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BEGIN:VEVENT
SUMMARY:Libby Taylor (Stanford University)
DTSTART:20200914T200000Z
DTEND:20200914T210000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/1
DESCRIPTION:Title: Fourier-Mukai theory for stacky genus 1 curves\nby Libby Taylor
(Stanford University) as part of American Graduate Student Algebraic Geome
try Seminar\n\n\nAbstract\nWe will discuss a theory of derived equivalence
s for certain Artin stacks. We will apply this theory to study the derive
d categories of genus 1 curves and of their Picard stacks. Some questions
we will answer: when are two $\\mathbb{G}_m$ gerbes over genus 1 curves d
erived equivalent? If $C$ and $C'$ are derived equivalent curves\, can we
prove that $C'$ is the moduli space of certain vector bundles on $C$? If
$C'=Pic^d(C)$\, is it true that $C=Pic^f(C')$ for some $f$\, and if so\,
can we use Fourier-Mukai theory to find $f$? (Spoilers: when one is $Pic^d
$ of the other\; yes\; yes and yes.) This is joint work with Soumya Sanka
r.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Chen (Stony Brook University)
DTSTART:20200921T200000Z
DTEND:20200921T210000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/2
DESCRIPTION:Title: A generic talk on irrationality\nby Nathan Chen (Stony Brook Uni
versity) as part of American Graduate Student Algebraic Geometry Seminar\n
\n\nAbstract\nGiven a smooth projective variety\, there are two natural qu
estions that can be asked: (1) How can we determine when it is rational? a
nd (2) If it is not rational\, can we measure how far it is from being rat
ional? There has been a great deal of recent progress towards developing i
nvariants with the second question in mind. We will explain some new techn
iques involved in bounding these invariants for certain classes of varieti
es.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastián Torres (UMass Amherst)
DTSTART:20200928T200000Z
DTEND:20200928T210000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/3
DESCRIPTION:Title: Bott vanishing using GIT and quantization\nby Sebastián Torres
(UMass Amherst) as part of American Graduate Student Algebraic Geometry Se
minar\n\n\nAbstract\nA smooth projective variety is said to satisfy Bott v
anishing if $\\Omega^j\\otimes L$ has no higher cohomology for every $j$ a
nd every ample line bundle $L$. This is a very restrictive property\, and
there are few non-toric examples known to satisfy it. I will present a new
class of examples obtained as smooth GIT quotients of $(\\mathbb{P}^{1})^
n$. For this\, I will need to use the work by Teleman and Halpern-Leistner
about the derived category of a GIT quotient\, and explain how this allow
s us\, in some cases\, to compute cohomologies directly in an ambient quot
ient stack.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sukjoo Lee (University of Pennsylvania)
DTSTART:20201005T200000Z
DTEND:20201005T210000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/4
DESCRIPTION:Title: P=W phenomena in Fano mirror symmetry\nby Sukjoo Lee (University
of Pennsylvania) as part of American Graduate Student Algebraic Geometry
Seminar\n\n\nAbstract\n$P=W$ phenomena\, originated from non-abelian Hodge
theory\, has been recently formulated by A. Harder\, L. Katzarkov and V.
Przyjalkowski in the context of mirror symmetry of log Calabi-Yau manifold
s. In particular\, if the log Calabi-Yau manifold admits Fano compactifica
tion $(X\,D)$ with smooth anti-canonical divisor $D$\, we can study $P=W$
phenomena from categorical viewpoint under the Fano/LG correspondence. In
this talk\, we will go over the story and generalize to the case where $D
$ has more than one component.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiyue Li (Brown University)
DTSTART:20201019T200000Z
DTEND:20201019T210000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/5
DESCRIPTION:Title: Topology of tropical moduli spaces of weighted stable curves in high
er genus\nby Shiyue Li (Brown University) as part of American Graduate
Student Algebraic Geometry Seminar\n\n\nAbstract\nTropical moduli spaces
of weighted stable curves are moduli spaces of metric weighted marked grap
hs satisfying certain stability conditions. The space of tropical weighted
curves of genus g and volume 1 is the dual complex of the divisor of sing
ular curves in Hassett's moduli space of weighted stable genus g curves. O
ne can derive plenty of topological properties of the Hassett spaces by st
udying the topology of these dual complexes. In this talk (and in a paper
coming soon)\, we show that the spaces of tropical weighted curves of genu
s g and volume 1 are simply-connected for all genus greater than zero and
all rational weights\, under the framework of symmetric Delta-complexes an
d via a result by Allcock-Corey-Payne 19. We also calculate the Euler char
acteristics of these spaces and the top weight Euler characteristics of th
e classical Hassett spaces in terms of the combinatorics of the weights.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Olander (Columbia University)
DTSTART:20201026T200000Z
DTEND:20201026T210000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/6
DESCRIPTION:Title: Orlov's Theorem for Smooth Proper Varieties\nby Noah Olander (Co
lumbia University) as part of American Graduate Student Algebraic Geometry
Seminar\n\n\nAbstract\nOrlov proved in 1996 that many functors between de
rived categories of smooth projective varieties are represented by kernels
\, i.e.\, complexes on the product. Since then\, Orlov's theorem has had a
profound influence on algebraic geometry. In this talk\, we discuss Orlov
's proof as well as some technical advances and new ideas which shed light
on it\, leading to an extension of the theorem to the smooth proper case.
\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raymond Cheng (Columbia University)
DTSTART:20201102T210000Z
DTEND:20201102T220000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/7
DESCRIPTION:Title: q-bic Hypersurfaces\nby Raymond Cheng (Columbia University) as p
art of American Graduate Student Algebraic Geometry Seminar\n\n\nAbstract\
nOne of the funny features of geometry in positive characteristic is that
equations behave of lower degree than they seem. In this talk\, I would li
ke to convince you that Fermat hypersurfaces of degree $q + 1$\, $q$ a pow
er of the ground field characteristic\, is geometrically analogous to quad
ric and cubic hypersurfaces. To me\, this example suggests a theme with wh
ich to understand some geometric features in positive characteristic\, lik
e the unexpected abundance of rational curves in certain varieties.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Marquand (Stony Brook University)
DTSTART:20201109T210000Z
DTEND:20201109T220000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/8
DESCRIPTION:Title: Hyperplane sections and Moduli\nby Lisa Marquand (Stony Brook Un
iversity) as part of American Graduate Student Algebraic Geometry Seminar\
n\n\nAbstract\nOne way to produce new varieties from a fixed subvariety of
projective space is to intersect with linear subspaces. When we consider
a cubic threefold $X$ in $\\mathbb{P}^4$\, we can consider hyperplane sect
ions: to every hyperplane (considered as a point in the dual projective sp
ace) we can associate a cubic surface namely the intersection $X \\cap H$.
One natural question is to ask\, given a cubic surface $Y$\, how many tim
es does it appear as a hyperplane section of $X$ (up to projective equival
ence)? More rigorously\, we can define a rational map which takes a hyperp
lane $H$ to the class of the intersection\, considered as a point in the m
oduli space of cubic surfaces (GIT). One can check that this is a generica
lly finite surjective map\, and thus answering our question is equivalent
to calculating the degree of this map. Although the question is enumerativ
e\, the techniques involved are particularly interesting: the wonderful bl
ow-up technique of De Concini-Procesi\, plus the dual perspective of the m
oduli of cubic surfaces. This is a work in progress\, and we will actually
consider a slight modification resulting in easier computations.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nawaz Sultani (University of Michigan)
DTSTART:20201116T210000Z
DTEND:20201116T220000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/9
DESCRIPTION:Title: Orbifold Gromov–Witten theory of complete intersections\nby Na
waz Sultani (University of Michigan) as part of American Graduate Student
Algebraic Geometry Seminar\n\n\nAbstract\nFor genus 0 GW invariants of sch
emes\, one can compute the GW theory of a complete intersection in project
ive space in terms of the GW theory of the ambient space through the so-ca
lled Quantum Lefschetz theorem (QL). However\, this theorem doesn't necess
arily hold when one considers stacky targets\, which makes such examples m
uch more difficult to understand.\n\nIn this talk\, I will discuss the fai
lure of QL in the orbifold case\, and present techniques that allow us to
compute the $g=0$ GW invariants in these cases when the target is a comple
te intersection in a stacky GIT quotient. The work presented is joint with
Felix Janda and Yang Zhou. I will also not assume you know anything about
GW theory prior.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Yáñez (University of Utah)
DTSTART:20201207T210000Z
DTEND:20201207T220000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/10
DESCRIPTION:Title: Birational automorphisms and movable cone of Calabi-Yau complete in
tersections\nby José Yáñez (University of Utah) as part of American
Graduate Student Algebraic Geometry Seminar\n\n\nAbstract\nIn 2013 Cantat
and Oguiso used Coxeter groups to calculate the birational automorphism g
roup and prove the Kawamata-Morrison conjecture for varieties of Wehler ty
pe. In this talk\, we use generalized geometric representations of Coxeter
groups to compute the movable cone and to extend Cantat-Oguiso's result t
o Calabi-Yau complete intersections in products of projective spaces.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lei Yang (Northeastern University)
DTSTART:20201012T200000Z
DTEND:20201012T210000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/11
DESCRIPTION:Title: Cox rings\, linear blow-ups and the generalized Nagata action\n
by Lei Yang (Northeastern University) as part of American Graduate Student
Algebraic Geometry Seminar\n\n\nAbstract\nNagata gave the first counterex
ample to Hilbert's 14th problem on the finite generation of invariant ring
s by actions of linear algebraic groups. His idea was to relate the ring o
f invariants to a Cox ring of a projective variety. Counterexamples of Nag
ata's type include the cases where the group is $G_a^m$ for $m=3\, 6\, 9$
or $13$. However\, for $m=2$\, the ring of invariants under the Nagata act
ion is finitely generated. It is still an open problem whether counterexam
ples exist for $m=2$. \n\nIn this talk we consider a generalized version o
f Nagata's action by H. Naito. Mukai envisioned that the ring of invariant
s in this case can still be related to a cox ring of certain linear blow-u
ps of $P^n$. We show that when $m=2$\, the Cox rings of this type of linea
r blow-ups are still finitely generated\, and we can describe their genera
tors. This answers the question by Mukai.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gwyneth Moreland (Harvard University)
DTSTART:20201123T210000Z
DTEND:20201123T220000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/12
DESCRIPTION:Title: Top weight cohomology of A_g\nby Gwyneth Moreland (Harvard Univ
ersity) as part of American Graduate Student Algebraic Geometry Seminar\n\
n\nAbstract\nI will discuss recent work on computing the top weight cohomo
logy of $A_g$ for $g$ up to 7. We use combinatorial methods coming from th
e relationship between the top weight cohomology of $A_g$ and the homology
of the link of the moduli space of tropical abelian varieties to carry ou
t the computation. This is joint work with Madeline Brandt\, Juliette Bruc
e\, Melody Chan\, Margarida Melo\, and Corey Wolfe.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weihong Xu (Rutgers University)
DTSTART:20201214T210000Z
DTEND:20201214T220000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/13
DESCRIPTION:Title: Quantum K-theory of Incidence Varieties\nby Weihong Xu (Rutgers
University) as part of American Graduate Student Algebraic Geometry Semin
ar\n\n\nAbstract\nCertain rational enumerative geometry problems can be fo
rmulated as intersection theory in the moduli space of stable maps M̅_{0\
,m}(X\,d). This moduli space is well-behaved when $X$ is a projective homo
geneous variety $G/P$. Non-trivial relations among solutions to these enum
erative geometry problems (Gromov-Witten invariants) enable the definition
of an associative product and in turn a formal deformation of the cohomol
ogy ring called the quantum cohomology ring of $X$. Similarly\, a deformat
ion of the Grothendieck ring $K(X)$ called the quantum K-theory ring of $X
$ is defined using sheaf-theoretic versions of Gromov-Witten invariants.\n
\nAfter introducing relevant background\, we will focus on the quantum K-t
heory of the projective homogeneous variety $Fl(1\,n-1\;n)$ (also called a
n incidence variety)\, where I have found explicit multiplication formulae
and computed some sheaf-theoretic Gromov-Witten invariants. These computa
tions lead to suspected rationality properties of some natural subvarietie
s of M̅_{0\,m}(X\,d).\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilong Zhang (Ohio State University)
DTSTART:20201130T210000Z
DTEND:20201130T220000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/14
DESCRIPTION:Title: Cubic Threefolds and Vanishing Cycles on its Hyperplane sections\nby Yilong Zhang (Ohio State University) as part of American Graduate St
udent Algebraic Geometry Seminar\n\n\nAbstract\nFor a general cubic threef
old\, a vanishing cycle on a smooth hyperplane section is an integral 2-cl
ass perpendicular to the hyperplane class with self-intersection equal to
-2. The question is what is a vanishing cycle on a singular hyperplane sec
tion? We will show that there is a certain moduli space parameterizing "va
nishing cycles" on all hyperplane sections and the boundary divisor answer
s the question. As a vanishing cycle on a smooth cubic surface is represen
ted by the difference of two skew lines\, such moduli space arises as a qu
otient of the Hilbert scheme of skew lines on the cubic threefold. Based o
n the Abel-Jacobi map on cubic threefolds studied by Clemens and Griffiths
\, we'll show that the moduli space is isomorphic to the blowup of the the
ta divisor of the at an isolated singularity.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Scavia (University of British Columbia)
DTSTART:20210125T210000Z
DTEND:20210125T220000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/15
DESCRIPTION:Title: Motivic classes of algebraic stacks\nby Federico Scavia (Univer
sity of British Columbia) as part of American Graduate Student Algebraic G
eometry Seminar\n\n\nAbstract\nThe Grothendieck ring of algebraic stacks w
as introduced by T. Ekedahl in 2009\, following up on work of other author
s. It is a generalization of the Grothendieck ring of varieties. If G is a
linear algebraic group\, it is an interesting problem to compute the moti
vic class of its classifying stack BG in this ring. I will give a brief in
troduction to the Grothendieck ring of stacks\, and then explain some of m
y results in the area.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yen-An Chen (University of Utah)
DTSTART:20210201T210000Z
DTEND:20210201T220000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/16
DESCRIPTION:Title: Generalized canonical models of foliated surfaces\nby Yen-An Ch
en (University of Utah) as part of American Graduate Student Algebraic Geo
metry Seminar\n\n\nAbstract\nBy work of McQuillan and Brunella\, it is kno
wn that foliated surfaces of general type with only canonical foliation si
ngularities admit a unique canonical model. It is then natural to investig
ate the moduli space parametrizing canonical models. One issue is that the
condition being a canonical model is neither open nor closed. In this tal
k\, I will introduce the generalized canonical models to fix this issue an
d study some properties (boundedness/ separatedness/ properness/ local-clo
sedness) of the moduli space of generalized canonical models.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiva Chidambaram (University of Chicago)
DTSTART:20210208T210000Z
DTEND:20210208T220000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/17
DESCRIPTION:Title: Moduli spaces of low dimensional abelian varieties with torsion
\nby Shiva Chidambaram (University of Chicago) as part of American Graduat
e Student Algebraic Geometry Seminar\n\n\nAbstract\nThe Siegel modular var
iety $A_2(3)$ which parametrizes abelian surfaces with split level 3 struc
ture is birational to the Burkhardt quartic threefold. This was shown to b
e rational over $\\mathbb{Q}$ by Bruin and Nasserden. What can we say abou
t its twist $A_2(\\rho)$ for a Galois representation $\\rho$ valued in $GS
p(4\, F_3)$? While it is not rational in general\, it is unirational over
$\\mathbb{Q}$ by a map of degree at most 6\, showing that $\\rho$ arises a
s the 3-torsion of infinitely many abelian surfaces. In joint work with Fr
ank Calegari and David Roberts\, we obtain an explicit description of the
universal object over a degree 6 cover using invariant theoretic ideas. Si
milar ideas work for $(g\,p) = (1\,2)\, (1\,3)\, (1\,5)\, (2\,2)\, (2\,3)$
and $(3\,2)$. When $(g\,p)$ is not one of these six tuples\, we discuss a
local obstruction for representations to arise as torsion.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Yun (Brown University)
DTSTART:20210215T210000Z
DTEND:20210215T220000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/18
DESCRIPTION:Title: The $S_n$-equivariant rational homology of the tropical moduli spac
es $\\Delta_{2\,n}$\nby Claudia Yun (Brown University) as part of Amer
ican Graduate Student Algebraic Geometry Seminar\n\n\nAbstract\nThe tropic
al moduli space $\\Delta_{g\,n}$ is a topological space that parametrizes
isomorphism classes of $n$-marked stable tropical curves of genus with tot
al volume 1. Its reduced rational homology has a natural structure of $S_n
$-representations induced by permuting markings. In this talk\, we focus o
n $\\Delta_{2\,n}$ and compute the characters of these $S_n$-representatio
ns for $n$ up to 8. We use the fact that $\\Delta_{2\,n}$ is a symmetric $
\\Delta$-complex\, a concept introduced by Chan\, Glatius\, and Payne. The
computation is done in SageMath.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Sherman-Bennett (UC Berkeley)
DTSTART:20210301T210000Z
DTEND:20210301T220000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/19
DESCRIPTION:Title: Cluster structures on Schubert varieties in the Grassmannian\nb
y Melissa Sherman-Bennett (UC Berkeley) as part of American Graduate Stude
nt Algebraic Geometry Seminar\n\n\nAbstract\nCluster algebras are a class
of commutative rings with a (usually infinite) set of distinguished genera
tors\, grouped together in overlapping subsets called "clusters." They wer
e defined by Fomin and Zelevinsky in the early 2000s\; since their definit
ion\, connections have been found to representation theory\, Teichmuller t
heory\, discrete dynamical systems\, and many other branches of math. I'll
discuss joint work with K. Serhiyenko and L. Williams\, in which we show
that homogeneous coordinate rings of Schubert varieties in the Grassmannia
n are cluster algebras\, with clusters coming from a particularly nice com
binatorial source.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jia-Choon Lee (University of Pennsylvania)
DTSTART:20210315T200000Z
DTEND:20210315T210000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/20
DESCRIPTION:Title: Semi-polarized meromorphic Hitchin and Calabi-Yau integrable system
s\nby Jia-Choon Lee (University of Pennsylvania) as part of American G
raduate Student Algebraic Geometry Seminar\n\n\nAbstract\nSince the semina
l work of Hitchin\, the moduli spaces of Higgs bundles\, also known as the
Hitchin systems\, have been studied extensively because of their rich geo
metry. In particular\, each of these moduli spaces admits the structure of
an algebraic integrable system. There is another class of algebraic integ
rable systems provided by the so-called non-compact Calabi-Yau integrable
systems. By the work of Diaconescu\, Donagi and Pantev\, it is shown that
Hitchin systems are isomorphic to certain Calabi-Yau integrable systems. I
n this talk\, I will discuss joint work with Sukjoo Lee on how to extend t
his correspondence to the meromorphic setting.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irit Huq-Kuruvilla (UC Berkeley)
DTSTART:20210222T210000Z
DTEND:20210222T220000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/21
DESCRIPTION:Title: Multiplicative Quantum Cobordism Theory\nby Irit Huq-Kuruvilla
(UC Berkeley) as part of American Graduate Student Algebraic Geometry Semi
nar\n\n\nAbstract\n$K$-theoretic Gromov-Witten invariants were proposed by
Kontsevich in the 80s\, and the foundations were developed by YP Lee in 1
999. I will introduce a modified form of these invariants obtained by twis
ting the virtual structure sheaf by an arbitrary characteristic class of t
he tangent bundle of the moduli space of stable maps\, and state a formula
relating the generating function for these invariants to the unmodified o
nes. I'll also discuss how these invariants can be used to define Gromov-W
itten invariants valued in other complex-oriented cohomology theories\, th
e universal example of which is cobordism theory. This talk is based on wo
rk from https://arxiv.org/abs/2101.09305.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Esser (UCLA)
DTSTART:20210308T210000Z
DTEND:20210308T220000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/22
DESCRIPTION:Title: Non-torsion Brauer groups\nby Louis Esser (UCLA) as part of Ame
rican Graduate Student Algebraic Geometry Seminar\n\n\nAbstract\nThe class
ical definition of the Brauer group of a field can be extended in differen
t ways to general schemes. I'll explain two methods of doing so in order
to motivate the question: when is the cohomological Brauer group torsion?
After reviewing some techniques for computing this group\, I'll present n
ew examples of normal surfaces in positive characteristic with non-torsion
Brauer group. This talk is based on work from https://arxiv.org/abs/2102
.01799.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lauren Heller (UC Berkeley)
DTSTART:20210405T200000Z
DTEND:20210405T210000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/23
DESCRIPTION:Title: Characterizations of multigraded regularity on products of projecti
ve spaces\nby Lauren Heller (UC Berkeley) as part of American Graduate
Student Algebraic Geometry Seminar\n\n\nAbstract\nEisenbud and Goto descr
ibed the Castelnuovo-Mumford regularity of a sheaf on projective space in
terms of three different properties of the corresponding graded module: it
s betti numbers\, its local cohomology\, and its truncations. For the mul
tigraded generalization of regularity defined by Maclagan and Smith\, thes
e three conditions are no longer equivalent. I will discuss some relation
ships between them for sheaves on products of projective spaces.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nolan Schock (University of Georgia)
DTSTART:20210322T200000Z
DTEND:20210322T210000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/24
DESCRIPTION:Title: Intersection theory on moduli of hyperplane arrangements and marked
del Pezzo surfaces\nby Nolan Schock (University of Georgia) as part o
f American Graduate Student Algebraic Geometry Seminar\n\n\nAbstract\nThis
talk is about the intersection theory of two of the first examples of com
pact moduli spaces of higher-dimensional varieties: the log canonical comp
actification of the moduli space of marked del Pezzo surfaces\, and the st
able pair compactification of the moduli space of hyperplane arrangements.
The latter space is the natural higher-dimensional version of $\\overline
{M}_{0\,n}$\, the moduli space of n-pointed rational curves\, but its geom
etry can in general be arbitrarily complicated. On the other hand\, the fo
rmer space\, which can also be viewed as a higher-dimensional generalizati
on of $\\overline{M}_{0\,n}$\, by construction has nice geometry on the bo
undary\, and this leads (conjecturally for degree 1\,2) to a presentation
of its Chow ring entirely analogous to Keel's famous presentation of the C
how ring of $\\overline{M}_{0\,n}$. I will describe work in progress using
the relationships between these moduli spaces in order to describe the in
tersection theory of the moduli space of stable hyperplane arrangements.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuomas Tajakka (University of Washington)
DTSTART:20210329T200000Z
DTEND:20210329T210000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/25
DESCRIPTION:Title: Uhlenbeck compactification as a Bridgeland moduli space\nby Tuo
mas Tajakka (University of Washington) as part of American Graduate Studen
t Algebraic Geometry Seminar\n\n\nAbstract\nIn recent years\, Bridgeland s
tability conditions have become a central tool in the study of moduli of s
heaves and their birational geometry. However\, moduli spaces of Bridgelan
d semistable objects are known to be projective only in a limited number o
f cases. After reviewing the classical moduli theory of sheaves on curves
and surfaces\, I will present a new projectivity result for a Bridgeland m
oduli space on an arbitrary smooth projective surface\, as well as discuss
how to interpret the Uhlenbeck compactification of the moduli of slope st
able vector bundles as a Bridgeland moduli space. The proof is based on st
udying a determinantal line bundle constructed by Bayer and Macrì. Time p
ermitting\, I will mention some ongoing work on PT-stability on a 3-fold.\
n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Thevis (Aachen University)
DTSTART:20210412T200000Z
DTEND:20210412T210000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/26
DESCRIPTION:Title: On the interaction of normal square-tiled surfaces and group theory
\nby Andrea Thevis (Aachen University) as part of American Graduate St
udent Algebraic Geometry Seminar\n\n\nAbstract\nA translation surface is o
btained by taking finitely many polygons in the Euclidean plane and gluing
them along their edges by translations. If we restrict to gluing unit squ
ares\, we obtain a square-tiled surface\, also known as origami. In the fi
rst part of the talk\, I explain some motivations for studying translation
surfaces. I especially aim to point out why it is natural to study square
-tiled surfaces in some of these contexts. In the second part of the talk\
, we consider certain square-tiled surfaces with maximal symmetry group in
more detail. More precisely\, we examine their types of singularities and
their Veech groups using group theoretic methods. This is partially joint
work with Johannes Flake.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yulieth K. Prieto (Università di Bologna)
DTSTART:20210419T200000Z
DTEND:20210419T210000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/27
DESCRIPTION:Title: On K3 surfaces admitting symplectic automorphism of order 3\nby
Yulieth K. Prieto (Università di Bologna) as part of American Graduate S
tudent Algebraic Geometry Seminar\n\n\nAbstract\nThe theory of K3 surfaces
with symplectic involutions and their quotients is now a well-understood
classical subject thanks to foundational works of Nikulin\, Morrison\, and
van Geemen and Sarti. In this talk\, we will try to develop analogous res
ults for K3 surfaces with symplectic automorphisms of order three: we will
explicitly describe the induced action of these automorphisms on the K3
-lattice\, which is isometric to the second cohomology group of a K3 surfa
ce\; we deduce the relation between the families that admitting these auto
morphisms and the ones given by their quotients. If time permits\, we give
some applications: one related to Shioda-Inose structures\, and another o
ne in the construction of infinite towers of isogeneous K3 surfaces. This
is joint work with Alice Garbagnati.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cesar Hilario (IMPA)
DTSTART:20210426T200000Z
DTEND:20210426T210000Z
DTSTAMP:20260404T131153Z
UID:AGSAGS/28
DESCRIPTION:Title: Bertini's theorem in positive characteristic\nby Cesar Hilario
(IMPA) as part of American Graduate Student Algebraic Geometry Seminar\n\n
\nAbstract\nThe Bertini-Sard theorem is a classical result in algebraic ge
ometry. It states that in characteristic zero almost all the fibers of a d
ominant morphism between two smooth algebraic varieties are smooth\; in ot
her words\, there do not exist fibrations by singular varieties with smoot
h total space. Unfortunately\, the Bertini-Sard theorem fails in positive
characteristic\, as was first observed by Zariski in the 1940s. Investigat
ing this failure naturally leads to the classification of its exceptions.
By a theorem of Tate\, a fibration by singular curves of arithmetic genus
g in characteristic p > 0 may exist only if p <= 2g + 1. When g = 1 and g
= 2\, these fibrations have been studied by Queen\, Borges Neto\, Stohr an
d Simarra Canate. A birational classification of the case g = 3 was starte
d by Stohr (p = 7\, 5)\, and then continued by Salomao (p = 3). In this ta
lk I will report on some progress in the case g = 3\, p = 2. In fact\, a g
reat variety of examples exist and very interesting geometric phenomena ar
ise from them.\n
LOCATION:https://stable.researchseminars.org/talk/AGSAGS/28/
END:VEVENT
END:VCALENDAR