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BEGIN:VEVENT
SUMMARY:Alexander Kuznetsov (Steklov Mathematical Institute)
DTSTART;VALUE=DATE-TIME:20201102T160000Z
DTEND;VALUE=DATE-TIME:20201102T170000Z
DTSTAMP;VALUE=DATE-TIME:20240328T223405Z
UID:BIRS_20w5176/1
DESCRIPTION:Title: Rationality and derived categories of some Fano threefolds over non-c
losed fields\nby Alexander Kuznetsov (Steklov Mathematical Institute)
as part of BIRS workshop: Derived\, Birational\, and Categorical Algebraic
Geometry\n\n\nAbstract\nIn a joint work with Yu.Prokhorov we established
rationality criteria for geometrically rational Fano threefolds over non-
closed fields of characteristic zero such that their geometric Picard numb
er is one. I will report on similar results for Fano threefolds whose geom
etric Picard number is higher but the Picard number over the base field is
one. I will also describe the derived categories of these varieties over
the base field and discuss the relation between their structure and ration
ality properties.\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5176/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rina Anno (Kansas State University)
DTSTART;VALUE=DATE-TIME:20201102T170000Z
DTEND;VALUE=DATE-TIME:20201102T180000Z
DTSTAMP;VALUE=DATE-TIME:20240328T223405Z
UID:BIRS_20w5176/2
DESCRIPTION:Title: Generalized braid group actions\nby Rina Anno (Kansas State Unive
rsity) as part of BIRS workshop: Derived\, Birational\, and Categorical Al
gebraic Geometry\n\n\nAbstract\nConsider a diagrammatic category whose obj
ects are partitions of n and whose morphisms are braids with multiplicitie
s where strands are allowed to merge and come apart\, so topologically suc
h a braid is a trivalent graph with boundary. In addition\, we add framing
on edges with multiplicities greater than 1. The usual (type A) braid gro
up is then the group of automorphisms of (1\,1\,...\,1). We prove that any
DG enhanceable triangulated category D with a braid group action (of whic
h there are numerous examples in algebraic geometry) can be completed to a
representation of this diagrammatic category. We do this by constructing
a monad over D that is best described as the nil Hecke algebra generated b
y the generators of the braid group action\, and considering suitable cate
gories of modules over its "block subalgebras". If D=D(X)\, those modules
would be complexes of sheaves on X with additional data. Similar structure
s 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 constru
ction is not the case). This is joint work in progress with Timothy Logvin
enko.\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5176/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ludmil Katzarkov (University of Miami)
DTSTART;VALUE=DATE-TIME:20201102T193000Z
DTEND;VALUE=DATE-TIME:20201102T203000Z
DTSTAMP;VALUE=DATE-TIME:20240328T223405Z
UID:BIRS_20w5176/3
DESCRIPTION:Title: New Birational Invariants\nby Ludmil Katzarkov (University of Mia
mi) as part of BIRS workshop: Derived\, Birational\, and Categorical Algeb
raic Geometry\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5176/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Maria Castravet (University of Paris-Saclay\, Versailles)
DTSTART;VALUE=DATE-TIME:20201103T160000Z
DTEND;VALUE=DATE-TIME:20201103T170000Z
DTSTAMP;VALUE=DATE-TIME:20240328T223405Z
UID:BIRS_20w5176/4
DESCRIPTION:Title: Exceptional collections on moduli spaces of pointed stable rational c
urves\nby Ana Maria Castravet (University of Paris-Saclay\, Versailles
) as part of BIRS workshop: Derived\, Birational\, and Categorical Algebra
ic Geometry\n\n\nAbstract\nI will report on joint work with Jenia Tevelev
answering a question of Orlov. We prove that the Grothendieck-Knudsen mod
uli spaces of pointed stable rational curves with n markings admit full\,
exceptional collections which are invariant under the action of the symmet
ric group $S_n$ permuting the markings. In particular\, a consequence is t
hat the K-group with integer coefficients is a permutation $S_n$-lattice.\
n
LOCATION:https://researchseminars.org/talk/BIRS_20w5176/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wemyss (University of Glasgow)
DTSTART;VALUE=DATE-TIME:20201103T170000Z
DTEND;VALUE=DATE-TIME:20201103T180000Z
DTSTAMP;VALUE=DATE-TIME:20240328T223405Z
UID:BIRS_20w5176/5
DESCRIPTION:Title: Stability conditions via Tits cone intersections\nby Michael Wemy
ss (University of Glasgow) as part of BIRS workshop: Derived\, Birational\
, and Categorical Algebraic Geometry\n\n\nAbstract\nI will explain that st
ability conditions for general Gorenstein terminal 3-fold flops can be des
cribed as a covering map over something reasonable. Basically\, part of t
he description comes from the movable cone\, and its image under tensoring
by line bundles. Alas\, there is more. This extra stuff is not immediat
ely "birational" information\, and it is a bit mysterious\, but it does ha
ve a very natural noncommutative interpretation\, with geometric corollari
es. In the process of this\, I'll describe some of the new hyperplane arr
angements that arise\, which visually are very beautiful. If time allows\
, I will also explain some applications to autoequivalences and to curve c
ounting. This is joint work with Yuki Hirano\, and with Osamu Iyama.\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5176/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Izzet Coskun (UIC)
DTSTART;VALUE=DATE-TIME:20201103T193000Z
DTEND;VALUE=DATE-TIME:20201103T203000Z
DTSTAMP;VALUE=DATE-TIME:20240328T223405Z
UID:BIRS_20w5176/6
DESCRIPTION:Title: Brill-Noether Theorems for moduli spaces of sheaves on surfaces\n
by Izzet Coskun (UIC) as part of BIRS workshop: Derived\, Birational\, and
Categorical Algebraic Geometry\n\n\nAbstract\nIn this talk\, I will discu
ss the problem of computing the cohomology of the general sheaf in a modul
i space of sheaves on a surface. I will concentrate on the case of rationa
l and K3 surfaces. The case of rational surfaces uses the stack of priorit
ary sheaves and is joint work with Jack Huizenga. The case of K3 surfaces
uses Bridgeland stability and is joint work with Howard Nuer and Kota Yosh
ioka.\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5176/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alice Rizzardo (University of Liverpool)
DTSTART;VALUE=DATE-TIME:20201104T160000Z
DTEND;VALUE=DATE-TIME:20201104T170000Z
DTSTAMP;VALUE=DATE-TIME:20240328T223405Z
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://researchseminars.org/talk/BIRS_20w5176/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Barbacovi (UCL)
DTSTART;VALUE=DATE-TIME:20201104T170000Z
DTEND;VALUE=DATE-TIME:20201104T180000Z
DTSTAMP;VALUE=DATE-TIME:20240328T223405Z
UID:BIRS_20w5176/8
DESCRIPTION:Title: A geometric presentation of the flop-flop autoequivalence as a(n inve
rse) spherical twist\nby Federico Barbacovi (UCL) as part of BIRS work
shop: Derived\, Birational\, and Categorical Algebraic Geometry\n\n\nAbstr
act\nThe homological interpretation of the Minimal Model Program conjectur
es 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 the fibr
e product. When this approach work\, we obtain an interesting autoequivale
nce of either side of the flop\, known as the “flop-flop autoequivalence
”. Understanding the structure of this functor (e.g. does it split as th
e composition of simpler functors?) is an interesting problem\, and it has
been extensively studied. In this talk I will explain that there is a nat
ural\, i.e. arising from the geometry\, way to realise the “flop-flop au
toequivalence” as the inverse of a spherical twist\, and that this prese
ntation can help us shed light on the structure of the autoequivalence its
elf.\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5176/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuele Macri (Université Paris-Saclay)
DTSTART;VALUE=DATE-TIME:20201104T193000Z
DTEND;VALUE=DATE-TIME:20201104T203000Z
DTSTAMP;VALUE=DATE-TIME:20240328T223405Z
UID:BIRS_20w5176/9
DESCRIPTION:Title: Antisymplectic involutions on projective hyperkähler manifolds\n
by Emanuele Macri (Université Paris-Saclay) as part of BIRS workshop: Der
ived\, Birational\, and Categorical Algebraic Geometry\n\n\nAbstract\nAn i
nvolution of a projective hyperkähler manifold is called antisymplectic i
f it acts as (-1) on the space of global holomorphic 2-forms. I will prese
nt joint work with Laure Flapan\, Kieran O'Grady\, and Giulia Saccà on an
tisymplectic involutions associated to polarizations of degree 2. We study
the number of connected components of the fixed loci and their geometry.\
n
LOCATION:https://researchseminars.org/talk/BIRS_20w5176/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Booth (University of Antwerp)
DTSTART;VALUE=DATE-TIME:20201105T160000Z
DTEND;VALUE=DATE-TIME:20201105T170000Z
DTSTAMP;VALUE=DATE-TIME:20240328T223405Z
UID:BIRS_20w5176/10
DESCRIPTION:Title: Topological Hochschild cohomology for schemes\nby Matt Booth (Un
iversity of Antwerp) as part of BIRS workshop: Derived\, Birational\, and
Categorical Algebraic Geometry\n\n\nAbstract\nHochschild cohomology behave
s well over a field\, and its derived analogue Shukla cohomology behaves w
ell over any base commutative ring. Both are intimately related to deforma
tion theory. To study `nonlinear' deformations (e.g. Z/p^2 over Z/p)\, one
wants to study Mac Lane cohomology\, which introduces nonadditive feature
s. Mac Lane cohomology ought to be the same thing as topological Hochschil
d cohomology\; the analogue for homology is known by work of Pirashvili an
d Waldhausen. I'll give a quick recap on topological Hochschild cohomology
\, which is morally just Shukla cohomology with base `ring' the sphere spe
ctrum. I'll then give a definition of THH^* for schemes\, along with some
comparison theorems showing that for reasonable schemes\, any of the `obvi
ous' definitions that one might make all agree. I'll give some (easy!) com
putations of THH^* for P^1 and P^2 over a finite field.\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5176/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Addington (University of Oregon)
DTSTART;VALUE=DATE-TIME:20201105T170000Z
DTEND;VALUE=DATE-TIME:20201105T180000Z
DTSTAMP;VALUE=DATE-TIME:20240328T223405Z
UID:BIRS_20w5176/11
DESCRIPTION:Title: A categorical sl_2 action on some moduli spaces of sheaves\nby N
icolas Addington (University of Oregon) as part of BIRS workshop: Derived\
, Birational\, and Categorical Algebraic Geometry\n\n\nAbstract\nWe study
certain sequences of moduli spaces of sheaves on K3 surfaces\, building on
work of Markman\, Yoshioka\, and Nakajima. We show that these sequences
can be given the structure of a geometric categorical sl_2 action in the s
ense of Cautis\, Kamnitzer\, and Licata. As a corollary\, we get an equiv
alence between derived categories of some moduli spaces that are birationa
l via stratified Mukai flops.\n\nI'll spend most of my time on a nice exam
ple. This is joint with my student Ryan Takahashi.\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5176/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jack Huizenga (Pennsylvania State University)
DTSTART;VALUE=DATE-TIME:20201105T193000Z
DTEND;VALUE=DATE-TIME:20201105T203000Z
DTSTAMP;VALUE=DATE-TIME:20240328T223405Z
UID:BIRS_20w5176/12
DESCRIPTION:Title: The cohomology of general tensor products of vector bundles on the p
rojective plane\nby Jack Huizenga (Pennsylvania State University) as p
art of BIRS workshop: Derived\, Birational\, and Categorical Algebraic Geo
metry\n\n\nAbstract\nUsing recent advances in the Minimal Model Program fo
r moduli spaces of sheaves on the projective plane\, we compute the cohomo
logy of the tensor product of general semistable bundles on the projective
plane. More precisely\, let V and W be two general stable bundles\, and
suppose the numerical invariants of W are sufficiently divisible. We full
y compute the cohomology of the tensor product of V and W. In particular\
, we show that if W is exceptional\, then the tensor product of V and W ha
s at most one nonzero cohomology group determined by the slope and the Eul
er characteristic\, generalizing foundational results of Drézet\, Göttsc
he and Hirschowitz. We also characterize when the tensor product of V and
W is globally generated. Crucially\, our computation is canonical given th
e birational geometry of the moduli space\, providing a roadmap for tackli
ng analogous problems on other surfaces. This is joint work with Izzet Co
skun and John Kopper.\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5176/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inbar Klang (Columbia University)
DTSTART;VALUE=DATE-TIME:20201106T170000Z
DTEND;VALUE=DATE-TIME:20201106T180000Z
DTSTAMP;VALUE=DATE-TIME:20240328T223405Z
UID:BIRS_20w5176/13
DESCRIPTION:Title: Hochschild homology for C_n -equivariant things\nby Inbar Klang
(Columbia University) as part of BIRS workshop: Derived\, Birational\, and
Categorical Algebraic Geometry\n\n\nAbstract\nAfter an overview of Hochsc
hild homology and topological \nHochschild homology\, I will talk about ab
out the twisted versions of \nthese that can be defined in the presence of
an action of a finite \ncyclic group. I will discuss joint work with Adam
yk\, Gerhardt\, Hess\, \nand Kong in which we develop a theoretical framew
ork and computational \ntools for these twisted Hochschild homology theori
es.\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5176/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sofia Tirabassi (Stockholm University)
DTSTART;VALUE=DATE-TIME:20201106T193000Z
DTEND;VALUE=DATE-TIME:20201106T203000Z
DTSTAMP;VALUE=DATE-TIME:20240328T223405Z
UID:BIRS_20w5176/14
DESCRIPTION:Title: The Brauer group of bielliptic surfaces\nby Sofia Tirabassi (Sto
ckholm University) as part of BIRS workshop: Derived\, Birational\, and Ca
tegorical Algebraic Geometry\n\n\nAbstract\nWe study the behavior of the
pullback map between the Brauer group of a bielliptic surface and that of
its canonical cover. This is joint work with E. Ferrari and. Vodrup.\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5176/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Bolognese (University of Sheffield)
DTSTART;VALUE=DATE-TIME:20201106T160000Z
DTEND;VALUE=DATE-TIME:20201106T170000Z
DTSTAMP;VALUE=DATE-TIME:20240328T223405Z
UID:BIRS_20w5176/15
DESCRIPTION:Title: A partial compactification of the stability manifold\nby Barbara
Bolognese (University of Sheffield) as part of BIRS workshop: Derived\, B
irational\, and Categorical Algebraic Geometry\n\n\nAbstract\nBridgeland s
tability manifolds of Calabi-Yau categories are of noticeable interest bot
h in mathematics and in physics. By looking at some of the known example\,
a pattern clearly emerges and gives a fairly precise description of how t
hey look like. In particular\, they all seem to have missing loci\, which
tend to correspond to degenerate stability conditions vanishing on spheric
al objects. Describing such missing strata is also interesting from a mirr
or-symmetric perspective\, as they conjecturally parametrize interesting t
ypes of degenerations of complex structures. All the naive attempts at con
structing modular partial compactifications show how elusive and subtle th
e problem in fact is: ideally\, the missing strata would correspond to sta
bility manifolds of quotient triangulated categories\, but establishing su
ch correspondence on geometric level and viewing stability conditions on q
uotients of the original triangulated category as suitable degenerations o
f stability conditions is not straightforward. In this talk\, I will prese
nt method to construct such partial compactifications if some additional h
ypoteses are satisfied\, by realizing our space of interest as a suitable
metric completion of the stability manifold.\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5176/15/
END:VEVENT
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