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BEGIN:VEVENT
SUMMARY:Alexander Kuznetsov (Steklov Mathematical Institute)
DTSTART:20201102T160000Z
DTEND:20201102T170000Z
DTSTAMP:20260404T060945Z
UID:BIRS_20w5176/1
DESCRIPTION:Title: Rationality and derived categories of some Fano threefolds ove
r non-closed fields\nby Alexander Kuznetsov (Steklov Mathematical Inst
itute) as part of BIRS workshop: Derived\, Birational\, and Categorical Al
gebraic Geometry\n\n\nAbstract\nIn a joint work with Yu.Prokhorov we estab
lished rationality criteria for geometrically rational Fano threefolds ov
er non-closed fields of characteristic zero such that their geometric Pica
rd number is one. I will report on similar results for Fano threefolds who
se geometric Picard number is higher but the Picard number over the base f
ield is one. I will also describe the derived categories of these varietie
s over the base field and discuss the relation between their structure and
rationality properties.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5176/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rina Anno (Kansas State University)
DTSTART:20201102T170000Z
DTEND:20201102T180000Z
DTSTAMP:20260404T060945Z
UID:BIRS_20w5176/2
DESCRIPTION:Title: Generalized braid group actions\nby Rina Anno (Kansas Stat
e University) as part of BIRS workshop: Derived\, Birational\, and Categor
ical Algebraic Geometry\n\n\nAbstract\nConsider a diagrammatic category wh
ose objects are partitions of n and whose morphisms are braids with multip
licities where strands are allowed to merge and come apart\, so topologica
lly such a braid is a trivalent graph with boundary. In addition\, we add
framing on edges with multiplicities greater than 1. The usual (type A) br
aid group is then the group of automorphisms of (1\,1\,...\,1). We prove t
hat any DG enhanceable triangulated category D with a braid group action (
of which there are numerous examples in algebraic geometry) can be complet
ed to a representation of this diagrammatic category. We do this by constr
ucting a monad over D that is best described as the nil Hecke algebra gene
rated by the generators of the braid group action\, and considering suitab
le categories of modules over its "block subalgebras". If D=D(X)\, those m
odules would be complexes of sheaves on X with additional data. Similar st
ructures have been known before\, but they satisfy stronger conditions (i.
e. the twist of framing on a multiple strand being a shift\, which in our
construction is not the case). This is joint work in progress with Timothy
Logvinenko.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5176/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ludmil Katzarkov (University of Miami)
DTSTART:20201102T193000Z
DTEND:20201102T203000Z
DTSTAMP:20260404T060945Z
UID:BIRS_20w5176/3
DESCRIPTION:Title: New Birational Invariants\nby Ludmil Katzarkov (University
of Miami) as part of BIRS workshop: Derived\, Birational\, and Categorica
l Algebraic Geometry\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5176/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Maria Castravet (University of Paris-Saclay\, Versailles)
DTSTART:20201103T160000Z
DTEND:20201103T170000Z
DTSTAMP:20260404T060945Z
UID:BIRS_20w5176/4
DESCRIPTION:Title: Exceptional collections on moduli spaces of pointed stable rat
ional curves\nby Ana Maria Castravet (University of Paris-Saclay\, Ver
sailles) as part of BIRS workshop: Derived\, Birational\, and Categorical
Algebraic Geometry\n\n\nAbstract\nI will report on joint work with Jenia T
evelev answering a question of Orlov. We prove that the Grothendieck-Knud
sen moduli spaces of pointed stable rational curves with n markings admit
full\, exceptional collections which are invariant under the action of the
symmetric group $S_n$ permuting the markings. In particular\, a consequen
ce is that the K-group with integer coefficients is a permutation $S_n$-la
ttice.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5176/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wemyss (University of Glasgow)
DTSTART:20201103T170000Z
DTEND:20201103T180000Z
DTSTAMP:20260404T060945Z
UID:BIRS_20w5176/5
DESCRIPTION:Title: Stability conditions via Tits cone intersections\nby Micha
el Wemyss (University of Glasgow) as part of BIRS workshop: Derived\, Bira
tional\, and Categorical Algebraic Geometry\n\n\nAbstract\nI will explain
that stability conditions for general Gorenstein terminal 3-fold flops can
be described as a covering map over something reasonable. Basically\, pa
rt of the description comes from the movable cone\, and its image under te
nsoring by line bundles. Alas\, there is more. This extra stuff is not i
mmediately "birational" information\, and it is a bit mysterious\, but it
does have a very natural noncommutative interpretation\, with geometric co
rollaries. In the process of this\, I'll describe some of the new hyperpl
ane arrangements that arise\, which visually are very beautiful. If time
allows\, I will also explain some applications to autoequivalences and to
curve counting. This is joint work with Yuki Hirano\, and with Osamu Iyama
.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5176/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Izzet Coskun (UIC)
DTSTART:20201103T193000Z
DTEND:20201103T203000Z
DTSTAMP:20260404T060945Z
UID:BIRS_20w5176/6
DESCRIPTION:Title: Brill-Noether Theorems for moduli spaces of sheaves on surface
s\nby Izzet Coskun (UIC) as part of BIRS workshop: Derived\, Birationa
l\, and Categorical Algebraic Geometry\n\n\nAbstract\nIn this talk\, I wil
l discuss the problem of computing the cohomology of the general sheaf in
a moduli space of sheaves on a surface. I will concentrate on the case of
rational and K3 surfaces. The case of rational surfaces uses the stack of
prioritary sheaves and is joint work with Jack Huizenga. The case of K3 su
rfaces uses Bridgeland stability and is joint work with Howard Nuer and Ko
ta Yoshioka.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5176/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alice Rizzardo (University of Liverpool)
DTSTART:20201104T160000Z
DTEND:20201104T170000Z
DTSTAMP:20260404T060945Z
UID:BIRS_20w5176/7
DESCRIPTION:by Alice Rizzardo (University of Liverpool) as part of BIRS wo
rkshop: Derived\, Birational\, and Categorical Algebraic Geometry\n\nAbstr
act: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5176/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Barbacovi (UCL)
DTSTART:20201104T170000Z
DTEND:20201104T180000Z
DTSTAMP:20260404T060945Z
UID:BIRS_20w5176/8
DESCRIPTION:Title: A geometric presentation of the flop-flop autoequivalence as a
(n inverse) spherical twist\nby Federico Barbacovi (UCL) as part of BI
RS workshop: Derived\, Birational\, and Categorical Algebraic Geometry\n\n
\nAbstract\nThe homological interpretation of the Minimal Model Program co
njectures that flips should correspond to embeddings of derived categories
\, and flops to equivalences. Even if the conjecture doesn’t provide us
with a preferred functor\, there is an obvious choice: the pull-push via t
he fibre product. When this approach work\, we obtain an interesting autoe
quivalence of either side of the flop\, known as the “flop-flop autoequi
valence”. Understanding the structure of this functor (e.g. does it spli
t as the composition of simpler functors?) is an interesting problem\, and
it has been extensively studied. In this talk I will explain that there i
s a natural\, i.e. arising from the geometry\, way to realise the “flop-
flop autoequivalence” as the inverse of a spherical twist\, and that thi
s presentation can help us shed light on the structure of the autoequivale
nce itself.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5176/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuele Macri (Université Paris-Saclay)
DTSTART:20201104T193000Z
DTEND:20201104T203000Z
DTSTAMP:20260404T060945Z
UID:BIRS_20w5176/9
DESCRIPTION:Title: Antisymplectic involutions on projective hyperkähler manifold
s\nby Emanuele Macri (Université Paris-Saclay) as part of BIRS worksh
op: Derived\, Birational\, and Categorical Algebraic Geometry\n\n\nAbstrac
t\nAn involution of a projective hyperkähler manifold is called antisympl
ectic if it acts as (-1) on the space of global holomorphic 2-forms. I wil
l present joint work with Laure Flapan\, Kieran O'Grady\, and Giulia Sacc
à on antisymplectic involutions associated to polarizations of degree 2.
We study the number of connected components of the fixed loci and their ge
ometry.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5176/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Booth (University of Antwerp)
DTSTART:20201105T160000Z
DTEND:20201105T170000Z
DTSTAMP:20260404T060945Z
UID:BIRS_20w5176/10
DESCRIPTION:Title: Topological Hochschild cohomology for schemes\nby Matt Bo
oth (University of Antwerp) as part of BIRS workshop: Derived\, Birational
\, and Categorical Algebraic Geometry\n\n\nAbstract\nHochschild cohomology
behaves well over a field\, and its derived analogue Shukla cohomology be
haves well over any base commutative ring. Both are intimately related to
deformation theory. To study `nonlinear' deformations (e.g. Z/p^2 over Z/p
)\, one wants to study Mac Lane cohomology\, which introduces nonadditive
features. Mac Lane cohomology ought to be the same thing as topological Ho
chschild cohomology\; the analogue for homology is known by work of Pirash
vili and Waldhausen. I'll give a quick recap on topological Hochschild coh
omology\, which is morally just Shukla cohomology with base `ring' the sph
ere spectrum. I'll then give a definition of THH^* for schemes\, along wit
h some comparison theorems showing that for reasonable schemes\, any of th
e `obvious' definitions that one might make all agree. I'll give some (eas
y!) computations of THH^* for P^1 and P^2 over a finite field.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5176/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Addington (University of Oregon)
DTSTART:20201105T170000Z
DTEND:20201105T180000Z
DTSTAMP:20260404T060945Z
UID:BIRS_20w5176/11
DESCRIPTION:Title: A categorical sl_2 action on some moduli spaces of sheaves\nby Nicolas Addington (University of Oregon) as part of BIRS workshop: D
erived\, Birational\, and Categorical Algebraic Geometry\n\n\nAbstract\nWe
study certain sequences of moduli spaces of sheaves on K3 surfaces\, buil
ding on work of Markman\, Yoshioka\, and Nakajima. We show that these seq
uences can be given the structure of a geometric categorical sl_2 action i
n the sense of Cautis\, Kamnitzer\, and Licata. As a corollary\, we get a
n equivalence between derived categories of some moduli spaces that are bi
rational via stratified Mukai flops.\n\nI'll spend most of my time on a ni
ce example. This is joint with my student Ryan Takahashi.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5176/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jack Huizenga (Pennsylvania State University)
DTSTART:20201105T193000Z
DTEND:20201105T203000Z
DTSTAMP:20260404T060945Z
UID:BIRS_20w5176/12
DESCRIPTION:Title: The cohomology of general tensor products of vector bundles o
n the projective plane\nby Jack Huizenga (Pennsylvania State Universit
y) as part of BIRS workshop: Derived\, Birational\, and Categorical Algebr
aic Geometry\n\n\nAbstract\nUsing recent advances in the Minimal Model Pro
gram for moduli spaces of sheaves on the projective plane\, we compute the
cohomology of the tensor product of general semistable bundles on the pro
jective plane. More precisely\, let V and W be two general stable bundle
s\, and suppose the numerical invariants of W are sufficiently divisible.
We fully compute the cohomology of the tensor product of V and W. In part
icular\, we show that if W is exceptional\, then the tensor product of V a
nd W has at most one nonzero cohomology group determined by the slope and
the Euler characteristic\, generalizing foundational results of Drézet\,
Göttsche and Hirschowitz. We also characterize when the tensor product of
V and W is globally generated. Crucially\, our computation is canonical g
iven the birational geometry of the moduli space\, providing a roadmap for
tackling analogous problems on other surfaces. This is joint work with I
zzet Coskun and John Kopper.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5176/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inbar Klang (Columbia University)
DTSTART:20201106T170000Z
DTEND:20201106T180000Z
DTSTAMP:20260404T060945Z
UID:BIRS_20w5176/13
DESCRIPTION:Title: Hochschild homology for C_n -equivariant things\nby Inbar
Klang (Columbia University) as part of BIRS workshop: Derived\, Birationa
l\, and Categorical Algebraic Geometry\n\n\nAbstract\nAfter an overview of
Hochschild homology and topological \nHochschild homology\, I will talk a
bout about the twisted versions of \nthese that can be defined in the pres
ence of an action of a finite \ncyclic group. I will discuss joint work wi
th Adamyk\, Gerhardt\, Hess\, \nand Kong in which we develop a theoretical
framework and computational \ntools for these twisted Hochschild homology
theories.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5176/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sofia Tirabassi (Stockholm University)
DTSTART:20201106T193000Z
DTEND:20201106T203000Z
DTSTAMP:20260404T060945Z
UID:BIRS_20w5176/14
DESCRIPTION:Title: The Brauer group of bielliptic surfaces\nby Sofia Tirabas
si (Stockholm University) as part of BIRS workshop: Derived\, Birational\,
and Categorical Algebraic Geometry\n\n\nAbstract\nWe study the behavior
of the pullback map between the Brauer group of a bielliptic surface and t
hat of its canonical cover. This is joint work with E. Ferrari and. Vodrup
.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5176/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Bolognese (University of Sheffield)
DTSTART:20201106T160000Z
DTEND:20201106T170000Z
DTSTAMP:20260404T060945Z
UID:BIRS_20w5176/15
DESCRIPTION:Title: A partial compactification of the stability manifold\nby
Barbara Bolognese (University of Sheffield) as part of BIRS workshop: Deri
ved\, Birational\, and Categorical Algebraic Geometry\n\n\nAbstract\nBridg
eland stability manifolds of Calabi-Yau categories are of noticeable inter
est both in mathematics and in physics. By looking at some of the known ex
ample\, a pattern clearly emerges and gives a fairly precise description o
f how they look like. In particular\, they all seem to have missing loci\,
which tend to correspond to degenerate stability conditions vanishing on
spherical objects. Describing such missing strata is also interesting from
a mirror-symmetric perspective\, as they conjecturally parametrize intere
sting types of degenerations of complex structures. All the naive attempts
at constructing modular partial compactifications show how elusive and su
btle the problem in fact is: ideally\, the missing strata would correspond
to stability manifolds of quotient triangulated categories\, but establis
hing such correspondence on geometric level and viewing stability conditio
ns on quotients of the original triangulated category as suitable degenera
tions of stability conditions is not straightforward. In this talk\, I wil
l present method to construct such partial compactifications if some addit
ional hypoteses are satisfied\, by realizing our space of interest as a su
itable metric completion of the stability manifold.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5176/15/
END:VEVENT
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