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BEGIN:VEVENT
SUMMARY:Bernd Sturmfels (UC Berkeley and MPI Leipzig)
DTSTART:20200422T200000Z
DTEND:20200422T210000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/1
DESCRIPTION:Title: Theta surfaces\nby Bernd Sturmfels (UC Berkeley and MPI Leipzi
g) as part of UC Davis algebraic geometry seminar\n\n\nAbstract\nA theta s
urface in affine 3-space is the zero set of a Riemann theta function in ge
nus 3. This includes surfaces arising from special plane quartics that are
singular or reducible. Lie and Poincaré showed that theta surfaces are p
recisely the surfaces of double translation\, i.e. obtained as the Minkows
ki sum of two space curves in two different ways. These curves are paramet
rized by abelian integrals\, so they are usually not algebraic. This paper
offers a new view on this classical topic through the lens of computation
. We present practical tools for passing between quartic curves and their
theta surfaces\, and we develop the numerical algebraic geometry of degene
rations of theta functions.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Crooks (Northeastern University)
DTSTART:20200429T200000Z
DTEND:20200429T210000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/2
DESCRIPTION:Title: Poisson slices and Hessenberg varieties\nby Peter Crooks (Nort
heastern University) as part of UC Davis algebraic geometry seminar\n\n\nA
bstract\nHessenberg varieties constitute a rich and well-studied class of
closed subvarieties in the flag variety. Prominent examples include Grothe
ndieck-Springer fibres\, the Peterson variety\, and the projective toric v
ariety associated to the Weyl chambers. These last two examples belong to
the family of standard Hessenberg varieties\, whose total space is known t
o be a log symplectic variety. I will exhibit this total space as a Poisso
n slice in the log cotangent bundle of the wonderful compactification\, th
ereby building on Balibanu's recent results. This will yield a canonical c
losed embedding of each standard Hessenberg variety into the wonderful com
pactification.\n\nThis represents joint work with Markus Röser.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:María Angélica Cueto (Ohio State University)
DTSTART:20200506T200000Z
DTEND:20200506T210000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/3
DESCRIPTION:Title: Combinatorics and real lifts of bitangents to tropical quartic cur
ves\nby María Angélica Cueto (Ohio State University) as part of UC D
avis algebraic geometry seminar\n\n\nAbstract\nSmooth algebraic plane quar
tics over algebraically closed fields have 28 bitangent lines. By contrast
\, their tropical counterparts have infinitely many bitangents. They are g
rouped into seven equivalence classes\, one for each linear system associa
ted to an effective tropical theta characteristic on the tropical quartic
curve.\n\nIn this talk\, I will discuss recent work joint with Hannah Mark
wig (arxiv:2004.10891) on the combinatorics of these bitangent classes and
its connection to the number of real bitangents to real smooth quartic cu
rves characterized by Pluecker. We will see that they are tropically conve
x sets and they come in 39 symmetry classes. The classical bitangents map
to specific vertices of these polyhedral complexes\, and each tropical bit
angent class captures four of the 28 bitangents. We will discuss the situa
tion over the reals and show that each tropical bitangent class has either
zero or four lifts to classical bitangent defined over the reals\, in agr
eement with Pluecker's classification.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Griffin (University of Washington)
DTSTART:20200520T200000Z
DTEND:20200520T210000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/4
DESCRIPTION:Title: Springer fibers\, rank varieties\, and generalized coinvariant rin
gs\nby Sean Griffin (University of Washington) as part of UC Davis alg
ebraic geometry seminar\n\n\nAbstract\nSpringer fibers are a family of var
ieties with the remarkable property that their cohomology rings $R_\\lambd
a$ have the structure of a symmetric group module\, even though there is n
o $S_n$ action on the varieties themselves. This is one of the first examp
les of a geometric representation. In the 80s\, De Concini and Procesi pro
ved that $R_\\lambda$ has another geometric description as the coordinate
ring of the scheme-theoretic intersection of a nilpotent orbit closure wit
h diagonal matrices. This led them to an explicit presentation for $R_\\la
mbda$ in terms of generators and relations\, which was further simplified
by Tanisaki. In this talk\, we present a generalization of this work to th
e coordinate ring of a scheme-theoretic intersection of Eisenbud-Saltman r
ank varieties. We then connect these coordinate rings to the generalized c
oinvariant rings recently introduced by Haglund\, Rhoades\, and Shimozono
in their work on the Delta Conjecture from Algebraic Combinatorics. We the
n give combinatorial formulas for the Hilbert series and graded Frobenius
series of our coordinate rings generalizing those of Haglund-Rhoades-Shimo
zono and Garsia-Procesi.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gurbir Dhillon (Stanford University)
DTSTART:20200527T200000Z
DTEND:20200527T210000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/5
DESCRIPTION:Title: Steinberg-Whittaker localization and affine Harish--Chandra bimodu
les\nby Gurbir Dhillon (Stanford University) as part of UC Davis algeb
raic geometry seminar\n\n\nAbstract\nA fundamental result in representatio
n theory is Beilinson--Bernstein localization\, which identifies the repre
sentations of a reductive Lie algebra with fixed central character with D-
modules on (partial) flag varieties. We will discuss a localization theor
em which identifies the same representations instead with (partial) Whitta
ker D-modules on the group. In this perspective\, representations with a f
ixed central character are equivalent to the parabolic induction of a 'Ste
inberg' category of D-modules for a Levi.\n\nTime permitting\, we will exp
lain how these methods can be used to identify a subcategory of Harish--Ch
andra bimodules for an affine Lie algebra and prove that it behaves analog
ously to Harish--Chandra bimodules with fixed central characters for a red
uctive Lie algebra. In particular\, it contains candidate principal series
representations for loop groups. This a report on work with Justin Campbe
ll.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Boixeda Álvarez (MIT)
DTSTART:20200603T200000Z
DTEND:20200603T210000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/6
DESCRIPTION:Title: On the center of the small quantum group\nby Pablo Boixeda Ál
varez (MIT) as part of UC Davis algebraic geometry seminar\n\n\nAbstract\n
We compute the $G$-equivariant part of the center of the small quantum gro
up at a regular block in terms of the cohomology of an equivalued affine S
pringer fiber.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Man-Wai Mandy Cheung (Harvard University)
DTSTART:20201007T180000Z
DTEND:20201007T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/7
DESCRIPTION:Title: Polytopes\, wall crossings\, and cluster varieties\nby Man-Wai
Mandy Cheung (Harvard University) as part of UC Davis algebraic geometry
seminar\n\n\nAbstract\nCluster varieties are log Calabi-Yau varieties whic
h are a union of algebraic tori glued by birational "mutation" maps. Parti
al compactifications of the varieties\, studied by Gross\, Hacking\, Keel\
, and Kontsevich\, generalize the polytope construction of toric varieties
. However\, it is not clear from the definitions how to characterize the p
olytopes giving compactifications of cluster varieties. We will show how t
o describe the compactifications easily by broken line convexity. As an ap
plication\, we will see the non-integral vertex in the Newton Okounkov bod
y of Gr(3\,6) comes from broken line convexity. Further\, we will also see
certain positive polytopes will give us hints about the Batyrev mirror in
the cluster setting. The mutations of the polytopes will be related to th
e almost toric fibration from the symplectic point of view. Finally\, we c
an see how to extend the idea of gluing of tori in Floer theory which then
ended up with the Family Floer Mirror for the del Pezzo surfaces of degre
e 5 and 6. The talk will be based on a series of joint works with Bossinge
r\, Lin\, Magee\, Najera-Chavez\, and Vienna.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Escobar (Washington University in St. Louis)
DTSTART:20201021T180000Z
DTEND:20201021T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/8
DESCRIPTION:Title: Wall-crossing phenomena for Newton-Okounkov bodies\nby Laura E
scobar (Washington University in St. Louis) as part of UC Davis algebraic
geometry seminar\n\n\nAbstract\nA Newton-Okounkov body is a convex set ass
ociated to a projective variety\, equipped with a valuation. These bodies
generalize the theory of Newton polytopes. Work of Kaveh-Manon gives an ex
plicit link between tropical geometry and Newton-Okounkov bodies. We use t
his link to describe a wall-crossing phenomenon for Newton-Okounkov bodies
. This is joint work with Megumi Harada.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (Michigan State University)
DTSTART:20201118T190000Z
DTEND:20201118T200000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/9
DESCRIPTION:Title: Augmentations\, Fillings\, and Clusters\nby Daping Weng (Michi
gan State University) as part of UC Davis algebraic geometry seminar\n\n\n
Abstract\nA Legendrian link is a 1-dimensional closed manifold that is emb
edded in \n$R^3$ and satisfies certain tangent conditions. Rainbow closure
s of positive braids are natural examples of Legendrian links. In the stud
y of Legendrian links\, one important task is to distinguish different exa
ct Lagrangian fillings of a Legendrian link\, up to Hamiltonian isotopy\,
in the \n$R^4$ symplectization. We introduce a cluster K2 structure on the
augmentation variety of the Chekanov-Eliashberg dga for the rainbow closu
re of any positive braid. Using the Ekholm-Honda-Kalman functor from the c
obordism category of Legendrian links to the category of dga’s\, we prov
e that a big family of fillings give rise to cluster seeds on the augmenta
tion variety of a positive braid closure\, and these cluster seeds can in
turn be used to distinguish non-Hamiltonian isotopic fillings. Moreover\,
by relating a cyclic rotation concordance on a positive braid closure with
the Donaldson-Thomas transformation on the corresponding augmentation var
iety\, we prove that other than a family of positive braids that are assoc
iated with finite type quivers\, the rainbow closure of all other positive
braids admit infinitely many non-Hamiltonian isotopic fillings. This is j
oint work with H. Gao and L. Shen.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iva Halacheva (Northeastern University)
DTSTART:20201104T190000Z
DTEND:20201104T200000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/10
DESCRIPTION:Title: Schubert calculus and Lagrangian correspondences\nby Iva Hala
cheva (Northeastern University) as part of UC Davis algebraic geometry sem
inar\n\n\nAbstract\nFor a reductive algebraic group G\, a natural question
is to consider the inclusions of partial flag varieties H/Q into G/P and
their pullbacks in equivariant cohomology\, in terms of Schubert classes.
We will look at the case of the symplectic and usual Grassmannian\, and de
scribe the pullback map combinatorially using puzzles. A generalization of
this construction involves Maulik-Okounkov classes and cotangent bundles
of the Grassmannians\, with Lagrangian correspondences playing a key role.
This is joint work with Allen Knutson and Paul Zinn-Justin.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavlo Pylyavskyy (University of Minnesota)
DTSTART:20201202T190000Z
DTEND:20201202T200000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/11
DESCRIPTION:by Pavlo Pylyavskyy (University of Minnesota) as part of UC Da
vis algebraic geometry seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Wormleighton (Washington University in St. Louis)
DTSTART:20201028T180000Z
DTEND:20201028T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/12
DESCRIPTION:Title: Symplectic embeddings via algebraic positivity\nby Ben Wormle
ighton (Washington University in St. Louis) as part of UC Davis algebraic
geometry seminar\n\n\nAbstract\nA fundamental and remarkably subtle questi
on in symplectic geometry is “when does one symplectic manifold embed in
another?”. There are two paths to approaching such problems: constructi
ng embeddings\, and obstructing embeddings\; I will focus on the latter. C
onnections with algebraic geometry emerged from work of Biran and McDuff-P
olterovich relating embeddings of disjoint unions of balls (i.e. ball pack
ing problems) and the algebraic geometry of blowups of \nP^2\, and this ta
lk will describe work over the last few years continuing in the vein of em
ploying algebraic techniques to study symplectic embedding problems. We de
scribe a sequence of invariants of a polarised algebraic surface that obst
ruct symplectic embeddings\, in many interesting cases sharply. Using this
perspective we prove a combinatorial bound on the Gromov width of toric s
urfaces conjectured by Averkov-Nill-Hofscheier\, and discuss related pheno
mena in algebraic positivity inspired by these symplectic findings.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Simental Rodriguez (University of California\, Davis)
DTSTART:20201014T180000Z
DTEND:20201014T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/13
DESCRIPTION:Title: Parabolic Hilbert schemes and representation theory\nby Jose
Simental Rodriguez (University of California\, Davis) as part of UC Davis
algebraic geometry seminar\n\n\nAbstract\nWe explicitly construct an actio
n of type A rational Cherednik algebras and\, more generally\, quantized G
ieseker varieties\, on the equivariant homology of the parabolic Hilbert s
cheme of points on the plane curve singularity $C=\\{x^m=y^n\\}$ where $m$
and $n$ are coprime positive integers. We show that the representation we
get is a highest weight irreducible representation and explicitly identif
y its highest weight. We will also place these results in the recent conte
xt of Coulomb branches and BFN Springer theory. This is joint work with Eu
gene Gorsky and Monica Vazirani.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Caitlyn Booms (University of Wisconsin)
DTSTART:20201209T190000Z
DTEND:20201209T200000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/14
DESCRIPTION:Title: Characteristic dependence of syzygies of random monomial ideals\nby Caitlyn Booms (University of Wisconsin) as part of UC Davis algebra
ic geometry seminar\n\n\nAbstract\nTo what extent do syzygies depend on th
e characteristic of the field? Even for well-studied families of examples\
, very little is known. We will explore this question for a family of rand
om monomial ideals\, namely the Stanley-Reisner ideals of random flag comp
lexes\, and we will then use our results to develop a heuristic for charac
teristic dependence of asymptotic syzygies in geometric settings.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martha Precup (Washington University in St. Louis)
DTSTART:20210112T190000Z
DTEND:20210112T200000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/15
DESCRIPTION:Title: The cohomology of nilpotent Hessenberg varieties and the dot acti
on representation\nby Martha Precup (Washington University in St. Loui
s) as part of UC Davis algebraic geometry seminar\n\n\nAbstract\nIn 2015\,
Brosnan and Chow\, and independently Guay-Paquet\, proved the Shareshian-
-Wachs conjecture\, which links the combinatorics of chromatic symmetric f
unctions to the geometry of Hessenberg varieties via a permutation group a
ction on the cohomology ring of regular semisimple Hessenberg varieties. T
his talk will give a brief overview of that story and discuss how the dot
action can be computed in all Lie types using the Betti numbers of certain
nilpotent Hessenberg varieties. As an application\, we obtain new geometr
ic insight into certain linear relations satisfied by chromatic symmetric
functions\, known as the modular law. This is joint work with Eric Sommers
.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Smirnov (UNC)
DTSTART:20210119T190000Z
DTEND:20210119T200000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/16
DESCRIPTION:Title: Elliptic stable envelope for Hilbert scheme of points in the comp
lex plane and 3D mirror symmetry\nby Andrey Smirnov (UNC) as part of U
C Davis algebraic geometry seminar\n\n\nAbstract\nIn this talk I discuss t
he elliptic stable envelope classes of torus fixed points in the Hilbert s
cheme of points in the complex plane. I describe the 3D-mirror self-dualit
y of the elliptic stable envelopes. The K-theoretic limits of these classe
s provide various special bases in the space of symmetric polynomials\, in
cluding well known bases of Macdonald or Schur functions. The mirror symme
try then translates to new symmetries for these functions. In particular\,
I outline a proof of conjectures by E.Gorsky and A.Negut on "Infinitesima
l change of stable basis''\, which relate the wall R-matrices of the Hilbe
rt scheme with the Leclerc-Thibon involution for \n$U_q(\\mathfrak{gl}_b).
$\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Bakker (Georgia Tech)
DTSTART:20210126T190000Z
DTEND:20210126T200000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/17
DESCRIPTION:Title: Hodge theory and o-minimality\nby Ben Bakker (Georgia Tech) a
s part of UC Davis algebraic geometry seminar\n\n\nAbstract\nThe cohomolog
y groups of complex algebraic varieties come equipped with a powerful but
intrinsically analytic invariant called a Hodge structure. Hodge structure
s of certain very special algebraic varieties are nonetheless parametrized
by algebraic varieties\, and while this leads to many important applicati
ons in algebraic and arithmetic geometry it fails badly in general. Joint
work with Y. Brunebarbe\, B. Klingler\, and J. Tsimerman remedies this fai
lure by showing that parameter spaces of Hodge structures always admit "ta
me" analytic structures in a sense made precise using ideas from model the
ory. A salient feature of the resulting tame analytic geometry is that it
allows for the local flexibility of the full analytic category while prese
rving the global behavior of the algebraic category.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eunjeong Lee (IBS)
DTSTART:20210203T000000Z
DTEND:20210203T010000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/18
DESCRIPTION:Title: Flag varieties and their associated polytopes\nby Eunjeong Le
e (IBS) as part of UC Davis algebraic geometry seminar\n\n\nAbstract\nLet
$G$ be a semisimple algebraic group and $B$ a Borel subgroup. The homogene
ous space $G/B$\, called the flag variety\, is a smooth projective variety
that has a fruitful connection with $G$-representations. Indeed\, the set
of global sections $H_0(G/B\,L)$ is an irreducible -representation for a
very ample line bundle $L\\to G/B$. On the other hand\, string polytopes a
re combinatorial objects which encode the characters of irreducible $G$-re
presentations. One of the most famous examples of string polytopes is the
Gelfand--Cetlin polytope\, and there might exist combinatorially different
string polytopes. The string polytopes are related with the flag varietie
s via the theory of Newton--Okounkov bodies. In this talk\, we will study
Gelfand--Cetlin type string polytopes\, their enumerations\, and we will p
resent small toric resolutions of certain string polytopes. This talk is b
ased on joint works with Yunhyung Cho\, Jang Soo Kim\, Yoosik Kim\, and Ky
eong-Dong Park.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Rutherford (Ball State University)
DTSTART:20210209T190000Z
DTEND:20210209T200000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/19
DESCRIPTION:Title: Augmentations and immersed Lagrangian fillings\nby Dan Ruther
ford (Ball State University) as part of UC Davis algebraic geometry semina
r\n\n\nAbstract\nThe Legendrian contact DGA (differential graded algebra)
is a fundamental invariant of Legendrian submanifolds that is functorial f
or a class of Lagrangian cobordisms. In particular\, a Lagrangian filling
of a Legendrian knot induces an augmentation\, i.e. a DGA map \n$\\mathcal
{A}(\\Lambda)\\to \\mathbb{F}$ to a base field. It is natural to ask: Can
every augmentation be induced by a Lagrangian filling?. The answer is no\,
and we will survey known obstructions to inducing augmentations by fillin
gs and give some new examples (joint with H. Gao) of non-fillable augmenta
tions of Legendrian twist knots. We will then present a complementary resu
lt (joint with Y. Pan) showing that any augmentation can in fact be induce
d by an immersed Lagrangian filling. Time permitting we will discuss (join
t work in progress with H. Gao) examples of immersed fillings related to r
uling stratifications of augmentation varieties.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Lam (University of Michigan)
DTSTART:20210223T190000Z
DTEND:20210223T200000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/20
DESCRIPTION:Title: Positroids\, clusters\, and Catalan numbers\nby Thomas Lam (U
niversity of Michigan) as part of UC Davis algebraic geometry seminar\n\n\
nAbstract\nPositroid varieties are subvarieties of the Grassmannian obtain
ed by intersecting cyclic rotations of Schubert varieties. I will talk abo
ut a recent result relating the (singular) cohomology of positroid varieti
es and to q\,t-Catalan theory. I will also explain some features of the co
homology of the more general class of cluster varieties.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davesh Maulik (MIT)
DTSTART:20210311T210000Z
DTEND:20210311T220000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/21
DESCRIPTION:Title: Intersection cohomology of the moduli of of 1-dimensional sheaves
and the moduli of Higgs bundles\nby Davesh Maulik (MIT) as part of UC
Davis algebraic geometry seminar\n\n\nAbstract\nIn general\, the topology
of the moduli space of semistable sheaves on an algebraic variety relies
heavily on the choice of the Euler characteristic of the sheaves being par
ametrized. I will explain two situations where the intersection cohomology
of the moduli space is independent of the choice of Euler characteristic:
moduli of one-dimensional sheaves on toric Fano surfaces and moduli of Hi
ggs bundles with poles. This confirms conjectures of Bousseau and Toda (in
certain cases)\, which predicts that this independence should occur quite
generally in the context of enumerative geometry of CY3-folds. Joint work
with Junliang Shen.\n\nNote updated date/time\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julianna Tymoczko (Smith College)
DTSTART:20210217T200000Z
DTEND:20210217T210000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/22
DESCRIPTION:Title: Comparing different bases of symmetric group representations\
nby Julianna Tymoczko (Smith College) as part of UC Davis algebraic geomet
ry seminar\n\n\nAbstract\nWe describe two different bases for irreducible
symmetric group representations: the tableaux basis from combinatorics (an
d from the geometry of a class of varieties called Springer fibers)\; and
the web basis from knot theory (and from the quantum representations of Li
e algebras). We then describe new results comparing the bases\, e.g. showi
ng that the change-of-basis matrix is upper-triangular\, and sketch some a
pplications to geometry and representation theory. This work is joint with
H. Russell\, as well as with T. Goldwasser and G. Sun.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Griffin (ICERM and UCSD)
DTSTART:20210302T190000Z
DTEND:20210302T200000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/23
DESCRIPTION:Title: The Delta conjecture and Springer fibers\nby Sean Griffin (IC
ERM and UCSD) as part of UC Davis algebraic geometry seminar\n\n\nAbstract
\nThe Delta Conjecture\, which was very recently proven by D'Adderio--Mell
it and Blasiak et al.\, gives a combinatorial formula for the result of ap
plying a certain Macdonald eigenoperator to an elementary symmetric functi
on. Pawlowski and Rhoades gave a geometric meaning to the t=0 case of this
symmetric function when they introduced the space of spanning line arrang
ements. In this talk\, I will introduce a new family of varieties\, simila
r to the type A Springer fibers\, that also give geometric meaning to the
t=0 case of the Delta Conjecture. Furthermore\, we will see how these new
varieties lead to an LLT-type formula\, and to a generalization of the Spr
inger correspondence to the setting of induced Specht modules. If time per
mits\, I will show how infinite unions of these varieties are related to t
he scheme of diagonal "rank deficient" matrices.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Negut (MIT)
DTSTART:20210330T180000Z
DTEND:20210330T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/24
DESCRIPTION:Title: On the Beauville-Voisin conjecture for Hilb(K3)\nby Andrei Ne
gut (MIT) as part of UC Davis algebraic geometry seminar\n\n\nAbstract\nWe
use representation theoretic techniques (particularly the Virasoro algebr
a) to prove the injectivity of the cycle class map from (a certain subring
of) the Chow ring to the cohomology ring of the Hilbert scheme of points
on a K3 surface\, thus yielding a version of the Beauville-Voisin conjectu
re for this particular hyperkahler manifold. Joint work with Davesh Maulik
.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richárd Rimányi (University of North Carolina)
DTSTART:20210406T180000Z
DTEND:20210406T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/25
DESCRIPTION:Title: Stable envelopes\, 3d mirror symmetry\, bow varieties\nby Ric
hárd Rimányi (University of North Carolina) as part of UC Davis algebrai
c geometry seminar\n\n\nAbstract\nThe role played by Schubert classes in t
he geometry of Grassmannians is played by the so-called stable envelopes i
n the geometry of Nakajima quiver varieties. Stable envelopes come in thre
e flavors: cohomological\, K theoretic\, and elliptic stable envelopes. We
will show examples\, and explore their appearances in enumerative geometr
y and representation theory. In the second part of the talk we will discus
s 3d mirror symmetry for characteristic classes’’\, namely\, the fact
that for certain pairs of seemingly unrelated spaces the elliptic stable e
nvelopes `match’ in some concrete (but non-obvious) sense. We will meet
Cherkis bow varieties\, a pool of spaces (conjecturally) closed under 3d m
irror symmetry for characteristic classes. The combinatorics necessary to
play Schubert calculus on bow varieties includes binary contingency tables
\, tie diagrams\, and the Hanany-Witten transition.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Rider (University of Georgia)
DTSTART:20210413T180000Z
DTEND:20210413T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/26
DESCRIPTION:Title: Modular Perverse Sheaves on the Affine Flag Variety\nby Laura
Rider (University of Georgia) as part of UC Davis algebraic geometry semi
nar\n\n\nAbstract\nThere are two categorical realizations of the affine He
cke algebra: constructible sheaves on the affine flag variety and coherent
sheaves on the Langlands dual Steinberg variety. A fundamental problem in
geometric representation theory is to relate these two categories by a ca
tegory equivalence. This was achieved by Bezrukavnikov in characteristic 0
about a decade ago. In this talk\, I will discuss a first step toward sol
ving this problem in the modular case joint with R. Bezrukavnikov and S. R
iche.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulia Sacca (Columbia University)
DTSTART:20210427T180000Z
DTEND:20210427T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/27
DESCRIPTION:Title: Fano manifolds associated to hyperkahler manifolds\nby Giulia
Sacca (Columbia University) as part of UC Davis algebraic geometry semina
r\n\n\nAbstract\nIt is known that to some Fano manifolds whose cohomology
looks like\nthat of a K3 surface\, one can associate\, via geometric const
ructions\,\nexamples of hyperkahler manifolds. In this talk I will report
on the\nfirst steps of a program whose aim is to reverse this construction
:\nstarting from a hyperkahler manifold how to recover geometrically a\nFa
no manifold? This is joint work with L. Flapan\, E.\nMacrì\, and K. O'Gra
dy.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melody Chan (Brown University)
DTSTART:20210504T180000Z
DTEND:20210504T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/28
DESCRIPTION:Title: The top-weight rational cohomology of $A_g$\nby Melody Chan (
Brown University) as part of UC Davis algebraic geometry seminar\n\n\nAbst
ract\nI'll report on recent work using tropical techniques to find new rat
ional cohomology classes in moduli spaces $A_g$ of abelian varieties\, bui
lding on previous joint work with Soren Galatius and Sam Payne on $M_g$. I
will try to give you a broad view. Joint work with Madeline Brandt\, Jul
iette Bruce\, Margarida Melo\, Gwyneth Moreland\, and Corey Wolfe.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Torres (University of Massachusetts)
DTSTART:20210511T180000Z
DTEND:20210511T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/29
DESCRIPTION:Title: Bott vanishing using GIT and quantization\nby Sebastian Torre
s (University of Massachusetts) as part of UC Davis algebraic geometry sem
inar\n\n\nAbstract\nA smooth projective variety is said to satisfy Bott va
nishing if\n$\\Omega^j\\otimes L$ has no higher cohomology for every $j$ a
nd every ample\nline bundle $L$. This is a very restrictive property\, and
there are few\nnon-toric examples known to satisfy it. I will present a n
ew class of\nexamples obtained as smooth GIT quotients of $(\\mathbb{P}^1)
^n$. For this\,\nI will need to use the work by Teleman and Halpern-Leistn
er about the\nderived category of a GIT quotient\, and explain how this al
lows us\, in\nsome cases\, to compute cohomologies directly in an ambient
quotient stack.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenny Ascher (Princeton University)
DTSTART:20210525T180000Z
DTEND:20210525T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/31
DESCRIPTION:Title: Birational geometry of moduli spaces of low degree K3 surfaces\nby Kenny Ascher (Princeton University) as part of UC Davis algebraic ge
ometry seminar\n\n\nAbstract\nWe discuss the relationships between various
compactifications of moduli spaces of low degree K3 surfaces constructed
using GIT\, Hodge theory\, and K-stability. This is based on joint works w
ith Kristin DeVleming and Yuchen Liu.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Oblomkov (University of Massachusetts)
DTSTART:20210420T180000Z
DTEND:20210420T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/32
DESCRIPTION:Title: Soergel bimodules and sheaves on the Hilbert scheme of points on
plane\nby Alexey Oblomkov (University of Massachusetts) as part of UC
Davis algebraic geometry seminar\n\n\nAbstract\nBased on joint work with R
ozansky. In my talk I outline a construction that produces a $\\mathbb{C}^
*\\times\\mathbb{C}^*$-equivariant complex of\nsheaves $S_b$ on $Hilb_n(\\
mathbb{C}^2)$ such that the space of global sections $H^*(S_b)$\nof the co
mplex are the Khovanov-Rozansky homology of the closure of the braid $b$.\
nThe construction is functorial with respect to adding a full twist to the
braid. Thus we prove a weak version of the conjecture by Gorsky-Negut-Ras
mussen.\nIn the heart of our construction is a fully faithful functor from
the category of Soergel bimodules to a particular category of matrix fact
orizations.\nI will keep the matrix factorization part minimal and concent
rate on the main idea of the construction as well as key properties of the
categories that we use.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Sherman-Bennett (UC Berkeley)
DTSTART:20210527T180000Z
DTEND:20210527T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/33
DESCRIPTION:Title: Cluster structures on subvarieties of the Grassmannian\nby Me
lissa Sherman-Bennett (UC Berkeley) as part of UC Davis algebraic geometry
seminar\n\n\nAbstract\nEarly in the history of cluster algebras\, Scott s
howed that the homogeneous coordinate ring of the Grassmannian is a cluste
r algebra\, with seeds given by Postnikov's plabic graphs for the Grassman
nian. Recently the analogous statement has been proved for open Schubert v
arieties (Leclerc\, Serhiyenko-SB-Williams) and more generally\, for open
positroid varieties (Galashin-Lam). I'll discuss joint work with Chris Fra
ser\, in which we provide a family of cluster structures for each open pos
itroid variety. Seeds for these cluster structures are given by relabeled
plabic graphs\, a natural generalization of Postnikov's construction. I'll
also explain how for Schubert varieties (and conjecturally in general)\,
relabeled plabic graphs give additional seeds for the standard" cluster st
ructure. Towards the end\, I'll also discuss joint work with M. Parisi and
L. Williams on the cluster structure of some subvarieties of Gr(2\, n) wh
ich arise naturally in the study of the m=2 amplituhedron. These subvariet
ies are closely related to positroid varieties but their cluster structure
has some intriguing dissimilarities.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Sala (University of Pisa)
DTSTART:20210601T180000Z
DTEND:20210601T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/34
DESCRIPTION:Title: Two-dimensional cohomological Hall algebras of curves and surface
s\, and their categorification\nby Francesco Sala (University of Pisa)
as part of UC Davis algebraic geometry seminar\n\n\nAbstract\nIn the pres
ent talk\, I will broadly introduce two-dimensional cohomological Hall alg
ebras of curves and surfaces\, and discuss their categorification. In the
second part of the talk\, I will discuss in detail an ongoing joint work w
ith Diaconescu\, Schiffmann\, and Vasserot\, in which we consider the coho
mological Hall algebra of a Kleinian surface singularity.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (University of Toronto)
DTSTART:20211012T180000Z
DTEND:20211012T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/35
DESCRIPTION:Title: Reverse plane partitions and components of quiver Grassmannians\nby Joel Kamnitzer (University of Toronto) as part of UC Davis algebrai
c geometry seminar\n\n\nAbstract\nA classic result in geometric representa
tion theory relates components of Springer fibres to semistandard Young ta
bleaux. I will explain how to generalize this result to reverse plane part
itions. These RPPs are decreasing functions on a minuscule heap and they p
rovide a combinatorial model for the crystal of the coordinate ring of a m
inuscule flag variety. Associated to the minuscule heap\, we define a modu
le for a preprojective algebra. The space of submodule of this module (cal
led a quiver Grassmannian) is isomorphic to the core of a Nakajima quiver
variety. Our main result is that these RPPs are in bijection with the irre
ducible components of this quiver Grassmannian.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angela Gibney (University of Pennsylvania)
DTSTART:20211019T180000Z
DTEND:20211019T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/36
DESCRIPTION:Title: Vector bundles on the moduli space of curves from vertex operator
algebras\nby Angela Gibney (University of Pennsylvania) as part of UC
Davis algebraic geometry seminar\n\n\nAbstract\nAlgebraic structures like
vector bundles\, their sections\, ranks\, and characteristic classes\, gi
ve information about spaces on which they are defined. The stack parametri
zing families of stable n-pointed curves of genus g\, and the space that (
coarsely) represents it\, give insight into curves and their degenerations
\, are prototypes for moduli of higher dimensional varieties\, and are int
eresting objects of study in their own right. Vertex operator algebras (VO
As) and their representation theory\, have had a profound influence on mat
hematics and mathematical physics\, playing a particularly important role
in understanding conformal field theories\, finite group theory\, and inva
riants in topology. In this talk I will discuss vector bundles on moduli o
f curves defined by certain representations of VOAs.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Logvinenko (Cardiff University)
DTSTART:20211026T180000Z
DTEND:20211026T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/37
DESCRIPTION:Title: The Heisenberg category of a category\nby Timothy Logvinenko
(Cardiff University) as part of UC Davis algebraic geometry seminar\n\n\nA
bstract\nIn 90s Nakajima and Grojnowski identified the total cohomology of
the Hilbert schemes of points on a smooth projective surface with the Foc
k space representation of the Heisenberg algebra associated to its cohomol
ogy lattice. Later\, Krug lifted this to derived categories and generalize
d it to the symmetric quotient stacks of any smooth projective variety.\n\
nOn the other hand\, Khovanov introduced a categorification of the free bo
son Heisenberg algebra\, i.e. the one associated to the rank 1 lattice. It
is a monoidal category whose morphisms are described by a certain planar
diagram calculus which categorifies the Heisenberg relations. A similar ca
tegorification was constructed by Cautis and Licata for the Heisenberg alg
ebras of ADE type root lattices.\n\nWe show how to associate the Heisenber
g 2-category to any smoooth and proper DG category and then define its Foc
k space 2-representation. This construction unifies all the results above
and extends them to what can be viewed as the generality of arbitrary nonc
ommutative smooth and proper schemes.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (UC Davis)
DTSTART:20211102T180000Z
DTEND:20211102T190000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/38
DESCRIPTION:Title: Cyclic Sieving and Cluster Duality for Grassmannian\nby Dapin
g Weng (UC Davis) as part of UC Davis algebraic geometry seminar\n\n\nAbst
ract\nFor any two positive integers a and b\, the homogeneous coordinate r
ing of Gr(a\,a+b) is isomorphic to a direct sum over all irreducible GL(a+
b) representations associated with weights that are multiples of w_a. Foll
owing a result of Scott\, the homogeneous coordinate ring of a Grassmannia
n has the structure of a cluster algebra. The Fock-Goncharov cluster duali
ty conjecture states that an (upper) cluster algebra admits a cluster cano
nical basis parametrized by the tropical integer points of the dual cluste
r variety. In a joint work with L. Shen\, we introduce a periodic configur
ation space of lines as the cluster dual for Gr(a\,a+b). We equip this clu
ster dual with a natural potential function W and obtain a cluster canonic
al basis for Gr(a\,a+b)\, parametrized by plane partitions. As an applicat
ion\, we prove a cyclic sieving phenomenon of plane partitions under a cer
tain toggling sequence.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angela Gibney (University of Pennsylvania)
DTSTART:20211109T190000Z
DTEND:20211109T200000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/39
DESCRIPTION:Title: Vector bundles on the moduli space of curves from vertex operator
algebras\nby Angela Gibney (University of Pennsylvania) as part of UC
Davis algebraic geometry seminar\n\n\nAbstract\nAlgebraic structures like
vector bundles\, their sections\, ranks\, and characteristic classes\, gi
ve information about spaces on which they are defined. The stack parametri
zing families of stable n-pointed curves of genus g\, and the space that (
coarsely) represents it\, give insight into curves and their degenerations
\, are prototypes for moduli of higher dimensional varieties\, and are int
eresting objects of study in their own right. Vertex operator algebras (VO
As) and their representation theory\, have had a profound influence on mat
hematics and mathematical physics\, playing a particularly important role
in understanding conformal field theories\, finite group theory\, and inva
riants in topology. In this talk I will discuss vector bundles on moduli o
f curves defined by certain representations of VOAs.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erik Carlsson (UC Davis)
DTSTART:20211116T190000Z
DTEND:20211116T200000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/40
DESCRIPTION:Title: GKM spaces and the nabla operator\nby Erik Carlsson (UC Davis
) as part of UC Davis algebraic geometry seminar\n\n\nAbstract\nI'll expla
in some recent results with A. Mellit which show that the matrix elements
of the nabla operator\, which is diagonal in the modified MacDonald basis
of symmetric functions\, compute the Frobenius character of the GKM cohomo
logy of the "unramified affine Springer fiber." From this we can see the q
\,t-symmetry\, and also a geometric interpretation of a conjecture about t
he signs of these coefficients.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Dinkins (University of North Carolina)
DTSTART:20211123T190000Z
DTEND:20211123T200000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/41
DESCRIPTION:Title: 3d mirror symmetry and vertex functions\nby Hunter Dinkins (U
niversity of North Carolina) as part of UC Davis algebraic geometry semina
r\n\n\nAbstract\nThe phenomenon of 3d mirror symmetry is a type of duality
for symplectic varieties that is intertwined with some deep objects in al
gebraic geometry\, representation theory\, and combinatorics. The main obj
ects of study are certain generating functions arising from quasimap count
s that solve q-difference equations described using representation theory.
Quasimap counts for a pair of 3d mirror dual varieties are expected to sa
tisfy the same collection of q-difference equations. There are known ways
to construct some explicit pairs of 3d mirror dual varieties. However\, ca
lculating quasimap counts and comparing the results are nontrivial tasks.
I will survey some of the expectations of 3d mirror symmetry\, discuss wha
t is presently known\, and provide some explicit examples.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allen Knutson (Cornell University)
DTSTART:20211130T190000Z
DTEND:20211130T200000Z
DTSTAMP:20260404T094752Z
UID:AG-Davis/42
DESCRIPTION:Title: The commuting scheme and generic pipe dreams\nby Allen Knutso
n (Cornell University) as part of UC Davis algebraic geometry seminar\n\n\
nAbstract\nThe space of pairs of commuting matrices is more mysterious tha
n you might think -- in particular\, Hochster's 1984 conjecture that it is
reduced remains unresolved. I'll explain how to degenerate it to one comp
onent of the "lower-upper scheme" {(X\,Y) : XY lower triangular\, YX upper
triangular}\, a reduced complete intersection\, and how to compute the de
gree of any component as a sum over "generic pipe dreams". As a consequenc
e\, this recovers both the "pipe dream" and "bumpless pipe dream" formulae
for double Schubert polynomials. Some of this work is joint with Paul Zin
n-Justin.\n
LOCATION:https://stable.researchseminars.org/talk/AG-Davis/42/
END:VEVENT
END:VCALENDAR