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SUMMARY:Libby Taylor (Stanford University)
DTSTART;VALUE=DATE-TIME:20200914T200000Z
DTEND;VALUE=DATE-TIME:20200914T210000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103452Z
UID:AGSAGS/1
DESCRIPTION:Title: Fourier-Mukai theory for stacky genus 1 curves\nby Libb
y Taylor (Stanford University) as part of American Graduate Student Algebr
aic Geometry Seminar\n\n\nAbstract\nWe will discuss a theory of derived eq
uivalences for certain Artin stacks. We will apply this theory to study t
he derived 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 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 $C'=Pic^d(C)$\, 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 Sou
mya Sankar.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Chen (Stony Brook University)
DTSTART;VALUE=DATE-TIME:20200921T200000Z
DTEND;VALUE=DATE-TIME:20200921T210000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103452Z
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\nAbstract\nGiven a smooth projective variety\, there are two n
atural questions that can be asked: (1) How can we determine when it is ra
tional? 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 dev
eloping invariants with the second question in mind. We will explain some
new techniques involved in bounding these invariants for certain classes o
f varieties.\n
END:VEVENT
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SUMMARY:Sebastián Torres (UMass Amherst)
DTSTART;VALUE=DATE-TIME:20200928T200000Z
DTEND;VALUE=DATE-TIME:20200928T210000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103452Z
UID:AGSAGS/3
DESCRIPTION:Title: Bott vanishing using GIT and quantization\nby Sebastiá
n Torres (UMass Amherst) as part of American Graduate Student Algebraic Ge
ometry Seminar\n\n\nAbstract\nA smooth projective variety is said to satis
fy Bott vanishing if $\\Omega^j\\otimes L$ has no higher cohomology for ev
ery $j$ and every ample line bundle $L$. This is a very restrictive proper
ty\, and there are few non-toric examples known to satisfy it. I will pres
ent 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 t
his allows us\, in some cases\, to compute cohomologies directly in an amb
ient quotient stack.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sukjoo Lee (University of Pennsylvania)
DTSTART;VALUE=DATE-TIME:20201005T200000Z
DTEND;VALUE=DATE-TIME:20201005T210000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103452Z
UID:AGSAGS/4
DESCRIPTION:Title: P=W phenomena in Fano mirror symmetry\nby Sukjoo Lee (U
niversity of Pennsylvania) as part of American Graduate Student Algebraic
Geometry Seminar\n\n\nAbstract\n$P=W$ phenomena\, originated from non-abel
ian Hodge theory\, has been recently formulated by A. Harder\, L. Katzarko
v and V. Przyjalkowski in the context of mirror symmetry of log Calabi-Yau
manifolds. In particular\, if the log Calabi-Yau manifold admits Fano com
pactification $(X\,D)$ with smooth anti-canonical divisor $D$\, we can stu
dy $P=W$ phenomena from categorical viewpoint under the Fano/LG correspond
ence. In this talk\, we will go over the story and generalize to the case
where $D$ has more than one component.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiyue Li (Brown University)
DTSTART;VALUE=DATE-TIME:20201019T200000Z
DTEND;VALUE=DATE-TIME:20201019T210000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103452Z
UID:AGSAGS/5
DESCRIPTION:Title: Topology of tropical moduli spaces of weighted stable c
urves in higher genus\nby Shiyue Li (Brown University) as part of American
Graduate Student Algebraic Geometry Seminar\n\n\nAbstract\nTropical modul
i spaces of weighted stable curves are moduli spaces of metric weighted ma
rked graphs satisfying certain stability conditions. The space of tropical
weighted curves of genus g and volume 1 is the dual complex of the diviso
r of singular curves in Hassett's moduli space of weighted stable genus g
curves. One can derive plenty of topological properties of the Hassett spa
ces 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 curve
s of genus g and volume 1 are simply-connected for all genus greater than
zero and all rational weights\, under the framework of symmetric Delta-com
plexes and via a result by Allcock-Corey-Payne 19. We also calculate the E
uler characteristics of these spaces and the top weight Euler characterist
ics of the classical Hassett spaces in terms of the combinatorics of the w
eights.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Olander (Columbia University)
DTSTART;VALUE=DATE-TIME:20201026T200000Z
DTEND;VALUE=DATE-TIME:20201026T210000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103452Z
UID:AGSAGS/6
DESCRIPTION:Title: Orlov's Theorem for Smooth Proper Varieties\nby Noah Ol
ander (Columbia University) as part of American Graduate Student Algebraic
Geometry Seminar\n\n\nAbstract\nOrlov proved in 1996 that many functors b
etween derived categories of smooth projective varieties are represented b
y kernels\, i.e.\, complexes on the product. Since then\, Orlov's theorem
has had a profound influence on algebraic geometry. In this talk\, we disc
uss Orlov's proof as well as some technical advances and new ideas which s
hed light on it\, leading to an extension of the theorem to the smooth pro
per case.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raymond Cheng (Columbia University)
DTSTART;VALUE=DATE-TIME:20201102T210000Z
DTEND;VALUE=DATE-TIME:20201102T220000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103452Z
UID:AGSAGS/7
DESCRIPTION:Title: q-bic Hypersurfaces\nby Raymond Cheng (Columbia Univers
ity) as part of American Graduate Student Algebraic Geometry Seminar\n\n\n
Abstract\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 like to convince you that Fermat hypersurfaces of degree $q + 1$\,
$q$ a power of the ground field characteristic\, is geometrically analogou
s to quadric and cubic hypersurfaces. To me\, this example suggests a them
e with which to understand some geometric features in positive characteris
tic\, like the unexpected abundance of rational curves in certain varietie
s.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Marquand (Stony Brook University)
DTSTART;VALUE=DATE-TIME:20201109T210000Z
DTEND;VALUE=DATE-TIME:20201109T220000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103452Z
UID:AGSAGS/8
DESCRIPTION:Title: Hyperplane sections and Moduli\nby Lisa Marquand (Stony
Brook University) as part of American Graduate Student Algebraic Geometry
Seminar\n\n\nAbstract\nOne way to produce new varieties from a fixed subv
ariety of projective space is to intersect with linear subspaces. When we
consider a cubic threefold $X$ in $\\mathbb{P}^4$\, we can consider hyperp
lane sections: to every hyperplane (considered as a point in the dual proj
ective space) 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 times does it appear as a hyperplane section of $X$ (up to projectiv
e 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 space of cubic surfaces (GIT). One can check that this is a
generically finite surjective map\, and thus answering our question is eq
uivalent to calculating the degree of this map. Although the question is e
numerative\, the techniques involved are particularly interesting: the won
derful blow-up technique of De Concini-Procesi\, plus the dual perspective
of the moduli of cubic surfaces. This is a work in progress\, and we will
actually consider a slight modification resulting in easier computations.
\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nawaz Sultani (University of Michigan)
DTSTART;VALUE=DATE-TIME:20201116T210000Z
DTEND;VALUE=DATE-TIME:20201116T220000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103452Z
UID:AGSAGS/9
DESCRIPTION:by Nawaz Sultani (University of Michigan) as part of American
Graduate Student Algebraic Geometry Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Yáñez (University of Utah)
DTSTART;VALUE=DATE-TIME:20201207T210000Z
DTEND;VALUE=DATE-TIME:20201207T220000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103452Z
UID:AGSAGS/10
DESCRIPTION:by José Yáñez (University of Utah) as part of American Grad
uate Student Algebraic Geometry Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lei Yang (Northeastern University)
DTSTART;VALUE=DATE-TIME:20201012T200000Z
DTEND;VALUE=DATE-TIME:20201012T210000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103452Z
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 Algebraic Geometry Seminar\n\n\nAbstract\nNagata gave the first c
ounterexample to Hilbert's 14th problem on the finite generation of invari
ant rings by actions of linear algebraic groups. His idea was to relate th
e ring of invariants to a Cox ring of a projective variety. Counterexample
s of Nagata'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 Na
gata action is finitely generated. It is still an open problem whether cou
nterexamples exist for $m=2$. \n\nIn this talk we consider a generalized v
ersion of Nagata's action by H. Naito. Mukai envisioned that the ring of i
nvariants in this case can still be related to a cox ring of certain linea
r 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 thei
r generators. This answers the question by Mukai.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gwyneth Moreland (Harvard University)
DTSTART;VALUE=DATE-TIME:20201123T210000Z
DTEND;VALUE=DATE-TIME:20201123T220000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103452Z
UID:AGSAGS/12
DESCRIPTION:by Gwyneth Moreland (Harvard University) as part of American G
raduate Student Algebraic Geometry Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weihong Xu (Rutgers University)
DTSTART;VALUE=DATE-TIME:20201214T210000Z
DTEND;VALUE=DATE-TIME:20201214T220000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103452Z
UID:AGSAGS/13
DESCRIPTION:by Weihong Xu (Rutgers University) as part of American Graduat
e Student Algebraic Geometry Seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilong Zhang (Ohio State University)
DTSTART;VALUE=DATE-TIME:20201130T210000Z
DTEND;VALUE=DATE-TIME:20201130T220000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103452Z
UID:AGSAGS/14
DESCRIPTION:by Yilong Zhang (Ohio State University) as part of American Gr
aduate Student Algebraic Geometry Seminar\n\nAbstract: TBA\n
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