncharacteristic $p$.\n\nGodeaux surfac
es $X$ in characteristic $5$ with\n$\\mathbb{Z}/5$\, $\\mu_5$\, and $\\al
pha_5$ in $\\text{Pic} X$ were constructed\nrespectively by Lang\, Miranda
and Liedtke as\nquotients of quintic surfaces $Y_5$ in $\\mathbb{P}^3$\ne
quivariant under an action of the dual group\nscheme $\\mu_5$\, $\\mathbb{
Z}/5$\, and $\\alpha_5$. All three of\nthese constructions can be put toge
ther in a\nsingle deformation family\, together with the\nclassical Godeau
x 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://researchseminars.org/talk/gic-seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clemens Koppensteiner (Oxford)
DTSTART:20210707T150000Z
DTEND:20210707T163000Z
DTSTAMP:20260422T225922Z
UID:gic-seminar/10
DESCRIPTION:Title: The Heisenberg category of a category\, I\nby Clemens Koppenstein
er (Oxford) as part of GiC (Geometry in Cardiff) seminar\n\n\nAbstract\nIn
this series of three talks we will discuss how to associate a Heisenberg
category to any smooth and proper dg category.\n\nIn this first introducto
ry talk\, we will consider the geometric motivation for the construction\,
review the theory of Heisenberg algebras\, and look at some categorificat
ions already in the literature. This is joint work with Ádám Gyenge and
Timothy Logvinenko.\n
LOCATION:https://researchseminars.org/talk/gic-seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ádám Gyenge (Alfréd Rényi\, Budapest)
DTSTART:20210714T150000Z
DTEND:20210714T163000Z
DTSTAMP:20260422T225922Z
UID:gic-seminar/11
DESCRIPTION:Title: The Heisenberg category of a category\, II\nby Ádám Gyenge (Alf
réd Rényi\, Budapest) as part of GiC (Geometry in Cardiff) seminar\n\n\n
Abstract\nKhovanov introduced recently a categorification of the infinite
Heisenberg algebra associated\nwith the free boson or\, equivalently\, a r
ank 1 lattice\, using a graphical construction involving planar diagrams.
We extend Khovanov’s graphical construction to derived categories of smo
oth and projective varieties or\, more generally\, to categories having a
Serre functor. In our case the underlying lattice will be the (numerical)
Grothendieck group of the category. We also obtain a 2-representation of o
ur Heisenberg category on a categorical analogue of the Fock space. Joint
work with Clemens Koppensteiner and Timothy Logvinenko.\n
LOCATION:https://researchseminars.org/talk/gic-seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Logvinenko (Cardiff)
DTSTART:20210721T150000Z
DTEND:20210721T163000Z
DTSTAMP:20260422T225922Z
UID:gic-seminar/12
DESCRIPTION:Title: The Heisenberg category of a category\, III\nby Timothy Logvinenk
o (Cardiff) as part of GiC (Geometry in Cardiff) seminar\n\n\nAbstract\nIn
this series of three talks we discuss how to associate a Heisenberg categ
ory to any smooth and proper dg category.\n\nIn this final talk\, we will
present the DG categorical version of our construction\, comparing it to t
he additive case construction discussed in the previous talk. The main cha
llenge here is a lack of the genuine Serre functor\, and thus the necessit
y of working with a homotopy one. We will discuss the unique features of o
ur construction introduced to overcome this and the other challenges we en
countered. We will also discuss the applications\, as well as the reasons
for working in the DG setting in the first place. This is joint work with
Ádám Gyenge and Clemens Koppensteiner.\n
LOCATION:https://researchseminars.org/talk/gic-seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophia Restad (Kansas State University)
DTSTART:20211110T160000Z
DTEND:20211110T173000Z
DTSTAMP:20260422T225922Z
UID:gic-seminar/13
DESCRIPTION:Title: Composing spherical twists\nby Sophia Restad (Kansas State Univer
sity) 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 spheric
al twist\, with a natural choice of a source category. We examine this con
struction further. The construction is based around gluing two dg categori
es along a certain bimodule. A natural question to ask is whether the glui
ng can be improved\, i.e. if choosing a different bimodule can lead to a p
ossibly simpler source category. We prove the answer is essentially no.\n
LOCATION:https://researchseminars.org/talk/gic-seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Barbacovi (UCL)
DTSTART:20211201T160000Z
DTEND:20211201T173000Z
DTSTAMP:20260422T225922Z
UID:gic-seminar/14
DESCRIPTION:Title: Spherical functors and the flop-flop autoequivalence\nby Federico
Barbacovi (UCL) as part of GiC (Geometry in Cardiff) seminar\n\nLecture h
eld in M/2.44a\, 2nd Floor\, School of Mathematics.\n\nAbstract\nBondal—
Orlov\, Kawamata conjecture predicts that certain birational transformatio
ns called flops should induce derived equivalences. Using such equivalence
s we can construct autoequivalences of derived categories which go under t
he name of flop-flop autoequivalences. In this talk I will explain how to
realise the flop-flop autoequivalence as (the inverse of) a spherical twis
t around a spherical functor\, thus repackaging the so-called flop-flop =
twist formulas in a single framework. We will also survey some examples of
this construction where a splitting of the flop-flop autoequivalence can
be read off from the source category of the spherical functor.\n
LOCATION:https://researchseminars.org/talk/gic-seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ed Segal (UCL)
DTSTART:20221215T160000Z
DTEND:20221215T173000Z
DTSTAMP:20260422T225922Z
UID:gic-seminar/15
DESCRIPTION:Title: A survey of hybrid models\nby Ed Segal (UCL) as part of GiC (Geom
etry in Cardiff) seminar\n\nLecture held in M/2.44a\, 2nd Floor\, School o
f Mathematics.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/gic-seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ed Segal (UCL)
DTSTART:20211215T150000Z
DTEND:20211215T173000Z
DTSTAMP:20260422T225922Z
UID:gic-seminar/16
DESCRIPTION:Title: A survey of hybrid models\nby Ed Segal (UCL) as part of GiC (Geom
etry in Cardiff) seminar\n\nLecture held in M/2.44a\, 2nd Floor\, School o
f Mathematics.\n\nAbstract\nThe Kuznetsov component of a Fano complete int
ersection can be realized as a `hybrid model' - a category of matrix facto
rizations on a vector bundle over weighted projective space. I'll explain
what all this means\, and then discuss some cases where the hybrid model d
escription can give us some geometric insight into the category.\n
LOCATION:https://researchseminars.org/talk/gic-seminar/16/
END:VEVENT
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