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BEGIN:VEVENT
SUMMARY:Bernd Sturmfels (UC Berkeley and MPI Leipzig)
DTSTART:20200422T200000Z
DTEND:20200422T210000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/1
DESCRIPTION:Title: Theta surfaces\nby Bernd Sturmfels (UC Berkeley and MPI Leipzig) as p
art of UC Davis algebraic geometry seminar\n\n\nAbstract\nA theta surface
in affine 3-space is the zero set of a Riemann theta function in genus 3.
This includes surfaces arising from special plane quartics that are singul
ar or reducible. Lie and Poincaré showed that theta surfaces are precisel
y the surfaces of double translation\, i.e. obtained as the Minkowski sum
of two space curves in two different ways. These curves are parametrized b
y abelian integrals\, so they are usually not algebraic. This paper offers
a new view on this classical topic through the lens of computation. We pr
esent practical tools for passing between quartic curves and their theta s
urfaces\, and we develop the numerical algebraic geometry of degenerations
of theta functions.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Crooks (Northeastern University)
DTSTART:20200429T200000Z
DTEND:20200429T210000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/2
DESCRIPTION:Title: Poisson slices and Hessenberg varieties\nby Peter Crooks (Northeaster
n University) as part of UC Davis algebraic geometry seminar\n\n\nAbstract
\nHessenberg varieties constitute a rich and well-studied class of closed
subvarieties in the flag variety. Prominent examples include Grothendieck-
Springer fibres\, the Peterson variety\, and the projective toric variety
associated to the Weyl chambers. These last two examples belong to the fam
ily of standard Hessenberg varieties\, whose total space is known to be a
log symplectic variety. I will exhibit this total space as a Poisson slice
in the log cotangent bundle of the wonderful compactification\, thereby b
uilding on Balibanu's recent results. This will yield a canonical closed e
mbedding of each standard Hessenberg variety into the wonderful compactifi
cation.\n\nThis represents joint work with Markus Röser.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:María Angélica Cueto (Ohio State University)
DTSTART:20200506T200000Z
DTEND:20200506T210000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/3
DESCRIPTION:Title: Combinatorics and real lifts of bitangents to tropical quartic curves
\nby María Angélica Cueto (Ohio State University) as part of UC Davis al
gebraic geometry seminar\n\n\nAbstract\nSmooth algebraic plane quartics ov
er algebraically closed fields have 28 bitangent lines. By contrast\, thei
r tropical counterparts have infinitely many bitangents. They are grouped
into seven equivalence classes\, one for each linear system associated to
an effective tropical theta characteristic on the tropical quartic curve.\
n\nIn this talk\, I will discuss recent work joint with Hannah Markwig (ar
xiv:2004.10891) on the combinatorics of these bitangent classes and its co
nnection to the number of real bitangents to real smooth quartic curves ch
aracterized by Pluecker. We will see that they are tropically convex sets
and they come in 39 symmetry classes. The classical bitangents map to spec
ific vertices of these polyhedral complexes\, and each tropical bitangent
class captures four of the 28 bitangents. We will discuss the situation ov
er the reals and show that each tropical bitangent class has either zero o
r four lifts to classical bitangent defined over the reals\, in agreement
with Pluecker's classification.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Griffin (University of Washington)
DTSTART:20200520T200000Z
DTEND:20200520T210000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/4
DESCRIPTION:Title: Springer fibers\, rank varieties\, and generalized coinvariant rings\
nby Sean Griffin (University of Washington) as part of UC Davis algebraic
geometry seminar\n\n\nAbstract\nSpringer fibers are a family of varieties
with the remarkable property that their cohomology rings $R_\\lambda$ have
the structure of a symmetric group module\, even though there is no $S_n$
action on the varieties themselves. This is one of the first examples of
a geometric representation. In the 80s\, De Concini and Procesi proved tha
t $R_\\lambda$ has another geometric description as the coordinate ring of
the scheme-theoretic intersection of a nilpotent orbit closure with diago
nal matrices. This led them to an explicit presentation for $R_\\lambda$ i
n terms of generators and relations\, which was further simplified by Tani
saki. In this talk\, we present a generalization of this work to the coord
inate ring of a scheme-theoretic intersection of Eisenbud-Saltman rank var
ieties. We then connect these coordinate rings to the generalized coinvari
ant rings recently introduced by Haglund\, Rhoades\, and Shimozono in thei
r work on the Delta Conjecture from Algebraic Combinatorics. We then give
combinatorial formulas for the Hilbert series and graded Frobenius series
of our coordinate rings generalizing those of Haglund-Rhoades-Shimozono an
d Garsia-Procesi.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gurbir Dhillon (Stanford University)
DTSTART:20200527T200000Z
DTEND:20200527T210000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/5
DESCRIPTION:Title: Steinberg-Whittaker localization and affine Harish--Chandra bimodules
\nby Gurbir Dhillon (Stanford University) as part of UC Davis algebraic ge
ometry seminar\n\n\nAbstract\nA fundamental result in representation theor
y is Beilinson--Bernstein localization\, which identifies the representati
ons of a reductive Lie algebra with fixed central character with D-modules
on (partial) flag varieties. We will discuss a localization theorem whic
h identifies the same representations instead with (partial) Whittaker D-m
odules on the group. In this perspective\, representations with a fixed ce
ntral character are equivalent to the parabolic induction of a 'Steinberg'
category of D-modules for a Levi.\n\nTime permitting\, we will explain ho
w these methods can be used to identify a subcategory of Harish--Chandra b
imodules for an affine Lie algebra and prove that it behaves analogously t
o Harish--Chandra bimodules with fixed central characters for a reductive
Lie algebra. In particular\, it contains candidate principal series repres
entations for loop groups. This a report on work with Justin Campbell.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Boixeda Álvarez (MIT)
DTSTART:20200603T200000Z
DTEND:20200603T210000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/6
DESCRIPTION:Title: On the center of the small quantum group\nby Pablo Boixeda Álvarez (
MIT) as part of UC Davis algebraic geometry seminar\n\n\nAbstract\nWe comp
ute the $G$-equivariant part of the center of the small quantum group at a
regular block in terms of the cohomology of an equivalued affine Springer
fiber.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Man-Wai Mandy Cheung (Harvard University)
DTSTART:20201007T180000Z
DTEND:20201007T190000Z
DTSTAMP:20260422T212749Z
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 which are a
union of algebraic tori glued by birational "mutation" maps. Partial comp
actifications of the varieties\, studied by Gross\, Hacking\, Keel\, and K
ontsevich\, generalize the polytope construction of toric varieties. Howev
er\, it is not clear from the definitions how to characterize the polytope
s giving compactifications of cluster varieties. We will show how to descr
ibe the compactifications easily by broken line convexity. As an applicati
on\, we will see the non-integral vertex in the Newton Okounkov body of Gr
(3\,6) comes from broken line convexity. Further\, we will also see certai
n positive polytopes will give us hints about the Batyrev mirror in the cl
uster setting. The mutations of the polytopes will be related to the almos
t toric fibration from the symplectic point of view. Finally\, we can 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 degree 5 and
6. The talk will be based on a series of joint works with Bossinger\, Lin
\, Magee\, Najera-Chavez\, and Vienna.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Escobar (Washington University in St. Louis)
DTSTART:20201021T180000Z
DTEND:20201021T190000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/8
DESCRIPTION:Title: Wall-crossing phenomena for Newton-Okounkov bodies\nby Laura Escobar
(Washington University in St. Louis) as part of UC Davis algebraic geometr
y seminar\n\n\nAbstract\nA Newton-Okounkov body is a convex set associated
to a projective variety\, equipped with a valuation. These bodies general
ize the theory of Newton polytopes. Work of Kaveh-Manon gives an explicit
link between tropical geometry and Newton-Okounkov bodies. We use this lin
k to describe a wall-crossing phenomenon for Newton-Okounkov bodies. This
is joint work with Megumi Harada.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (Michigan State University)
DTSTART:20201118T190000Z
DTEND:20201118T200000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/9
DESCRIPTION:Title: Augmentations\, Fillings\, and Clusters\nby Daping Weng (Michigan Sta
te University) as part of UC Davis algebraic geometry seminar\n\n\nAbstrac
t\nA Legendrian link is a 1-dimensional closed manifold that is embedded i
n \n$R^3$ and satisfies certain tangent conditions. Rainbow closures of po
sitive braids are natural examples of Legendrian links. In the study of Le
gendrian links\, one important task is to distinguish different exact Lagr
angian fillings of a Legendrian link\, up to Hamiltonian isotopy\, in the
\n$R^4$ symplectization. We introduce a cluster K2 structure on the augmen
tation variety of the Chekanov-Eliashberg dga for the rainbow closure of a
ny positive braid. Using the Ekholm-Honda-Kalman functor from the cobordis
m category of Legendrian links to the category of dga’s\, we prove that
a big family of fillings give rise to cluster seeds on the augmentation va
riety of a positive braid closure\, and these cluster seeds can in turn be
used to distinguish non-Hamiltonian isotopic fillings. Moreover\, by rela
ting a cyclic rotation concordance on a positive braid closure with the Do
naldson-Thomas transformation on the corresponding augmentation variety\,
we prove that other than a family of positive braids that are associated w
ith finite type quivers\, the rainbow closure of all other positive braids
admit infinitely many non-Hamiltonian isotopic fillings. This is joint wo
rk with H. Gao and L. Shen.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iva Halacheva (Northeastern University)
DTSTART:20201104T190000Z
DTEND:20201104T200000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/10
DESCRIPTION:Title: Schubert calculus and Lagrangian correspondences\nby Iva Halacheva (
Northeastern University) as part of UC Davis algebraic geometry seminar\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 p
ullbacks in equivariant cohomology\, in terms of Schubert classes. We will
look at the case of the symplectic and usual Grassmannian\, and describe
the pullback map combinatorially using puzzles. A generalization of this c
onstruction involves Maulik-Okounkov classes and cotangent bundles of the
Grassmannians\, with Lagrangian correspondences playing a key role. This i
s joint work with Allen Knutson and Paul Zinn-Justin.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavlo Pylyavskyy (University of Minnesota)
DTSTART:20201202T190000Z
DTEND:20201202T200000Z
DTSTAMP:20260422T212749Z
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://researchseminars.org/talk/AG-Davis/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Wormleighton (Washington University in St. Louis)
DTSTART:20201028T180000Z
DTEND:20201028T190000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/12
DESCRIPTION:Title: Symplectic embeddings via algebraic positivity\nby Ben Wormleighton
(Washington University in St. Louis) as part of UC Davis algebraic geometr
y seminar\n\n\nAbstract\nA fundamental and remarkably subtle question in s
ymplectic geometry is “when does one symplectic manifold embed in anothe
r?”. There are two paths to approaching such problems: constructing embe
ddings\, and obstructing embeddings\; I will focus on the latter. Connecti
ons with algebraic geometry emerged from work of Biran and McDuff-Polterov
ich relating embeddings of disjoint unions of balls (i.e. ball packing pro
blems) and the algebraic geometry of blowups of \nP^2\, and this talk will
describe work over the last few years continuing in the vein of employing
algebraic techniques to study symplectic embedding problems. We describe
a sequence of invariants of a polarised algebraic surface that obstruct sy
mplectic embeddings\, in many interesting cases sharply. Using this perspe
ctive we prove a combinatorial bound on the Gromov width of toric surfaces
conjectured by Averkov-Nill-Hofscheier\, and discuss related phenomena in
algebraic positivity inspired by these symplectic findings.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Simental Rodriguez (University of California\, Davis)
DTSTART:20201014T180000Z
DTEND:20201014T190000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/13
DESCRIPTION:Title: Parabolic Hilbert schemes and representation theory\nby Jose Simenta
l Rodriguez (University of California\, Davis) as part of UC Davis algebra
ic geometry seminar\n\n\nAbstract\nWe explicitly construct an action of ty
pe A rational Cherednik algebras and\, more generally\, quantized Gieseker
varieties\, on the equivariant homology of the parabolic Hilbert scheme o
f 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 identify its h
ighest weight. We will also place these results in the recent context of C
oulomb branches and BFN Springer theory. This is joint work with Eugene Go
rsky and Monica Vazirani.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Caitlyn Booms (University of Wisconsin)
DTSTART:20201209T190000Z
DTEND:20201209T200000Z
DTSTAMP:20260422T212749Z
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 algebraic geom
etry seminar\n\n\nAbstract\nTo what extent do syzygies depend on the chara
cteristic of the field? Even for well-studied families of examples\, very
little is known. We will explore this question for a family of random mono
mial ideals\, namely the Stanley-Reisner ideals of random flag complexes\,
and we will then use our results to develop a heuristic for characteristi
c dependence of asymptotic syzygies in geometric settings.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martha Precup (Washington University in St. Louis)
DTSTART:20210112T190000Z
DTEND:20210112T200000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/15
DESCRIPTION:Title: The cohomology of nilpotent Hessenberg varieties and the dot action repr
esentation\nby Martha Precup (Washington University in St. Louis) as p
art of UC Davis algebraic geometry seminar\n\n\nAbstract\nIn 2015\, Brosna
n and Chow\, and independently Guay-Paquet\, proved the Shareshian--Wachs
conjecture\, which links the combinatorics of chromatic symmetric function
s to the geometry of Hessenberg varieties via a permutation group action o
n the cohomology ring of regular semisimple Hessenberg varieties. This tal
k 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 nilpot
ent Hessenberg varieties. As an application\, we obtain new geometric insi
ght into certain linear relations satisfied by chromatic symmetric functio
ns\, known as the modular law. This is joint work with Eric Sommers.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Smirnov (UNC)
DTSTART:20210119T190000Z
DTEND:20210119T200000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/16
DESCRIPTION:Title: Elliptic stable envelope for Hilbert scheme of points in the complex pla
ne and 3D mirror symmetry\nby Andrey Smirnov (UNC) as part of UC Davis
algebraic geometry seminar\n\n\nAbstract\nIn this talk I discuss the elli
ptic stable envelope classes of torus fixed points in the Hilbert scheme o
f points in the complex plane. I describe the 3D-mirror self-duality of th
e elliptic stable envelopes. The K-theoretic limits of these classes provi
de various special bases in the space of symmetric polynomials\, including
well known bases of Macdonald or Schur functions. The mirror symmetry the
n translates to new symmetries for these functions. In particular\, I outl
ine a proof of conjectures by E.Gorsky and A.Negut on "Infinitesimal chang
e of stable basis''\, which relate the wall R-matrices of the Hilbert sche
me with the Leclerc-Thibon involution for \n$U_q(\\mathfrak{gl}_b).$\n
LOCATION:https://researchseminars.org/talk/AG-Davis/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Bakker (Georgia Tech)
DTSTART:20210126T190000Z
DTEND:20210126T200000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/17
DESCRIPTION:Title: Hodge theory and o-minimality\nby Ben Bakker (Georgia Tech) as part
of UC Davis algebraic geometry seminar\n\n\nAbstract\nThe cohomology group
s of complex algebraic varieties come equipped with a powerful but intrins
ically analytic invariant called a Hodge structure. Hodge structures of ce
rtain very special algebraic varieties are nonetheless parametrized by alg
ebraic varieties\, and while this leads to many important applications in
algebraic and arithmetic geometry it fails badly in general. Joint work wi
th Y. Brunebarbe\, B. Klingler\, and J. Tsimerman remedies this failure by
showing that parameter spaces of Hodge structures always admit "tame" ana
lytic structures in a sense made precise using ideas from model theory. A
salient feature of the resulting tame analytic geometry is that it allows
for the local flexibility of the full analytic category while preserving t
he global behavior of the algebraic category.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eunjeong Lee (IBS)
DTSTART:20210203T000000Z
DTEND:20210203T010000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/18
DESCRIPTION:Title: Flag varieties and their associated polytopes\nby Eunjeong Lee (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 homogeneous spa
ce $G/B$\, called the flag variety\, is a smooth projective variety that h
as a fruitful connection with $G$-representations. Indeed\, the set of glo
bal sections $H_0(G/B\,L)$ is an irreducible -representation for a very am
ple line bundle $L\\to G/B$. On the other hand\, string polytopes are comb
inatorial objects which encode the characters of irreducible $G$-represent
ations. 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 varieties via t
he theory of Newton--Okounkov bodies. In this talk\, we will study Gelfand
--Cetlin type string polytopes\, their enumerations\, and we will present
small toric resolutions of certain string polytopes. This talk is based on
joint works with Yunhyung Cho\, Jang Soo Kim\, Yoosik Kim\, and Kyeong-Do
ng Park.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Rutherford (Ball State University)
DTSTART:20210209T190000Z
DTEND:20210209T200000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/19
DESCRIPTION:Title: Augmentations and immersed Lagrangian fillings\nby Dan Rutherford (B
all State University) as part of UC Davis algebraic geometry seminar\n\n\n
Abstract\nThe Legendrian contact DGA (differential graded algebra) is a fu
ndamental invariant of Legendrian submanifolds that is functorial for a cl
ass of Lagrangian cobordisms. In particular\, a Lagrangian filling of a Le
gendrian knot induces an augmentation\, i.e. a DGA map \n$\\mathcal{A}(\\L
ambda)\\to \\mathbb{F}$ to a base field. It is natural to ask: Can every a
ugmentation be induced by a Lagrangian filling?. The answer is no\, and we
will survey known obstructions to inducing augmentations by fillings and
give some new examples (joint with H. Gao) of non-fillable augmentations o
f Legendrian twist knots. We will then present a complementary result (joi
nt with Y. Pan) showing that any augmentation can in fact be induced by an
immersed Lagrangian filling. Time permitting we will discuss (joint work
in progress with H. Gao) examples of immersed fillings related to ruling s
tratifications of augmentation varieties.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Lam (University of Michigan)
DTSTART:20210223T190000Z
DTEND:20210223T200000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/20
DESCRIPTION:Title: Positroids\, clusters\, and Catalan numbers\nby Thomas Lam (Universi
ty of Michigan) as part of UC Davis algebraic geometry seminar\n\n\nAbstra
ct\nPositroid varieties are subvarieties of the Grassmannian obtained by i
ntersecting cyclic rotations of Schubert varieties. I will talk about a re
cent result relating the (singular) cohomology of positroid varieties and
to q\,t-Catalan theory. I will also explain some features of the cohomolog
y of the more general class of cluster varieties.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davesh Maulik (MIT)
DTSTART:20210311T210000Z
DTEND:20210311T220000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/21
DESCRIPTION:Title: Intersection cohomology of the moduli of of 1-dimensional sheaves and th
e 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 parametriz
ed. 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 Higgs bun
dles with poles. This confirms conjectures of Bousseau and Toda (in certai
n cases)\, which predicts that this independence should occur quite genera
lly in the context of enumerative geometry of CY3-folds. Joint work with J
unliang Shen.\n\nNote updated date/time\n
LOCATION:https://researchseminars.org/talk/AG-Davis/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julianna Tymoczko (Smith College)
DTSTART:20210217T200000Z
DTEND:20210217T210000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/22
DESCRIPTION:Title: Comparing different bases of symmetric group representations\nby Jul
ianna Tymoczko (Smith College) as part of UC Davis algebraic geometry semi
nar\n\n\nAbstract\nWe describe two different bases for irreducible symmetr
ic group representations: the tableaux basis from combinatorics (and from
the geometry of a class of varieties called Springer fibers)\; and the web
basis from knot theory (and from the quantum representations of Lie algeb
ras). We then describe new results comparing the bases\, e.g. showing that
the change-of-basis matrix is upper-triangular\, and sketch some applicat
ions to geometry and representation theory. This work is joint with H. Rus
sell\, as well as with T. Goldwasser and G. Sun.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Griffin (ICERM and UCSD)
DTSTART:20210302T190000Z
DTEND:20210302T200000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/23
DESCRIPTION:Title: The Delta conjecture and Springer fibers\nby Sean Griffin (ICERM and
UCSD) as part of UC Davis algebraic geometry seminar\n\n\nAbstract\nThe D
elta Conjecture\, which was very recently proven by D'Adderio--Mellit and
Blasiak et al.\, gives a combinatorial formula for the result of applying
a certain Macdonald eigenoperator to an elementary symmetric function. Paw
lowski and Rhoades gave a geometric meaning to the t=0 case of this symmet
ric function when they introduced the space of spanning line arrangements.
In this talk\, I will introduce a new family of varieties\, similar to th
e type A Springer fibers\, that also give geometric meaning to the t=0 cas
e of the Delta Conjecture. Furthermore\, we will see how these new varieti
es lead to an LLT-type formula\, and to a generalization of the Springer c
orrespondence to the setting of induced Specht modules. If time permits\,
I will show how infinite unions of these varieties are related to the sche
me of diagonal "rank deficient" matrices.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Negut (MIT)
DTSTART:20210330T180000Z
DTEND:20210330T190000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/24
DESCRIPTION:Title: On the Beauville-Voisin conjecture for Hilb(K3)\nby Andrei Negut (MI
T) as part of UC Davis algebraic geometry seminar\n\n\nAbstract\nWe use re
presentation theoretic techniques (particularly the Virasoro algebra) to p
rove the injectivity of the cycle class map from (a certain subring of) th
e Chow ring to the cohomology ring of the Hilbert scheme of points on a K3
surface\, thus yielding a version of the Beauville-Voisin conjecture for
this particular hyperkahler manifold. Joint work with Davesh Maulik.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richárd Rimányi (University of North Carolina)
DTSTART:20210406T180000Z
DTEND:20210406T190000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/25
DESCRIPTION:Title: Stable envelopes\, 3d mirror symmetry\, bow varieties\nby Richárd R
imányi (University of North Carolina) as part of UC Davis algebraic geome
try seminar\n\n\nAbstract\nThe role played by Schubert classes in the geom
etry of Grassmannians is played by the so-called stable envelopes in the g
eometry of Nakajima quiver varieties. Stable envelopes come in three flavo
rs: cohomological\, K theoretic\, and elliptic stable envelopes. We will s
how examples\, and explore their appearances in enumerative geometry and r
epresentation theory. In the second part of the talk we will discuss 3d mi
rror symmetry for characteristic classes’’\, namely\, the fact that fo
r certain pairs of seemingly unrelated spaces the elliptic stable envelope
s `match’ in some concrete (but non-obvious) sense. We will meet Cherkis
bow varieties\, a pool of spaces (conjecturally) closed under 3d mirror s
ymmetry for characteristic classes. The combinatorics necessary to play Sc
hubert calculus on bow varieties includes binary contingency tables\, tie
diagrams\, and the Hanany-Witten transition.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Rider (University of Georgia)
DTSTART:20210413T180000Z
DTEND:20210413T190000Z
DTSTAMP:20260422T212749Z
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 seminar\n\n
\nAbstract\nThere are two categorical realizations of the affine Hecke alg
ebra: constructible sheaves on the affine flag variety and coherent sheave
s on the Langlands dual Steinberg variety. A fundamental problem in geomet
ric representation theory is to relate these two categories by a category
equivalence. This was achieved by Bezrukavnikov in characteristic 0 about
a decade ago. In this talk\, I will discuss a first step toward solving th
is problem in the modular case joint with R. Bezrukavnikov and S. Riche.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulia Sacca (Columbia University)
DTSTART:20210427T180000Z
DTEND:20210427T190000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/27
DESCRIPTION:Title: Fano manifolds associated to hyperkahler manifolds\nby Giulia Sacca
(Columbia University) as part of UC Davis algebraic geometry seminar\n\n\n
Abstract\nIt is known that to some Fano manifolds whose cohomology looks l
ike\nthat of a K3 surface\, one can associate\, via geometric construction
s\,\nexamples of hyperkahler manifolds. In this talk I will report on the\
nfirst steps of a program whose aim is to reverse this construction:\nstar
ting from a hyperkahler manifold how to recover geometrically a\nFano mani
fold? This is joint work with L. Flapan\, E.\nMacrì\, and K. O'Grady.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melody Chan (Brown University)
DTSTART:20210504T180000Z
DTEND:20210504T190000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/28
DESCRIPTION:Title: The top-weight rational cohomology of $A_g$\nby Melody Chan (Brown U
niversity) as part of UC Davis algebraic geometry seminar\n\n\nAbstract\nI
'll report on recent work using tropical techniques to find new rational c
ohomology classes in moduli spaces $A_g$ of abelian varieties\, building o
n previous joint work with Soren Galatius and Sam Payne on $M_g$. I will t
ry to give you a broad view. Joint work with Madeline Brandt\, Juliette B
ruce\, Margarida Melo\, Gwyneth Moreland\, and Corey Wolfe.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Torres (University of Massachusetts)
DTSTART:20210511T180000Z
DTEND:20210511T190000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/29
DESCRIPTION:Title: Bott vanishing using GIT and quantization\nby Sebastian Torres (Univ
ersity of Massachusetts) as part of UC Davis algebraic geometry seminar\n\
n\nAbstract\nA smooth projective variety is said to satisfy Bott vanishing
if\n$\\Omega^j\\otimes L$ has no higher cohomology for every $j$ and ever
y 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 new clas
s of\nexamples obtained as smooth GIT quotients of $(\\mathbb{P}^1)^n$. Fo
r this\,\nI will need to use the work by Teleman and Halpern-Leistner abou
t the\nderived category of a GIT quotient\, and explain how this allows us
\, in\nsome cases\, to compute cohomologies directly in an ambient quotien
t stack.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenny Ascher (Princeton University)
DTSTART:20210525T180000Z
DTEND:20210525T190000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/31
DESCRIPTION:Title: Birational geometry of moduli spaces of low degree K3 surfaces\nby K
enny Ascher (Princeton University) as part of UC Davis algebraic geometry
seminar\n\n\nAbstract\nWe discuss the relationships between various compac
tifications of moduli spaces of low degree K3 surfaces constructed using G
IT\, Hodge theory\, and K-stability. This is based on joint works with Kri
stin DeVleming and Yuchen Liu.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Oblomkov (University of Massachusetts)
DTSTART:20210420T180000Z
DTEND:20210420T190000Z
DTSTAMP:20260422T212749Z
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 a
lgebraic geometry seminar\n\n\nAbstract\nBased on joint work with Rozansky
. In my talk I outline a construction that produces a $\\mathbb{C}^*\\time
s\\mathbb{C}^*$-equivariant complex of\nsheaves $S_b$ on $Hilb_n(\\mathbb{
C}^2)$ such that the space of global sections $H^*(S_b)$\nof the complex a
re the Khovanov-Rozansky homology of the closure of the braid $b$.\nThe co
nstruction is functorial with respect to adding a full twist to the braid.
Thus we prove a weak version of the conjecture by Gorsky-Negut-Rasmussen.
\nIn the heart of our construction is a fully faithful functor from the ca
tegory of Soergel bimodules to a particular category of matrix factorizati
ons.\nI will keep the matrix factorization part minimal and concentrate on
the main idea of the construction as well as key properties of the catego
ries that we use.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Sherman-Bennett (UC Berkeley)
DTSTART:20210527T180000Z
DTEND:20210527T190000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/33
DESCRIPTION:Title: Cluster structures on subvarieties of the Grassmannian\nby Melissa S
herman-Bennett (UC Berkeley) as part of UC Davis algebraic geometry semina
r\n\n\nAbstract\nEarly in the history of cluster algebras\, Scott showed t
hat the homogeneous coordinate ring of the Grassmannian is a cluster algeb
ra\, with seeds given by Postnikov's plabic graphs for the Grassmannian. R
ecently the analogous statement has been proved for open Schubert varietie
s (Leclerc\, Serhiyenko-SB-Williams) and more generally\, for open positro
id varieties (Galashin-Lam). I'll discuss joint work with Chris Fraser\, i
n which we provide a family of cluster structures for each open positroid
variety. Seeds for these cluster structures are given by relabeled plabic
graphs\, a natural generalization of Postnikov's construction. I'll also e
xplain how for Schubert varieties (and conjecturally in general)\, relabel
ed plabic graphs give additional seeds for the standard" cluster structure
. Towards the end\, I'll also discuss joint work with M. Parisi and L. Wil
liams on the cluster structure of some subvarieties of Gr(2\, n) which ari
se naturally in the study of the m=2 amplituhedron. These subvarieties are
closely related to positroid varieties but their cluster structure has so
me intriguing dissimilarities.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Sala (University of Pisa)
DTSTART:20210601T180000Z
DTEND:20210601T190000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/34
DESCRIPTION:Title: Two-dimensional cohomological Hall algebras of curves and surfaces\, and
their categorification\nby Francesco Sala (University of Pisa) as par
t of UC Davis algebraic geometry seminar\n\n\nAbstract\nIn the present tal
k\, I will broadly introduce two-dimensional cohomological Hall algebras o
f curves and surfaces\, and discuss their categorification. In the second
part of the talk\, I will discuss in detail an ongoing joint work with Dia
conescu\, Schiffmann\, and Vasserot\, in which we consider the cohomologic
al Hall algebra of a Kleinian surface singularity.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (University of Toronto)
DTSTART:20211012T180000Z
DTEND:20211012T190000Z
DTSTAMP:20260422T212749Z
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 algebraic geome
try seminar\n\n\nAbstract\nA classic result in geometric representation th
eory relates components of Springer fibres to semistandard Young tableaux.
I will explain how to generalize this result to reverse plane partitions.
These RPPs are decreasing functions on a minuscule heap and they provide
a combinatorial model for the crystal of the coordinate ring of a minuscul
e flag variety. Associated to the minuscule heap\, we define a module for
a preprojective algebra. The space of submodule of this module (called a q
uiver Grassmannian) is isomorphic to the core of a Nakajima quiver variety
. Our main result is that these RPPs are in bijection with the irreducible
components of this quiver Grassmannian.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angela Gibney (University of Pennsylvania)
DTSTART:20211019T180000Z
DTEND:20211019T190000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/36
DESCRIPTION:Title: Vector bundles on the moduli space of curves from vertex operator algebr
as\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\, give info
rmation about spaces on which they are defined. The stack parametrizing fa
milies of stable n-pointed curves of genus g\, and the space that (coarsel
y) represents it\, give insight into curves and their degenerations\, are
prototypes for moduli of higher dimensional varieties\, and are interestin
g objects of study in their own right. Vertex operator algebras (VOAs) and
their representation theory\, have had a profound influence on mathematic
s and mathematical physics\, playing a particularly important role in unde
rstanding conformal field theories\, finite group theory\, and invariants
in topology. In this talk I will discuss vector bundles on moduli of curve
s defined by certain representations of VOAs.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Logvinenko (Cardiff University)
DTSTART:20211026T180000Z
DTEND:20211026T190000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/37
DESCRIPTION:Title: The Heisenberg category of a category\nby Timothy Logvinenko (Cardif
f University) as part of UC Davis algebraic geometry seminar\n\n\nAbstract
\nIn 90s Nakajima and Grojnowski identified the total cohomology of the Hi
lbert schemes of points on a smooth projective surface with the Fock space
representation of the Heisenberg algebra associated to its cohomology lat
tice. Later\, Krug lifted this to derived categories and generalized it to
the symmetric quotient stacks of any smooth projective variety.\n\nOn the
other hand\, Khovanov introduced a categorification of the free boson Hei
senberg algebra\, i.e. the one associated to the rank 1 lattice. It is a m
onoidal category whose morphisms are described by a certain planar diagram
calculus which categorifies the Heisenberg relations. A similar categorif
ication was constructed by Cautis and Licata for the Heisenberg algebras o
f ADE type root lattices.\n\nWe show how to associate the Heisenberg 2-cat
egory to any smoooth and proper DG category and then define its Fock space
2-representation. This construction unifies all the results above and ext
ends them to what can be viewed as the generality of arbitrary noncommutat
ive smooth and proper schemes.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (UC Davis)
DTSTART:20211102T180000Z
DTEND:20211102T190000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/38
DESCRIPTION:Title: Cyclic Sieving and Cluster Duality for Grassmannian\nby Daping Weng
(UC Davis) as part of UC Davis algebraic geometry seminar\n\n\nAbstract\nF
or any two positive integers a and b\, the homogeneous coordinate ring of
Gr(a\,a+b) is isomorphic to a direct sum over all irreducible GL(a+b) repr
esentations associated with weights that are multiples of w_a. Following a
result of Scott\, the homogeneous coordinate ring of a Grassmannian has t
he structure of a cluster algebra. The Fock-Goncharov cluster duality conj
ecture states that an (upper) cluster algebra admits a cluster canonical b
asis parametrized by the tropical integer points of the dual cluster varie
ty. In a joint work with L. Shen\, we introduce a periodic configuration s
pace of lines as the cluster dual for Gr(a\,a+b). We equip this cluster du
al with a natural potential function W and obtain a cluster canonical basi
s for Gr(a\,a+b)\, parametrized by plane partitions. As an application\, w
e prove a cyclic sieving phenomenon of plane partitions under a certain to
ggling sequence.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angela Gibney (University of Pennsylvania)
DTSTART:20211109T190000Z
DTEND:20211109T200000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/39
DESCRIPTION:Title: Vector bundles on the moduli space of curves from vertex operator algebr
as\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\, give info
rmation about spaces on which they are defined. The stack parametrizing fa
milies of stable n-pointed curves of genus g\, and the space that (coarsel
y) represents it\, give insight into curves and their degenerations\, are
prototypes for moduli of higher dimensional varieties\, and are interestin
g objects of study in their own right. Vertex operator algebras (VOAs) and
their representation theory\, have had a profound influence on mathematic
s and mathematical physics\, playing a particularly important role in unde
rstanding conformal field theories\, finite group theory\, and invariants
in topology. In this talk I will discuss vector bundles on moduli of curve
s defined by certain representations of VOAs.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erik Carlsson (UC Davis)
DTSTART:20211116T190000Z
DTEND:20211116T200000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/40
DESCRIPTION:Title: GKM spaces and the nabla operator\nby Erik Carlsson (UC Davis) as pa
rt of UC Davis algebraic geometry seminar\n\n\nAbstract\nI'll explain 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 symm
etric functions\, compute the Frobenius character of the GKM cohomology of
the "unramified affine Springer fiber." From this we can see the q\,t-sym
metry\, and also a geometric interpretation of a conjecture about the sign
s of these coefficients.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Dinkins (University of North Carolina)
DTSTART:20211123T190000Z
DTEND:20211123T200000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/41
DESCRIPTION:Title: 3d mirror symmetry and vertex functions\nby Hunter Dinkins (Universi
ty of North Carolina) as part of UC Davis algebraic geometry seminar\n\n\n
Abstract\nThe phenomenon of 3d mirror symmetry is a type of duality for sy
mplectic varieties that is intertwined with some deep objects in algebraic
geometry\, representation theory\, and combinatorics. The main objects of
study are certain generating functions arising from quasimap counts that
solve q-difference equations described using representation theory. Quasim
ap counts for a pair of 3d mirror dual varieties are expected to satisfy t
he same collection of q-difference equations. There are known ways to cons
truct some explicit pairs of 3d mirror dual varieties. However\, calculati
ng quasimap counts and comparing the results are nontrivial tasks. I will
survey some of the expectations of 3d mirror symmetry\, discuss what is pr
esently known\, and provide some explicit examples.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allen Knutson (Cornell University)
DTSTART:20211130T190000Z
DTEND:20211130T200000Z
DTSTAMP:20260422T212749Z
UID:AG-Davis/42
DESCRIPTION:Title: The commuting scheme and generic pipe dreams\nby Allen Knutson (Corn
ell University) as part of UC Davis algebraic geometry seminar\n\n\nAbstra
ct\nThe space of pairs of commuting matrices is more mysterious than you m
ight think -- in particular\, Hochster's 1984 conjecture that it is reduce
d remains unresolved. I'll explain how to degenerate it to one component o
f the "lower-upper scheme" {(X\,Y) : XY lower triangular\, YX upper triang
ular}\, a reduced complete intersection\, and how to compute the degree of
any component as a sum over "generic pipe dreams". As a consequence\, thi
s recovers both the "pipe dream" and "bumpless pipe dream" formulae for do
uble Schubert polynomials. Some of this work is joint with Paul Zinn-Justi
n.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/42/
END:VEVENT
END:VCALENDAR