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BEGIN:VEVENT
SUMMARY:Libby Taylor (Stanford University)
DTSTART;VALUE=DATE-TIME:20200914T200000Z
DTEND;VALUE=DATE-TIME:20200914T210000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/1
DESCRIPTION:Title: F
ourier-Mukai theory for stacky genus 1 curves\nby Libby Taylor (Stanfo
rd University) as part of American Graduate Student Algebraic Geometry Sem
inar\n\n\nAbstract\nWe will discuss a theory of derived equivalences for c
ertain Artin stacks. We will apply this theory to study the derived categ
ories of genus 1 curves and of their Picard stacks. Some questions we wil
l answer: when are two $\\mathbb{G}_m$ gerbes over genus 1 curves derived
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 $C'=Pi
c^d(C)$\, 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 th
e other\; yes\; yes and yes.) This is joint work with Soumya Sankar.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Chen (Stony Brook University)
DTSTART;VALUE=DATE-TIME:20200921T200000Z
DTEND;VALUE=DATE-TIME:20200921T210000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/2
DESCRIPTION:Title: A
generic talk on irrationality\nby Nathan Chen (Stony Brook University
) as part of American Graduate Student Algebraic Geometry Seminar\n\n\nAbs
tract\nGiven a smooth projective variety\, there are two natural questions
that can be asked: (1) How can we determine when it is rational? and (2)
If it is not rational\, can we measure how far it is from being rational?
There has been a great deal of recent progress towards developing invarian
ts with the second question in mind. We will explain some new techniques i
nvolved in bounding these invariants for certain classes of varieties.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastián Torres (UMass Amherst)
DTSTART;VALUE=DATE-TIME:20200928T200000Z
DTEND;VALUE=DATE-TIME:20200928T210000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/3
DESCRIPTION:Title: B
ott vanishing using GIT and quantization\nby Sebastián Torres (UMass
Amherst) as part of American Graduate Student Algebraic Geometry Seminar\n
\n\nAbstract\nA smooth projective variety is said to satisfy Bott vanishin
g if $\\Omega^j\\otimes L$ has no higher cohomology for every $j$ and ever
y ample line bundle $L$. This is a very restrictive property\, and there a
re 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 allows us\,
in some cases\, to compute cohomologies directly in an ambient quotient st
ack.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sukjoo Lee (University of Pennsylvania)
DTSTART;VALUE=DATE-TIME:20201005T200000Z
DTEND;VALUE=DATE-TIME:20201005T210000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/4
DESCRIPTION:Title: P
=W phenomena in Fano mirror symmetry\nby Sukjoo Lee (University of Pen
nsylvania) 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. Przyjal
kowski in the context of mirror symmetry of log Calabi-Yau manifolds. In p
articular\, if the log Calabi-Yau manifold admits Fano compactification $(
X\,D)$ with smooth anti-canonical divisor $D$\, we can study $P=W$ phenome
na from categorical viewpoint under the Fano/LG correspondence. In this ta
lk\, we will go over the story and generalize to the case where $D$ has m
ore than one component.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiyue Li (Brown University)
DTSTART;VALUE=DATE-TIME:20201019T200000Z
DTEND;VALUE=DATE-TIME:20201019T210000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/5
DESCRIPTION:Title: T
opology of tropical moduli spaces of weighted stable curves in higher genu
s\nby Shiyue Li (Brown University) as part of American Graduate Studen
t Algebraic Geometry Seminar\n\n\nAbstract\nTropical moduli spaces of weig
hted stable curves are moduli spaces of metric weighted marked graphs sati
sfying certain stability conditions. The space of tropical weighted curves
of genus g and volume 1 is the dual complex of the divisor of singular cu
rves in Hassett's moduli space of weighted stable genus g curves. One can
derive plenty of topological properties of the Hassett spaces by studying
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 genus g and
volume 1 are simply-connected for all genus greater than zero and all rat
ional weights\, under the framework of symmetric Delta-complexes and via a
result by Allcock-Corey-Payne 19. We also calculate the Euler characteris
tics of these spaces and the top weight Euler characteristics of the class
ical Hassett spaces in terms of the combinatorics of the weights.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Olander (Columbia University)
DTSTART;VALUE=DATE-TIME:20201026T200000Z
DTEND;VALUE=DATE-TIME:20201026T210000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/6
DESCRIPTION:Title: O
rlov's Theorem for Smooth Proper Varieties\nby Noah Olander (Columbia
University) as part of American Graduate Student Algebraic Geometry Semina
r\n\n\nAbstract\nOrlov proved in 1996 that many functors between derived c
ategories of smooth projective varieties are represented by kernels\, i.e.
\, complexes on the product. Since then\, Orlov's theorem has had a profou
nd influence on algebraic geometry. In this talk\, we discuss Orlov's proo
f 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://researchseminars.org/talk/AGSAGS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raymond Cheng (Columbia University)
DTSTART;VALUE=DATE-TIME:20201102T210000Z
DTEND;VALUE=DATE-TIME:20201102T220000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/7
DESCRIPTION:Title: q
-bic Hypersurfaces\nby Raymond Cheng (Columbia University) as part of
American Graduate Student Algebraic Geometry Seminar\n\n\nAbstract\nOne of
the funny features of geometry in positive characteristic is that equatio
ns behave of lower degree than they seem. In this talk\, I would like to c
onvince you that Fermat hypersurfaces of degree $q + 1$\, $q$ a power of t
he ground field characteristic\, is geometrically analogous to quadric and
cubic hypersurfaces. To me\, this example suggests a theme with which to
understand some geometric features in positive characteristic\, like the u
nexpected abundance of rational curves in certain varieties.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Marquand (Stony Brook University)
DTSTART;VALUE=DATE-TIME:20201109T210000Z
DTEND;VALUE=DATE-TIME:20201109T220000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/8
DESCRIPTION:Title: H
yperplane sections and Moduli\nby Lisa Marquand (Stony Brook Universit
y) as part of American Graduate Student Algebraic Geometry Seminar\n\n\nAb
stract\nOne way to produce new varieties from a fixed subvariety of projec
tive space is to intersect with linear subspaces. When we consider a cubic
threefold $X$ in $\\mathbb{P}^4$\, we can consider hyperplane sections: t
o every hyperplane (considered as a point in the dual projective space) we
can associate a cubic surface namely the intersection $X \\cap H$. One na
tural question is to ask\, given a cubic surface $Y$\, how many times does
it appear as a hyperplane section of $X$ (up to projective equivalence)?
More rigorously\, we can define a rational map which takes a hyperplane $H
$ to the class of the intersection\, considered as a point in the moduli s
pace of cubic surfaces (GIT). One can check that this is a generically fin
ite surjective map\, and thus answering our question is equivalent to calc
ulating the degree of this map. Although the question is enumerative\, the
techniques involved are particularly interesting: the wonderful blow-up t
echnique of De Concini-Procesi\, plus the dual perspective of the moduli o
f cubic surfaces. This is a work in progress\, and we will actually consid
er a slight modification resulting in easier computations.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nawaz Sultani (University of Michigan)
DTSTART;VALUE=DATE-TIME:20201116T210000Z
DTEND;VALUE=DATE-TIME:20201116T220000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/9
DESCRIPTION:Title: O
rbifold Gromov–Witten theory of complete intersections\nby Nawaz Sul
tani (University of Michigan) as part of American Graduate Student Algebra
ic Geometry Seminar\n\n\nAbstract\nFor genus 0 GW invariants of schemes\,
one can compute the GW theory of a complete intersection in projective spa
ce in terms of the GW theory of the ambient space through the so-called Qu
antum Lefschetz theorem (QL). However\, this theorem doesn't necessarily h
old when one considers stacky targets\, which makes such examples much mor
e difficult to understand.\n\nIn this talk\, I will discuss the failure 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 complete inte
rsection 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 the
ory prior.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Yáñez (University of Utah)
DTSTART;VALUE=DATE-TIME:20201207T210000Z
DTEND;VALUE=DATE-TIME:20201207T220000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/10
DESCRIPTION:Title:
Birational automorphisms and movable cone of Calabi-Yau complete intersect
ions\nby José Yáñez (University of Utah) as part of American Gradua
te Student Algebraic Geometry Seminar\n\n\nAbstract\nIn 2013 Cantat and Og
uiso used Coxeter groups to calculate the birational automorphism group an
d prove the Kawamata-Morrison conjecture for varieties of Wehler type. In
this talk\, we use generalized geometric representations of Coxeter groups
to compute the movable cone and to extend Cantat-Oguiso's result to Calab
i-Yau complete intersections in products of projective spaces.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lei Yang (Northeastern University)
DTSTART;VALUE=DATE-TIME:20201012T200000Z
DTEND;VALUE=DATE-TIME:20201012T210000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/11
DESCRIPTION:Title:
Cox rings\, linear blow-ups and the generalized Nagata action\nby Lei
Yang (Northeastern University) as part of American Graduate Student Algebr
aic Geometry Seminar\n\n\nAbstract\nNagata gave the first counterexample t
o Hilbert's 14th problem on the finite generation of invariant rings by ac
tions of linear algebraic groups. His idea was to relate the ring of invar
iants to a Cox ring of a projective variety. Counterexamples of Nagata's t
ype 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 action is
finitely generated. It is still an open problem whether counterexamples ex
ist for $m=2$. \n\nIn this talk we consider a generalized version of Nagat
a's action by H. Naito. Mukai envisioned that the ring of invariants in th
is case can still be related to a cox ring of certain linear blow-ups of $
P^n$. We show that when $m=2$\, the Cox rings of this type of linear blow-
ups are still finitely generated\, and we can describe their generators. T
his answers the question by Mukai.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gwyneth Moreland (Harvard University)
DTSTART;VALUE=DATE-TIME:20201123T210000Z
DTEND;VALUE=DATE-TIME:20201123T220000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/12
DESCRIPTION:Title:
Top weight cohomology of A_g\nby Gwyneth Moreland (Harvard University)
as part of American Graduate Student Algebraic Geometry Seminar\n\n\nAbst
ract\nI will discuss recent work on computing the top weight cohomology of
$A_g$ for $g$ up to 7. We use combinatorial methods coming from the relat
ionship between the top weight cohomology of $A_g$ and the homology of the
link of the moduli space of tropical abelian varieties to carry out the c
omputation. This is joint work with Madeline Brandt\, Juliette Bruce\, Mel
ody Chan\, Margarida Melo\, and Corey Wolfe.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weihong Xu (Rutgers University)
DTSTART;VALUE=DATE-TIME:20201214T210000Z
DTEND;VALUE=DATE-TIME:20201214T220000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/13
DESCRIPTION:Title:
Quantum K-theory of Incidence Varieties\nby Weihong Xu (Rutgers Univer
sity) as part of American Graduate Student Algebraic Geometry Seminar\n\n\
nAbstract\nCertain rational enumerative geometry problems can be formulate
d 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 homogeneous
variety $G/P$. Non-trivial relations among solutions to these enumerative
geometry problems (Gromov-Witten invariants) enable the definition of an
associative product and in turn a formal deformation of the cohomology rin
g called the quantum cohomology ring of $X$. Similarly\, a deformation of
the Grothendieck ring $K(X)$ called the quantum K-theory ring of $X$ is de
fined using sheaf-theoretic versions of Gromov-Witten invariants.\n\nAfter
introducing relevant background\, we will focus on the quantum K-theory o
f the projective homogeneous variety $Fl(1\,n-1\;n)$ (also called an incid
ence variety)\, where I have found explicit multiplication formulae and co
mputed some sheaf-theoretic Gromov-Witten invariants. These computations l
ead to suspected rationality properties of some natural subvarieties of M
̅_{0\,m}(X\,d).\n
LOCATION:https://researchseminars.org/talk/AGSAGS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilong Zhang (Ohio State University)
DTSTART;VALUE=DATE-TIME:20201130T210000Z
DTEND;VALUE=DATE-TIME:20201130T220000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/14
DESCRIPTION:Title:
Cubic Threefolds and Vanishing Cycles on its Hyperplane sections\nby Y
ilong Zhang (Ohio State University) as part of American Graduate Student A
lgebraic Geometry Seminar\n\n\nAbstract\nFor a general cubic threefold\, a
vanishing cycle on a smooth hyperplane section is an integral 2-class per
pendicular to the hyperplane class with self-intersection equal to -2. The
question is what is a vanishing cycle on a singular hyperplane section? W
e will show that there is a certain moduli space parameterizing "vanishing
cycles" on all hyperplane sections and the boundary divisor answers the q
uestion. As a vanishing cycle on a smooth cubic surface is represented by
the difference of two skew lines\, such moduli space arises as a quotient
of the Hilbert scheme of skew lines on the cubic threefold. Based on the A
bel-Jacobi map on cubic threefolds studied by Clemens and Griffiths\, we'l
l show that the moduli space is isomorphic to the blowup of the theta divi
sor of the at an isolated singularity.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Scavia (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20210125T210000Z
DTEND;VALUE=DATE-TIME:20210125T220000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/15
DESCRIPTION:Title:
Motivic classes of algebraic stacks\nby Federico Scavia (University of
British Columbia) as part of American Graduate Student Algebraic Geometry
Seminar\n\n\nAbstract\nThe Grothendieck ring of algebraic stacks was intr
oduced by T. Ekedahl in 2009\, following up on work of other authors. It i
s a generalization of the Grothendieck ring of varieties. If G is a linear
algebraic group\, it is an interesting problem to compute the motivic cla
ss of its classifying stack BG in this ring. I will give a brief introduct
ion to the Grothendieck ring of stacks\, and then explain some of my resul
ts in the area.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yen-An Chen (University of Utah)
DTSTART;VALUE=DATE-TIME:20210201T210000Z
DTEND;VALUE=DATE-TIME:20210201T220000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/16
DESCRIPTION:Title:
Generalized canonical models of foliated surfaces\nby Yen-An Chen (Uni
versity of Utah) as part of American Graduate Student Algebraic Geometry S
eminar\n\n\nAbstract\nBy work of McQuillan and Brunella\, it is known that
foliated surfaces of general type with only canonical foliation singulari
ties admit a unique canonical model. It is then natural to investigate the
moduli space parametrizing canonical models. One issue is that the condit
ion being a canonical model is neither open nor closed. In this talk\, I w
ill introduce the generalized canonical models to fix this issue and study
some properties (boundedness/ separatedness/ properness/ local-closedness
) of the moduli space of generalized canonical models.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiva Chidambaram (University of Chicago)
DTSTART;VALUE=DATE-TIME:20210208T210000Z
DTEND;VALUE=DATE-TIME:20210208T220000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/17
DESCRIPTION:Title:
Moduli spaces of low dimensional abelian varieties with torsion\nby Sh
iva Chidambaram (University of Chicago) as part of American Graduate Stude
nt Algebraic Geometry Seminar\n\n\nAbstract\nThe Siegel modular variety $A
_2(3)$ which parametrizes abelian surfaces with split level 3 structure is
birational to the Burkhardt quartic threefold. This was shown to be ratio
nal over $\\mathbb{Q}$ by Bruin and Nasserden. What can we say about its t
wist $A_2(\\rho)$ for a Galois representation $\\rho$ valued in $GSp(4\, F
_3)$? While it is not rational in general\, it is unirational over $\\math
bb{Q}$ by a map of degree at most 6\, showing that $\\rho$ arises as the 3
-torsion of infinitely many abelian surfaces. In joint work with Frank Cal
egari and David Roberts\, we obtain an explicit description of the univers
al object over a degree 6 cover using invariant theoretic ideas. Similar i
deas 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://researchseminars.org/talk/AGSAGS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Yun (Brown University)
DTSTART;VALUE=DATE-TIME:20210215T210000Z
DTEND;VALUE=DATE-TIME:20210215T220000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/18
DESCRIPTION:Title:
The $S_n$-equivariant rational homology of the tropical moduli spaces $\\D
elta_{2\,n}$\nby Claudia Yun (Brown University) as part of American Gr
aduate Student Algebraic Geometry Seminar\n\n\nAbstract\nThe tropical modu
li space $\\Delta_{g\,n}$ is a topological space that parametrizes isomorp
hism classes of $n$-marked stable tropical curves of genus with total volu
me 1. Its reduced rational homology has a natural structure of $S_n$-repre
sentations induced by permuting markings. In this talk\, we focus on $\\De
lta_{2\,n}$ and compute the characters of these $S_n$-representations 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 comput
ation is done in SageMath.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Sherman-Bennett (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20210301T210000Z
DTEND;VALUE=DATE-TIME:20210301T220000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/19
DESCRIPTION:Title:
Cluster structures on Schubert varieties in the Grassmannian\nby Melis
sa Sherman-Bennett (UC Berkeley) as part of American Graduate Student Alge
braic Geometry Seminar\n\n\nAbstract\nCluster algebras are a class of comm
utative rings with a (usually infinite) set of distinguished generators\,
grouped together in overlapping subsets called "clusters." They were defin
ed by Fomin and Zelevinsky in the early 2000s\; since their definition\, c
onnections have been found to representation theory\, Teichmuller theory\,
discrete dynamical systems\, and many other branches of math. I'll discus
s joint work with K. Serhiyenko and L. Williams\, in which we show that ho
mogeneous coordinate rings of Schubert varieties in the Grassmannian are c
luster algebras\, with clusters coming from a particularly nice combinator
ial source.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jia-Choon Lee (University of Pennsylvania)
DTSTART;VALUE=DATE-TIME:20210315T200000Z
DTEND;VALUE=DATE-TIME:20210315T210000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/20
DESCRIPTION:Title:
Semi-polarized meromorphic Hitchin and Calabi-Yau integrable systems\n
by Jia-Choon Lee (University of Pennsylvania) as part of American Graduate
Student Algebraic Geometry Seminar\n\n\nAbstract\nSince the seminal work
of Hitchin\, the moduli spaces of Higgs bundles\, also known as the Hitchi
n systems\, have been studied extensively because of their rich geometry.
In particular\, each of these moduli spaces admits the structure of an alg
ebraic integrable system. There is another class of algebraic integrable s
ystems 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. In this
talk\, I will discuss joint work with Sukjoo Lee on how to extend this cor
respondence to the meromorphic setting.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irit Huq-Kuruvilla (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20210222T210000Z
DTEND;VALUE=DATE-TIME:20210222T220000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/21
DESCRIPTION:Title:
Multiplicative Quantum Cobordism Theory\nby Irit Huq-Kuruvilla (UC Ber
keley) as part of American Graduate Student Algebraic Geometry Seminar\n\n
\nAbstract\n$K$-theoretic Gromov-Witten invariants were proposed by Kontse
vich in the 80s\, and the foundations were developed by YP Lee in 1999. I
will introduce a modified form of these invariants obtained by twisting th
e virtual structure sheaf by an arbitrary characteristic class of the tang
ent bundle of the moduli space of stable maps\, and state a formula relati
ng the generating function for these invariants to the unmodified ones. I'
ll also discuss how these invariants can be used to define Gromov-Witten i
nvariants valued in other complex-oriented cohomology theories\, the unive
rsal example of which is cobordism theory. This talk is based on work from
https://arxiv.org/abs/2101.09305.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Esser (UCLA)
DTSTART;VALUE=DATE-TIME:20210308T210000Z
DTEND;VALUE=DATE-TIME:20210308T220000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/22
DESCRIPTION:Title:
Non-torsion Brauer groups\nby Louis Esser (UCLA) as part of American G
raduate Student Algebraic Geometry Seminar\n\n\nAbstract\nThe classical de
finition of the Brauer group of a field can be extended in different ways
to general schemes. I'll explain two methods of doing so in order to moti
vate the question: when is the cohomological Brauer group torsion? After
reviewing some techniques for computing this group\, I'll present new exam
ples 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://researchseminars.org/talk/AGSAGS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lauren Heller (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20210405T200000Z
DTEND;VALUE=DATE-TIME:20210405T210000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/23
DESCRIPTION:Title:
Characterizations of multigraded regularity on products of projective spac
es\nby Lauren Heller (UC Berkeley) as part of American Graduate Studen
t Algebraic Geometry Seminar\n\n\nAbstract\nEisenbud and Goto described th
e Castelnuovo-Mumford regularity of a sheaf on projective space in terms o
f three different properties of the corresponding graded module: its betti
numbers\, its local cohomology\, and its truncations. For the multigrade
d generalization of regularity defined by Maclagan and Smith\, these three
conditions are no longer equivalent. I will discuss some relationships b
etween them for sheaves on products of projective spaces.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nolan Schock (University of Georgia)
DTSTART;VALUE=DATE-TIME:20210322T200000Z
DTEND;VALUE=DATE-TIME:20210322T210000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/24
DESCRIPTION:Title:
Intersection theory on moduli of hyperplane arrangements and marked del Pe
zzo surfaces\nby Nolan Schock (University of Georgia) as part of Ameri
can Graduate Student Algebraic Geometry Seminar\n\n\nAbstract\nThis talk i
s about the intersection theory of two of the first examples of compact mo
duli spaces of higher-dimensional varieties: the log canonical compactific
ation of the moduli space of marked del Pezzo surfaces\, and the stable pa
ir compactification of the moduli space of hyperplane arrangements. The la
tter space is the natural higher-dimensional version of $\\overline{M}_{0\
,n}$\, the moduli space of n-pointed rational curves\, but its geometry ca
n in general be arbitrarily complicated. On the other hand\, the former sp
ace\, which can also be viewed as a higher-dimensional generalization of $
\\overline{M}_{0\,n}$\, by construction has nice geometry on the boundary\
, and this leads (conjecturally for degree 1\,2) to a presentation of its
Chow ring entirely analogous to Keel's famous presentation of the Chow rin
g of $\\overline{M}_{0\,n}$. I will describe work in progress using the re
lationships between these moduli spaces in order to describe the intersect
ion theory of the moduli space of stable hyperplane arrangements.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuomas Tajakka (University of Washington)
DTSTART;VALUE=DATE-TIME:20210329T200000Z
DTEND;VALUE=DATE-TIME:20210329T210000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/25
DESCRIPTION:Title:
Uhlenbeck compactification as a Bridgeland moduli space\nby Tuomas Taj
akka (University of Washington) as part of American Graduate Student Algeb
raic Geometry Seminar\n\n\nAbstract\nIn recent years\, Bridgeland stabilit
y conditions have become a central tool in the study of moduli of sheaves
and their birational geometry. However\, moduli spaces of Bridgeland semis
table objects are known to be projective only in a limited number of cases
. After reviewing the classical moduli theory of sheaves on curves and sur
faces\, I will present a new projectivity result for a Bridgeland moduli s
pace on an arbitrary smooth projective surface\, as well as discuss how to
interpret the Uhlenbeck compactification of the moduli of slope stable ve
ctor bundles as a Bridgeland moduli space. The proof is based on studying
a determinantal line bundle constructed by Bayer and Macrì. Time permitti
ng\, I will mention some ongoing work on PT-stability on a 3-fold.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Thevis (Aachen University)
DTSTART;VALUE=DATE-TIME:20210412T200000Z
DTEND;VALUE=DATE-TIME:20210412T210000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/26
DESCRIPTION:Title:
On the interaction of normal square-tiled surfaces and group theory\nb
y Andrea Thevis (Aachen University) as part of American Graduate Student A
lgebraic Geometry Seminar\n\n\nAbstract\nA translation surface is obtained
by taking finitely many polygons in the Euclidean plane and gluing them a
long their edges by translations. If we restrict to gluing unit squares\,
we obtain a square-tiled surface\, also known as origami. In the first par
t of the talk\, I explain some motivations for studying translation surfac
es. 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 co
nsider certain square-tiled surfaces with maximal symmetry group in more d
etail. More precisely\, we examine their types of singularities and their
Veech groups using group theoretic methods. This is partially joint work w
ith Johannes Flake.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yulieth K. Prieto (Università di Bologna)
DTSTART;VALUE=DATE-TIME:20210419T200000Z
DTEND;VALUE=DATE-TIME:20210419T210000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
UID:AGSAGS/27
DESCRIPTION:Title:
On K3 surfaces admitting symplectic automorphism of order 3\nby Yuliet
h K. Prieto (Università di Bologna) as part of American Graduate Student
Algebraic Geometry Seminar\n\n\nAbstract\nThe theory of K3 surfaces with s
ymplectic involutions and their quotients is now a well-understood classic
al subject thanks to foundational works of Nikulin\, Morrison\, and van Ge
emen and Sarti. In this talk\, we will try to develop analogous results fo
r K3 surfaces with symplectic automorphisms of order three: we will explic
itly describe the induced action of these automorphisms on the K3-lattic
e\, which is isometric to the second cohomology group of a K3 surface\; we
deduce the relation between the families that admitting these automorphis
ms and the ones given by their quotients. If time permits\, we give some a
pplications: one related to Shioda-Inose structures\, and another one in t
he construction of infinite towers of isogeneous K3 surfaces. This is join
t work with Alice Garbagnati.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cesar Hilario (IMPA)
DTSTART;VALUE=DATE-TIME:20210426T200000Z
DTEND;VALUE=DATE-TIME:20210426T210000Z
DTSTAMP;VALUE=DATE-TIME:20240719T144939Z
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\nAbstr
act\nThe Bertini-Sard theorem is a classical result in algebraic geometry.
It states that in characteristic zero almost all the fibers of a dominant
morphism between two smooth algebraic varieties are smooth\; in other wor
ds\, there do not exist fibrations by singular varieties with smooth total
space. Unfortunately\, the Bertini-Sard theorem fails in positive charact
eristic\, as was first observed by Zariski in the 1940s. Investigating thi
s failure naturally leads to the classification of its exceptions. By a th
eorem of Tate\, a fibration by singular curves of arithmetic genus g in ch
aracteristic p > 0 may exist only if p <= 2g + 1. When g = 1 and g = 2\, t
hese fibrations have been studied by Queen\, Borges Neto\, Stohr and Simar
ra Canate. A birational classification of the case g = 3 was started by St
ohr (p = 7\, 5)\, and then continued by Salomao (p = 3). In this talk I wi
ll report on some progress in the case g = 3\, p = 2. In fact\, a great va
riety of examples exist and very interesting geometric phenomena arise fro
m them.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/28/
END:VEVENT
END:VCALENDAR