BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Alexander Kuznetsov (Steklov and HSE\, Moscow)
DTSTART:20201201T160000Z
DTEND:20201201T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/1
DESCRIPTION:Title: Simultaneous categorical resolutions of singularities\nby Alexan
der Kuznetsov (Steklov and HSE\, Moscow) as part of Derived seminar\n\nAbs
tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau (University Paris-Saclay)
DTSTART:20210112T160000Z
DTEND:20210112T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/2
DESCRIPTION:Title: Holomorphic curves\, Lagrangians\, and coherent sheaves\nby Pier
rick Bousseau (University Paris-Saclay) as part of Derived seminar\n\nAbst
ract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theo Raedschelders (Free University of Brussels)
DTSTART:20210119T160000Z
DTEND:20210119T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/3
DESCRIPTION:Title: A categorification of Galkin-Shinder's Y-F(Y) relation\nby Theo
Raedschelders (Free University of Brussels) as part of Derived seminar\n\n
\nAbstract\nFor a smooth cubic hypersurface Y\, Sergey Galkin and Evgeny S
hinder exhibited a relation between the naive motives of Y\, the Fano var
iety F(Y) of lines and the Hilbert scheme Y^{[2]} of two points on Y. This
relation has been shown to persist both on the level of rational Chow mot
ives and integral Hodge structures. In a joint work with Pieter Belmans an
d Lie Fu\, we lift this relation to derived categories by exhibiting a cor
responding semi-orthogonal decomposition for the derived category of Y^{[2
]}. I will explain how to obtain this semi-orthogonal decomposition from a
refinement of Bondal-Orlov's results on derived categories of flips and h
ow to further deduce an isomorphism of integral Chow motives using a recen
t result of Qingyuan Jiang.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jørgen Rennemo (University of Oslo)
DTSTART:20210126T160000Z
DTEND:20210126T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/4
DESCRIPTION:Title: K-theorietic sheaf-counting invariants of Quot^n(C^4)\nby Jørge
n Rennemo (University of Oslo) as part of Derived seminar\n\n\nAbstract\nC
onsider the Quot scheme parametrising length n quotients of the rank r tri
vial bundle on C^4. There's a natural torus action on this scheme\, for wh
ich the fix points are labelled by r-tuples of solid partitions of total s
ize n. Nekrasov and Piazzalunga have assigned rational function weights to
these fix points and conjectured a formula for the generating function of
weighted counts of fix points. Oh and Thomas have defined general K-theor
etic sheaf counting invariants for Calabi-Yau 4-folds and proved a torus l
ocalisation formula for these. We show that Nekrasov-Piazzalunga's weights
agree with weights coming from the Oh-Thomas localisation formula (matchi
ng up the signs is the tricky part). We use this to prove that Nekrasov-Pi
azzalunga's conjectured formula for the generating function is correct. Th
is is joint work with Martijn Kool.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Pertusi (University of Milan)
DTSTART:20210202T160000Z
DTEND:20210202T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/5
DESCRIPTION:Title: Cubic fourfolds and moduli spaces of O'Grady 10 type\nby Laura P
ertusi (University of Milan) as part of Derived seminar\n\n\nAbstract\nIn
this talk we study certain moduli spaces of semistable objects in the Kuzn
etsov component of a cubic fourfold. We show that they admit a symplectic
resolution \\tilde{M} which is a smooth projective hyperkaehler manifold d
eformation equivalent to the 10-dimensional example constructed by O’Gra
dy. As a first application\, we construct a birational model of \\tilde{M}
which is a compactification of the twisted intermediate Jacobian of the c
ubic fourfold. Secondly\, we show that \\tilde{M} is the MRC quotient of t
he main component of the Hilbert scheme of elliptic quintic curves in the
cubic fourfold\, as conjectured by Castravet. This is a joint work with Ch
unyi Li and Xiaolei Zhao.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Stapleton (University of California\, San Diego)
DTSTART:20210209T160000Z
DTEND:20210209T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/6
DESCRIPTION:Title: Studying Fano hypersurface with holomorphic forms\nby David Stap
leton (University of California\, San Diego) as part of Derived seminar\n\
nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ignacio Barros (University Paris-Saclay)
DTSTART:20210216T160000Z
DTEND:20210216T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/7
DESCRIPTION:Title: On the irrationality of moduli spaces of K3 surfaces\nby Ignacio
Barros (University Paris-Saclay) as part of Derived seminar\n\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qingyuan Jiang (University of Edinburgh)
DTSTART:20210223T160000Z
DTEND:20210223T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/8
DESCRIPTION:Title: On the derived categories of Quot-schemes of locally free quotients<
/a>\nby Qingyuan Jiang (University of Edinburgh) as part of Derived semina
r\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Bragg (University of California\, Berkeley)
DTSTART:20210302T160000Z
DTEND:20210302T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/9
DESCRIPTION:Title: Compactifications of supersingular twistor spaces\nby Daniel Bra
gg (University of California\, Berkeley) as part of Derived seminar\n\nAbs
tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gavril Farkas (Humboldt University of Berlin)
DTSTART:20210309T160000Z
DTEND:20210309T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/10
DESCRIPTION:Title: Moduli of K3 surfaces via cubic 4-folds\nby Gavril Farkas (Humb
oldt University of Berlin) as part of Derived seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alicia Lamarche (University of Utah)
DTSTART:20210316T160000Z
DTEND:20210316T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/11
DESCRIPTION:Title: Derived Categories\, Arithmetic\, and Rationality\nby Alicia La
marche (University of Utah) as part of Derived seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lenny Taelman (University of Amsterdam)
DTSTART:20210330T150000Z
DTEND:20210330T160000Z
DTSTAMP:20260404T092653Z
UID:DerSem/12
DESCRIPTION:Title: Deformations of Calabi-Yau categories\nby Lenny Taelman (Univer
sity of Amsterdam) as part of Derived seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Larson (Stanford University)
DTSTART:20210323T160000Z
DTEND:20210323T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/13
DESCRIPTION:Title: The rational Chow rings of M_7\, M_8\, and M_9\nby Hannah Larso
n (Stanford University) as part of Derived seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Neguţ (MIT)
DTSTART:20210406T150000Z
DTEND:20210406T160000Z
DTSTAMP:20260404T092653Z
UID:DerSem/14
DESCRIPTION:Title: Lie algebra actions on the Chow ring of Hilb(K3)\nby Andrei Neg
uţ (MIT) as part of Derived seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fei Xie (University of Edinburgh)
DTSTART:20210413T150000Z
DTEND:20210413T160000Z
DTSTAMP:20260404T092653Z
UID:DerSem/15
DESCRIPTION:Title: Nodal quintic del Pezzo threefolds and their derived categories
\nby Fei Xie (University of Edinburgh) as part of Derived seminar\n\nAbstr
act: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thorsten Beckmann (University of Bonn)
DTSTART:20210420T150000Z
DTEND:20210420T160000Z
DTSTAMP:20260404T092653Z
UID:DerSem/16
DESCRIPTION:Title: Derived categories of hyper-Kähler manifolds via the extended Muka
i lattice\nby Thorsten Beckmann (University of Bonn) as part of Derive
d seminar\n\n\nAbstract\nThe derived category of a K3 surface is governed
by its integral cohomology together with its Hodge structure and to object
s we can functorially assign a Mukai vector in this lattice. We show an an
alogous picture for higher-dimensional hyper-Kähler manifolds using the e
xtended Mukai lattice. In particular\, we construct a vector for certain o
bjects in the derived category taking values in the extended Mukai lattice
and we obtain a rank 25 integral lattice with a Hodge structure which is
a derived invariant for hyper-Kähler manifolds deformation-equivalent to
the Hilbert scheme of n points on a K3 surface.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Halpern-Leistner (Cornell University)
DTSTART:20210427T150000Z
DTEND:20210427T160000Z
DTSTAMP:20260404T092653Z
UID:DerSem/17
DESCRIPTION:Title: Window categories and wall crossing\nby Daniel Halpern-Leistner
(Cornell University) as part of Derived seminar\n\n\nAbstract\nThe D-equi
valence conjecture\, due to Bondal\, Orlov\, and Kawamata\, predicts that
a birational equivalence between smooth projective varieties that preserve
s the canonical bundle should induce an equivalence of derived categories
of coherent sheaves. I will give an overview of "window categories" in equ
ivariant derived categories of coherent sheaves\, which can be used to con
struct derived equivalences for birational transformations coming from var
iation of GIT quotient. I will then discuss how these were used recently t
o prove the D-equivalence conjecture for projective Calabi-Yau manifolds i
n the birational equivalence class of a moduli space of sheaves on a K3 su
rface.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lie Fu (Radboud University / Université Lyon 1)
DTSTART:20210608T150000Z
DTEND:20210608T160000Z
DTSTAMP:20260404T092653Z
UID:DerSem/18
DESCRIPTION:Title: Generalized Franchetta conjecture for certain families of K3 surfac
es and hyper-Kähler varieties\nby Lie Fu (Radboud University / Univer
sité Lyon 1) as part of Derived seminar\n\n\nAbstract\nIn 2013\, as an an
alogue of Franchetta's classical conjecture on the Picard group of the uni
versal genus g curve\, O'Grady asked whether the Chow group of zero-cycles
of the generic fiber of the universal genus-g K3 surface is cyclic. I wil
l discuss some recent progress that I obtained in collaboration with Later
veer and Vial on this conjecture as well as its higher dimensional version
for hyper-Kähler varieties. The main feature of our argument is the comb
ination of the projective geometry of cubic fourfolds on one hand and modu
li spaces of Bridgeland stable objects in their Kuznetsov components on th
e other hand.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soheyla Feyzbakhsh (Imperial College)
DTSTART:20210622T150000Z
DTEND:20210622T160000Z
DTSTAMP:20260404T092653Z
UID:DerSem/20
DESCRIPTION:Title: Rank r DT theory from rank 1\nby Soheyla Feyzbakhsh (Imperial C
ollege) as part of Derived seminar\n\n\nAbstract\nFix a Calabi-Yau 3-fold
X satisfying the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda\, such
as the quintic 3-fold. I will explain joint works in progress with Richar
d Thomas that aim to express Joyce’s generalised DT invariants counting
Gieseker semistable sheaves of any rank r on X in terms of those counting
sheaves of rank 1. By the MNOP conjecture\, the latter are determined by t
he Gromov-Witten invariants of X. Our technique is to use wall-crossing wi
th respect to weak Bridgeland stability conditions on X.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Perry (University of Michigan)
DTSTART:20210629T150000Z
DTEND:20210629T160000Z
DTSTAMP:20260404T092653Z
UID:DerSem/21
DESCRIPTION:Title: Serre functors of semiorthogonal components\nby Alexander Perry
(University of Michigan) as part of Derived seminar\n\n\nAbstract\nThe Se
rre functor of a triangulated category is one of its most important invari
ants\, playing the role of the dualizing complex of a variety in noncommut
ative algebraic geometry. I will explain how to describe the Serre functor
s of many semiorthogonal components of varieties in terms of spherical twi
sts\, with applications to a dimension formula for Kuznetsov components of
complete intersections conjectured by Katzarkov and Kontsevich\, to the n
onexistence of Serre invariant stability conditions\, and to the construct
ion of Calabi-Yau categories as crepant contractions. This is joint work w
ith Alexander Kuznetsov.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Addington (University of Oregon)
DTSTART:20210601T150000Z
DTEND:20210601T160000Z
DTSTAMP:20260404T092653Z
UID:DerSem/22
DESCRIPTION:Title: Derived autoequivalences of moduli spaces of sheaves on K3 surfaces
\nby Nicolas Addington (University of Oregon) as part of Derived semin
ar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (MIT)
DTSTART:20210504T150000Z
DTEND:20210504T160000Z
DTSTAMP:20260404T092653Z
UID:DerSem/23
DESCRIPTION:Title: Geometry of the Gopakumar-Vafa theory.\nby Junliang Shen (MIT)
as part of Derived seminar\n\n\nAbstract\nMotivated by classical enumerati
ve geometry and mathematical physics\, counting curves in Calabi-Yau 3-fol
ds has been studied intensively for decades\, including Gromov-Witten theo
ry and Donaldson-Thomas theory. In recent years\, mathematical theory (by
Hosono-Saito-Takahashi\, Kiem-Li\, Maulik-Toda etc) has been developed to
realize the idea of Gopakumar and Vafa to recover the curve-counting invar
iants using the geometry of 1-dimensional sheaves. These developments shed
new light on both enumerative geometry and the classical geometry of the
relevant moduli spaces. I will discuss 3 particular cases (1) Higgs bundle
s (2) K3 surfaces\, and (3) CP^2\, where the Gopakumar-Vafa theory inter
acts with some other structures and conjectures in a surprising way.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georg Oberdieck (University of Bonn)
DTSTART:20210615T150000Z
DTEND:20210615T160000Z
DTSTAMP:20260404T092653Z
UID:DerSem/24
DESCRIPTION:Title: Another visit to the Donaldson-Thomas theory of K3xE\nby Georg
Oberdieck (University of Bonn) as part of Derived seminar\n\n\nAbstract\nI
n this talk we consider the (reduced) Donaldson-Thomas theory of the produ
ct of a K3 surface and an elliptic curve. In rank 1\, these invariants can
be viewed as enumerating algebraic curves and are known for fiber classes
over the elliptic curve (work of Pandharipande and Thomas)\, and for clas
ses primitive over the K3 (work of Pixton\, Shen and myself). I will expla
in how to extend these results to arbitrary curve classes. If time permits
\, I will also give an outlook on the higher rank case (work in progress).
\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ed Segal (University College London)
DTSTART:20210518T150000Z
DTEND:20210518T160000Z
DTSTAMP:20260404T092653Z
UID:DerSem/25
DESCRIPTION:Title: Mirrors to surfaces and twisted derived categories\nby Ed Segal
(University College London) as part of Derived seminar\n\n\nAbstract\nPun
ctured surfaces are the simplest class of symplectic manifolds and there a
re many constructions of homological mirrors for them\, i.e. constructions
in algebraic geometry of a category equivalent to the Fukaya category of
the surface. To make the Fukaya category Z-graded\, not just Z/2-graded\,
you need to choose a line-field on the surface. I'll explain what this cho
ice corresponds to in (some of) the mirror constructions\, it leads to a k
ind of twisted derived category which doesn't seem to have been widely stu
died.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Stellari (Università di Milano)
DTSTART:20210511T150000Z
DTEND:20210511T160000Z
DTSTAMP:20260404T092653Z
UID:DerSem/26
DESCRIPTION:Title: Uniqueness of enhancements for derived and geometric categories
\nby Paolo Stellari (Università di Milano) as part of Derived seminar\n\n
\nAbstract\nIn this talk we address several open questions and generalize
the\nexisting results about the uniqueness of enhancements for triangulate
d\ncategories which arise as derived categories of abelian categories or\n
from geometric contexts. If time permits\, we will also discuss applicatio
ns to the description of exact equivalences. This is joint\nwork with A. C
anonaco and A. Neeman.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitrii Pirozhkov (Université de Paris)
DTSTART:20210525T150000Z
DTEND:20210525T160000Z
DTSTAMP:20260404T092653Z
UID:DerSem/27
DESCRIPTION:Title: Stably semiorthogonally indecomposable varieties\nby Dmitrii Pi
rozhkov (Université de Paris) as part of Derived seminar\n\n\nAbstract\nA
triangulated category is said to be indecomposable if it admits no nontri
vial semiorthogonal decompositions. For a derived category of coherent she
aves on a variety Y\, we propose a stronger condition\, which implies\, am
ong other things\, that for any variety X\, any semiorthogonal decompositi
on of the product X x Y is induced from a decomposition of X. For X = {pt}
this implies the usual indecomposability. We show that varieties with fin
ite Albanese morphism\, e.g.\, curves of positive genus\, are stably semio
rthogonally indecomposable in this sense. From this\, we deduce the non-ex
istence of phantom subcategories in the product surfaces C x P^1\, where C
is a smooth projective curve of positive genus\, and in some other exampl
es as well.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Schnell (Stony Brook)
DTSTART:20211012T150000Z
DTEND:20211012T160000Z
DTSTAMP:20260404T092653Z
UID:DerSem/28
DESCRIPTION:Title: Finiteness for self-dual classes in variations of Hodge structure\nby Christian Schnell (Stony Brook) as part of Derived seminar\n\n\nAbs
tract\nI will talk about a new finiteness theorem for variations of Hodge
structure. It is a generalization of the Cattani-Deligne-Kaplan theorem fr
om Hodge classes to so-called self-dual (and anti-self-dual) classes. For
example\, among integral cohomology classes of degree 4\, those of type (4
\,0) + (2\,2) + (0\,4) are self-dual\, and those of type (3\,1) + (1\,3) a
re anti-self-dual. The result is suggested by considerations in theoretica
l physics\, and the proof uses o-minimality and the definability of period
mappings. This is joint work with Benjamin Bakker\, Thomas Grimm\, and Ja
cob Tsimerman.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastián Torres (IMSA)
DTSTART:20211019T150000Z
DTEND:20211019T160000Z
DTSTAMP:20260404T092653Z
UID:DerSem/29
DESCRIPTION:Title: The BGMN conjecture via windows and stable pairs\nby Sebastián
Torres (IMSA) as part of Derived seminar\n\n\nAbstract\nLet C be a smooth
projective curve of genus at least 2 and let N be the moduli space of sta
ble rank-two bundles on C of odd degree. We construct a semi-orthogonal de
composition in the derived category of N conjectured by Narasimhan and by
Belmans\, Galkin and Mukhopadhyay. It contains two copies of the i-th symm
etric power of C for i=0\,...\,g-2\, one copy of the (g-1)-st symmetric po
wer\, and possibly a semi-orthogonal complement to all those blocks. This
complement is expected to be trivial by the BGMN conjecture. Our approach
is based on an analysis of wall-crossing between moduli spaces of stable p
airs\, combining classical vector bundles techniques with the method of wi
ndows. This is joint work with Jenia Tevelev.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoon-Joo Kim (Stony Brook)
DTSTART:20211207T160000Z
DTEND:20211207T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/30
DESCRIPTION:Title: The dual Lagrangian fibration of compact hyper-Kähler manifolds\nby Yoon-Joo Kim (Stony Brook) as part of Derived seminar\n\n\nAbstract\
nA compact hyper-Kähler manifold is a higher dimensional generalization o
f K3 surfaces. An elliptic fibration of a K3 surface correspondingly gener
alizes to the so-called Lagrangian fibration of a compact hyper-Kähler ma
nifold. It is known that an elliptic fibration of a K3 surface is always "
self-dual" in a certain sense. This turns out to be not the case for highe
r-dimensional Lagrangian fibrations. In this talk\, I will propose a const
ruction for the dual Lagrangian fibration of all currently known examples
of compact hyper-Kähler manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Thomas (Imperial College London)
DTSTART:20211109T160000Z
DTEND:20211109T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/31
DESCRIPTION:Title: Higher rank DT theory from curve counts\nby Richard Thomas (Imp
erial College London) as part of Derived seminar\n\n\nAbstract\nFix a Cala
bi-Yau 3-fold X. Its DT invariants count stable bundles and sheaves on X.
The generalised DT invariants of Joyce-Song count semistable bundles and s
heaves on X. I will describe work with Soheyla Feyzbakhsh using the weak s
tability conditions of Bayer-Macrì -Toda to show these generalised DT inv
ariants in any rank r can be written in terms of rank 1 invariants. By the
MNOP conjecture the latter are determined by the GW invariants of X.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pieter Belmans (University of Luxembourg)
DTSTART:20211116T160000Z
DTEND:20211116T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/32
DESCRIPTION:Title: The Hirzebruch isomorphism for exotic noncommutative surfaces\n
by Pieter Belmans (University of Luxembourg) as part of Derived seminar\n\
n\nAbstract\nThe isomorphism between the first Hirzebruch surface and the
blowup of the projective plane in a point is a well-known result\, due to
Hirzebruch. From a numerical classification of Grothendieck groups of rank
4 which behave like the Grothendieck group of a smooth projective surface
we expect the existence of exotic noncommutative surfaces\, which are sur
faces not obtained via deforming commutative surfaces. There exist two con
structions: one as an asymmetric noncommutative P^1-bundle (due to de Than
hoffer--Presotto)\, one as a fat point blowup (joint work with Presotto).
I will explain how a Hirzebruch isomorphism for these two families of surf
aces exists as an equivalence of (derived) categories\, and how this is re
lated to some very classical geometry of linear systems. This is joint wor
k with Dennis Presotto and Michel Van den Bergh.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Smirnov (Augsburg and MPI Bonn)
DTSTART:20211123T160000Z
DTEND:20211123T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/33
DESCRIPTION:Title: Residual categories of Grassmannians\nby Maxim Smirnov (Augsbur
g and MPI Bonn) as part of Derived seminar\n\n\nAbstract\nWe will define r
esidual categories of Lefschetz exceptional collections and discuss some c
onjectural relations between the structure of quantum cohomology and resid
ual categories. We will illustrate this relationship in the case of some i
sotropic Grassmannians. Based on joint works with Alexander Kuznetsov.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Špela Špenko (Vrije University Brussel)
DTSTART:20211130T160000Z
DTEND:20211130T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/34
DESCRIPTION:Title: Comparing commutative and noncommutative resolutions of singulariti
es\nby Špela Špenko (Vrije University Brussel) as part of Derived se
minar\n\n\nAbstract\nQuotient varieties for reductive groups admit the Kir
wan (partial) resolution of singularities\, and quite often also a noncomm
utative crepant resolution (NCCR). We will construct a (Orlov's type) semi
-orthogonal decomposition of the derived category of the Kirwan resolution
which has the derived category of the NCCR as a component\, and where oth
er components also have a concrete (almost) geometric description. This is
a joint work with Michel Van den Bergh.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Yue Yu (Caltech)
DTSTART:20211102T160000Z
DTEND:20211102T170000Z
DTSTAMP:20260404T092653Z
UID:DerSem/35
DESCRIPTION:Title: Non-archimedean Quantum K-invariants\nby Tony Yue Yu (Caltech)
as part of Derived seminar\n\n\nAbstract\nWe construct quantum K-invariant
s in non-archimedean analytic geometry. Our approach differs from the clas
sical one in algebraic geometry via perfect obstruction theory. Instead\,
we build on our previous works on the foundation of derived non-archimedea
n geometry\, the representability theorem and Gromov compactness. We obtai
n a list of natural geometric relations between the stacks of stable maps\
, directly at the derived level\, with respect to elementary operations on
graphs\, namely\, products\, cutting edges\, forgetting tails and contrac
ting edges. They imply immediately the corresponding properties of K-theor
etic invariants. The derived approach produces highly intuitive statements
and functorial proofs. The flexibility of our derived approach to quantum
K-invariants allows us to impose not only simple incidence conditions for
marked points\, but also incidence conditions with multiplicities. This l
eads to a new set of enumerative invariants. Our motivations come from non
-archimedean enumerative geometry and mirror symmetry. Joint work with M P
orta.\n
LOCATION:https://stable.researchseminars.org/talk/DerSem/35/
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