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BEGIN:VEVENT
SUMMARY:Maxence Mayrand (University of Toronto)
DTSTART:20200903T185000Z
DTEND:20200903T195000Z
DTSTAMP:20260422T225840Z
UID:GPRTatNU/1
DESCRIPTION:Title: Symplectic reduction along a submanifold and the Moore-Tachikawa TQFT
\nby Maxence Mayrand (University of Toronto) as part of Geometry\, Physics
\, and Representation Theory Seminar\n\n\nAbstract\nIn 2011\, Moore and Ta
chikawa conjectured the existence of certain complex Hamiltonian varieties
which generate two-dimensional TQFTs where the target category has comple
x reductive groups as objects and holomorphic symplectic varieties as arro
ws. It was solved by Ginzburg and Kazhdan using an ad hoc technique which
can be thought of as a kind of "symplectic reduction by a group scheme." W
e clarify their construction by introducing a general notion of "symplecti
c reduction by a groupoid along a submanifold\," which generalizes many co
nstructions at once\, such as standard symplectic reduction\, preimages of
Slodowy slices\, the Mikami-Weinstein reduction\, and the Ginzburg-Kazhda
n examples. This is joint work with Peter Crooks.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svetlana Makarova (University of Pennsylvania)
DTSTART:20200910T185000Z
DTEND:20200910T195000Z
DTSTAMP:20260422T225840Z
UID:GPRTatNU/2
DESCRIPTION:Title: Moduli spaces of stable sheaves over quasipolarized K3 surfaces and Stran
ge Duality\nby Svetlana Makarova (University of Pennsylvania) as part
of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nI
n this talk\, I will show a construction of relative moduli spaces of stab
le sheaves over the stack of quasipolarized K3 surfaces of degree two. For
this\, we use the theory of good moduli spaces\, whose study was initiate
d by Alper. As a corollary\, we obtain the generic Strange Duality for K3
surfaces of degree two\, extending the results of Marian and Oprea on the
generic Strange Duality for K3 surfaces.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Jeffrey (University of Toronto)
DTSTART:20200917T185000Z
DTEND:20200917T195000Z
DTSTAMP:20260422T225840Z
UID:GPRTatNU/3
DESCRIPTION:Title: Flat connections and the $SU(2)$ commutator map\nby Lisa Jeffrey (Uni
versity of Toronto) as part of Geometry\, Physics\, and Representation The
ory Seminar\n\n\nAbstract\nThis talk is joint work with Nan-Kuo Ho\, Paul
Selick and Eugene Xia. We describe the space of conjugacy classes of repre
sentations of the fundamental group of a genus 2 oriented 2-manifold into
$G := SU(2)$.\n\nWe identify the cohomology ring and a cell decomposition
of a\; space homotopy equivalent to the space of commuting pairs in $SU(2)
$.\n\nWe compute the cohomology of the space $M:= \\mu^{-1}(-I)$\, where $
\\mu:G^4 \\to G$ is the product of commutators.\n\nWe give a new proof of
the cohomology of $A:= M/G$\, both as a group and as a ring. The group str
ucture is due to Atiyah and Bott in their landmark 1983 paper. The ring st
ructure is due to Michael Thaddeus 1992.\n\nWe compute the cohomology of t
he total space of the prequantum line bundle over $A$.\n\nWe identify the
transition functions of the induced $SO(3)$ bundle $M\\to A$.\n\nTo appear
in QJM (Atiyah memorial special issue). arXiv:2005.07390\n\nReferences:\n
\n[1] M.F. Atiyah\, R. Bott\, The Yang-Mills equations over Riemann surfac
es\, Phil. Trans. Roy. Soc. Lond. A308 (1983) 523-615.\n\n[2] T. Baird\, L
. Jeffrey\, P. Selick\, The space of commuting n-tuples in $SU(2)$\, Illin
ois J. Math. 55 (2011)\, no. 3\, 805–813.\n\n[3] M. Crabb\, Spaces of co
mmuting elements in $SU(2)$\, Proc. Edin. Math. Soc. 54 (2011)\, no. 1\, 6
7–75.\n\n[4] N. Ho\, L. Jeffrey\, K. Nguyen\, E. Xia\, The $SU(2)$-chara
cter variety of the closed surface of genus 2. Geom. Dedicata 192 (2018)\,
171–187.\n\n[5] N. Ho\, L. Jeffrey\, P. Selick\, E. Xia\, Flat connecti
ons and the commutator map for $SU(2)$\, Oxford Quart. J. Math.\, to appea
r (in the Atiyah memorial special issue).\n\n[6] L. Jeffrey\, A. Lindberg\
, S. Rayan\, Explicit Poincar´e duality in the cohomology ring of the $SU
(2)$ character variety of a surface. Expos. Math.\, to appear.\n\n[7] M.S.
Narasimhan and C.S. Seshadri\, Stable and unitary vector bundles on a com
pact Riemann surface. Ann. of Math. 82 (1965) 540–567.\n\n[8] P. Newstea
d\, Topological properties of some spaces of stable bundles\, Topology 6 (
1967)\, 241–262.\n\n[9] C.T.C Wall\, Classification problems in differen
tial topology. V. On certain 6-manifolds. Invent. Math. 1 (1966)\, 355–3
74\; corrigendum\, ibid.\, 2 (1966) 306.\n\n[10] M. Thaddeus\, Conformal f
ield theory and the cohomology of the moduli space of stable bundles. J. D
ifferential Geom. 35 (1992) 131–149.\n\n[11] E. Witten\, Two dimensional
gauge theories revisited\, J. Geom. Phys. 9 (1992) 303-368.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Smirnov (University of North Carolina at Chapel Hill)
DTSTART:20201001T185000Z
DTEND:20201001T195000Z
DTSTAMP:20260422T225840Z
UID:GPRTatNU/4
DESCRIPTION:Title: Quantum difference equations\, monodromies and mirror symmetry\nby An
drey Smirnov (University of North Carolina at Chapel Hill) as part of Geom
etry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nAn impor
tant enumerative invariant of a symplectic variety $X$ is its vertex funct
ion. The vertex function is the analog of J-function in Gromov-Witten theo
ry: it is the generating function for the numbers of rational curves in $X
$.\n\nIn representation theory these functions feature as solutions of var
ious $q$-difference and differential equations associated with $X$\, with
examples including qKZ and quantum dynamical equations for quantum loop gr
oups\, Casimir connections for Yangians and other objects.\n\nIn this talk
I explain how these equations can be extracted from algebraic topology of
symplectic dual variety $X^!$\, also known as $3D$-mirror of $X$. This ca
n be summarized as "identity"\n$$\n\\text{Enumerative geometry of }X = \\t
ext{algebraic topology of }X^!\n$$\nThe talk is based on work in progress
with Y.Kononov arXiv:2004.07862\; arXiv:2008.06309.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soheyla Feyzbakhsh (Imperial College)
DTSTART:20201015T185000Z
DTEND:20201015T195000Z
DTSTAMP:20260422T225840Z
UID:GPRTatNU/5
DESCRIPTION:Title: An application of Bogomolov-Gieseker type inequality to counting invarian
ts\nby Soheyla Feyzbakhsh (Imperial College) as part of Geometry\, Phy
sics\, and Representation Theory Seminar\n\n\nAbstract\nIn this talk\, I w
ill work on a smooth projective threefold $X$ which satisfies the Bogomolo
v-Gieseker conjecture of Bayer-Macrì-Toda\, such as the projective space
$\\mathbb{P}^3$ or the quintic threefold. I will show certain moduli space
s of 2-dimensional torsion sheaves on $X$ are smooth bundles over Hilbert
schemes of ideal sheaves of curves and points in $X$. When $X$ is Calabi-Y
au this gives a simple wall crossing formula expressing curve counts (and
so ultimately Gromov-Witten invariants) in terms of counts of D4-D2-D0 bra
nes. This is joint work with Richard Thomas\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Alekseev (University of Geneva)
DTSTART:20201022T185000Z
DTEND:20201022T195000Z
DTSTAMP:20260422T225840Z
UID:GPRTatNU/6
DESCRIPTION:Title: Poisson-Lie groups\, integrable systems and the Berenstein-Kazhdan potent
ial\nby Anton Alekseev (University of Geneva) as part of Geometry\, Ph
ysics\, and Representation Theory Seminar\n\n\nAbstract\nIntegrable system
s and Poisson-Lie groups are closely related topics. In this talk\, we wil
l explain how integrability helps in understanding Poisson geometry of the
dual Poisson-Lie group $K^*$ of a compact Lie group $K$. One of our main
tools will be the Berenstein-Kazhdan potential from the theory of canonica
l bases.\n\nThe talk is based on joint works with A. Berenstein\, I. David
enkova\, B. Hoffman\, J. Lane and Y. Li.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Balázs Elek (Cornell University)
DTSTART:20200924T185000Z
DTEND:20200924T195000Z
DTSTAMP:20260422T225840Z
UID:GPRTatNU/7
DESCRIPTION:Title: Heaps\, Crystals and Preprojective algebra modules\nby Balázs Elek (
Cornell University) as part of Geometry\, Physics\, and Representation The
ory Seminar\n\n\nAbstract\nKashiwara crystals are combinatorial gadgets as
sociated to a representation of a reductive algebraic group that enable us
to understand the structure of the representation in purely combinatorial
terms. We will describe a type-independent construction of crystals of ce
rtain representations\, using the heap associated to a fully commutative e
lement in the Weyl group. Then we will discuss how these heaps also lead u
s to the construction of modules for the preprojective algebra of the Dynk
in quiver. Using the rank-nullity theorem\, we will see how the Kashiwara
operators have a surprisingly nice description in terms of these preprojec
tive algebra modules. This is work in progress joint with Anne Dranowski\,
Joel Kamnitzer\, Tanny Libman and Calder Morton-Ferguson.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolle González (University of California at Los Angeles)
DTSTART:20201008T185000Z
DTEND:20201008T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/8
DESCRIPTION:Title: A Skein theoretic Carlsson-Mellit algebra\nby Nicolle González (Univ
ersity of California at Los Angeles) as part of Geometry\, Physics\, and R
epresentation Theory Seminar\n\n\nAbstract\nThe Carlsson-Mellit algebra ar
ose for the first time in the proof of the shuffle conjecture\, which give
s an explicit combinatorial formula for the Frobenius character of the spa
ce of diagonal harmonics in terms of parking functions. Its polynomial rep
resentation\, given by certain complicated plethystic operators over exten
sions of the ring of symmetric functions\, plays a particularly important
role as it encodes much of the underlying combinatorial theory. By various
results of Gorsky\, Mellit and Carlsson it was shown that this algebra ca
n be used to construct generators of the Elliptic Hall algebra in addition
to having deep connections to the homology of torus knots. Thus\, a natur
al starting point in the search to categorify these structures is the cate
gorification of the Carlsson-Mellit algebra and its polynomial representat
ion. \n\nIn this talk I will explain joint work with Matt Hogancamp where
we constructed a purely skein theoretic formulation of this algebra and re
alized its generators as certain braid diagrams on a thickened annulus. Co
nsequently\, we used this framework to categorify the polynomial represent
ation of the Carlsson-Mellit algebra as a family of functors over the deri
ved trace of the Soergel category.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Simental Rodríguez (University of California at Davis)
DTSTART:20201029T185000Z
DTEND:20201029T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/9
DESCRIPTION:Title: Parabolic Hilbert schemes and representation theory\nby José Simenta
l Rodríguez (University of California at Davis) as part of Geometry\, Phy
sics\, and Representation Theory Seminar\n\n\nAbstract\nWe explicitly cons
truct an action of type A rational Cherednik algebras and\, more generally
\, quantized Gieseker varieties\, on the equivariant homology of the parab
olic Hilbert scheme 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 identify its highest weight. We will also place these resul
ts in the recent context of Coulomb branches and BFN Springer theory. This
is joint work with Eugene Gorsky and Monica Vazirani.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah White (Australian National University)
DTSTART:20201105T195000Z
DTEND:20201105T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/10
DESCRIPTION:Title: Cactus group actions and cell modules\nby Noah White (Australian Nat
ional University) as part of Geometry\, Physics\, and Representation Theor
y Seminar\n\n\nAbstract\nThe cactus group associated to a Coxeter group ca
n be thought of as an asymptotic version of the braid group. It has been o
bserved by many authors that interesting cactus group actions can be const
ructed in many situations when one has a representation of the braid group
. In this talk I will explain what the cactus group is\, and what is meant
by "asymptotic". I will also explain how to construct cactus group action
s associated to cell modules of the Hecke algebra\, a description of this
action using Lusztig’s isomorphism between the Hecke algebra and group a
lgebra and point to some interesting questions along the way. Much of this
talk is work joint with Raphael Rouquier.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrike Rieß (ETH Zürich)
DTSTART:20201112T195000Z
DTEND:20201112T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/11
DESCRIPTION:Title: On the Kähler cone of irreducible symplectic orbifolds\nby Ulrike R
ieß (ETH Zürich) as part of Geometry\, Physics\, and Representation Theo
ry Seminar\n\n\nAbstract\nIn this talk I report on recent joint work with
G. Menet: We generalize a series of classical results on irreducible sympl
ectic manifolds to the orbifold setting. In particular we prove a characte
rization of the Kähler cone using wall divisors. This generalizes results
of Mongardi for the smooth case. I will finish the talk by applying these
results to study a concrete example.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rekha Biswal (University of Edinburgh)
DTSTART:20201119T195000Z
DTEND:20201119T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/12
DESCRIPTION:Title: Macdonald polynomials and level two Demazure modules for affine $\\mathf
rak{sl}_{n+1}$\nby Rekha Biswal (University of Edinburgh) as part of G
eometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nAn im
portant result due to Sanderson and Ion says that characters of level one
Demazure modules are specialized Macdonald polynomials. In this talk\, I w
ill introduce a new class of symmetric polynomials indexed by a pair of do
minant weights of $\\mathfrak{sl}_{n+1}$ which is expressed as linear comb
ination of specialized symmetric Macdonald polynomials with coefficients d
efined recursively. These polynomials arose in my own work while investiga
ting the characters of higher level Demazure modules. Using representation
theory\, we will see that these new family of polynomials interpolate bet
ween characters of level one and level two Demazure modules for affine $\\
mathfrak{sl}_{n+1}$ and give rise to new results in the representation the
ory of current algebras as a corollary. This is based on joint work with V
yjayanthi Chari\, Peri Shereen and Jeffrey Wand.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li Yu (University of Chicago)
DTSTART:20201203T195000Z
DTEND:20201203T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/13
DESCRIPTION:Title: Wonderful compactification of a Cartan subalgebra of a semisimple Lie al
gebra\nby Li Yu (University of Chicago) as part of Geometry\, Physics\
, and Representation Theory Seminar\n\n\nAbstract\nLet $H$ be a Cartan sub
group of a semisimple algebraic group $G$ over the complex numbers. The wo
nderful compactification $\\overline{H}$ of $H$ was introduced and studied
by De Concini and Procesi. For the Lie algebra $\\mathfrak{h}$ of $H$\, w
e define an analogous compactification $\\overline{\\mathfrak{h}}$ of $\\m
athfrak{h}$\, to be referred to as the wonderful compactification of $\\ma
thfrak{h}$. The wonderful compactification of $\\mathfrak{h}$ is an exampl
e of an "additive toric variety". We establish a bijection between the set
of irreducible components of the boundary $\\overline{\\mathfrak{h}} - \\
mathfrak{h}$ of $\\mathfrak{h}$ and the set of maximal closed root subsyst
ems of the root system for $(G\, H)$ of rank $r - 1\,$ where $r$ is the di
mension of $\\mathfrak{h}$. An algorithm based on Borel-de Siebenthal theo
ry that constructs all such root subsystems is given. We prove that each i
rreducible component of $\\overline{\\mathfrak{h}}- \\mathfrak{h}$ is isom
orphic to the wonderful compactification of a Lie subalgebra of $\\mathfra
k{h}$ and is of dimension $r - 1$. In particular\, the boundary $\\overli
ne{\\mathfrak{h}} - \\mathfrak{h}$ is equidimensional. We describe a large
subset of the regular locus of $\\overline{\\mathfrak{h}}$. As a conseque
nce\, we prove that $\\overline{\\mathfrak{h}}$ is a normal variety.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Wen (Northeastern University)
DTSTART:20210128T195000Z
DTEND:20210128T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/14
DESCRIPTION:Title: Towards wreath Macdonald theory\nby Joshua Wen (Northeastern Univers
ity) as part of Geometry\, Physics\, and Representation Theory Seminar\n\n
\nAbstract\nWreath Macdonald polynomials are generalizations of Macdonald
polynomials wherein the symmetric groups are replaced with their wreath pr
oducts with a cyclic group of order $\\ell$. They were defined by Haiman\,
and mirroring the usual Macdonald theory\, it is not obvious that they ex
ist. Haiman also conjectured for them a generalization of his celebrated p
roof of Macdonald positivity where the Hilbert scheme of points on the pla
ne is replaced with certain cyclic Nakajima quiver varieties. This conject
ure was proven by Bezrukavnikov and Finkelberg\, which also implies the ex
istence of the polynomials. Analogues of standard formulas and results of
usual Macdonald theory remain to be explored. I will present an approach t
o the study of the wreath variants via the quantum toroidal algebra of $\\
mathfrak{sl}_\\ell$\, generalizing the fruitful interactions between the u
sual Macdonald theory and the quantum toroidal algebra of $\\mathfrak{gl}_
1$. As applications\, I'll present an analogue of the norm formula and a c
onjectural path towards "wreath Macdonald operators" that makes contact wi
th the spin Ruijsenaars-Schneider integrable system.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martha Precup (Washington University at St. Louis)
DTSTART:20210204T195000Z
DTEND:20210204T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/15
DESCRIPTION:Title: The cohomology of nilpotent Hessenberg varieties and the dot action repr
esentation\nby Martha Precup (Washington University at St. Louis) as p
art of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstrac
t\nIn 2015\, Brosnan and Chow\, and independently Guay-Paquet\, proved the
Shareshian--Wachs conjecture\, which links the combinatorics of chromatic
symmetric functions to the geometry of Hessenberg varieties via a permuta
tion group action on the cohomology ring of regular semisimple Hessenberg
varieties. This 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 numbe
rs of certain nilpotent Hessenberg varieties. As an application\, we obtai
n new geometric insight into certain linear relations satisfied by chromat
ic symmetric functions\, known as the modular law. This is joint work wit
h Eric Sommers.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Cliff (University of Sydney)
DTSTART:20210211T195000Z
DTEND:20210211T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/16
DESCRIPTION:Title: Moduli of principal bundles for 2-groups\nby Emily Cliff (University
of Sydney) as part of Geometry\, Physics\, and Representation Theory Semi
nar\n\n\nAbstract\nA 2-group is a categorified version of a group. In this
talk\, we will study the structure of moduli stacks and spaces of princip
al bundles for 2-groups. In a special case where the isomorphism classes o
f objects in our 2-group form a finite (ordinary) group $G$\, we show that
the moduli stack provides a higher-categorical enhancement of the Freed--
Quinn line bundle appearing in Chern--Simons theory for the finite group $
G$. This is joint work with Eric Berry\, Dan Berwick-Evans\, Laura Murray\
, Apurva Nakade\, and Emma Phillips.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabell Hellmann (HCM Bonn)
DTSTART:20210218T195000Z
DTEND:20210218T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/17
DESCRIPTION:Title: The nilpotent cone in the Mukai system of rank two and genus two\nby
Isabell Hellmann (HCM Bonn) as part of Geometry\, Physics\, and Represent
ation Theory Seminar\n\n\nAbstract\nLet $S$ be a K3 surface and $C$ a smoo
th curve in $S$. We consider the moduli space $M$ of coherent sheaves on $
S$ which are supported on a curve rational equivalent to $nC$ and have fix
ed Euler characteristic (coprime to $n$). Then $M$ is an irreducible holom
orphic symplectic manifold equipped with a Lagrangian fibration given by t
aking supports. This is the beautiful Mukai system.\n\nOne source of inter
est in the Mukai system is\, that it deforms to the Hitchin system on $C$.
And there is a notion of the nilpotent cone in the Mukai system deforming
to the nilpotent cone in the Hitchin system. In my talk\, I present some
results about the nilpotent cone on the Mukai side (in the lowest dimensio
nal case)\, which can then be transferred to the Hitchin side.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oksana Yakimova (University of Jena)
DTSTART:20210304T195000Z
DTEND:20210304T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/18
DESCRIPTION:Title: Symmetrisation and the Feigin-Frenkel centre\nby Oksana Yakimova (Un
iversity of Jena) as part of Geometry\, Physics\, and Representation Theor
y Seminar\n\n\nAbstract\nLet $G$ be a complex reductive group\, set $\\mat
hfrak g={\\mathrm{Lie\\\,}}G$. The algebra ${\\mathcal S}(\\mathfrak g)^{\
\mathfrak g}$ of symmetric $\\mathfrak g$-invariants and the centre ${\\ma
thcal Z}(\\mathfrak g)$ of the enveloping algebra ${\\mathcal U}(\\mathfra
k g)$ are polynomial rings in ${\\mathrm{rk\\\,}}\\mathfrak g$ generators.
There are several isomorphisms between them\, including the symmetrisatio
n map $\\varpi$\, which exists also for the Lie algebras $\\mathfrak q$ wi
th $\\dim\\mathfrak q=\\infty$.\n\nHowever\, in the infinite dimensional c
ase\, one may need to complete ${\\mathcal U}(\\mathfrak q)$ in order to r
eplace ${\\mathcal Z}(\\mathfrak q)$ with an interesting related object. R
oughly speaking\, the Feigin-Frenkel centre arises as a result of such com
pletion in case of an affine Kac-Moody algebra. From 1982 until 2006\, thi
s algebra existed as an intriguing black box with many applications. Then
explicit formulas for its elements appeared first in type ${\\sf A}$\, lat
er in all other classical types\, and it was discovered that the FF-centre
is the centraliser of the quadratic Casimir element.\n\nWe will discuss t
he type-free role of the symmetrisation map in the description of the FF-c
entre and present new explicit formulas for its generators in types ${\\sf
B}$\, ${\\sf C}$\, ${\\sf D}$\, and ${\\sf G}_2$. One of our main technic
al tools is a certain map from ${\\mathcal S}^{k}(\\mathfrak g)$ to $\\Lam
bda^2\\mathfrak g \\otimes {\\mathcal S}^{k-3}(\\mathfrak g)$.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Dinkins (UNC Chapel Hill)
DTSTART:20210225T195000Z
DTEND:20210225T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/19
DESCRIPTION:Title: Combinatorics of 3d Mirror Symmetry\nby Hunter Dinkins (UNC Chapel H
ill) as part of Geometry\, Physics\, and Representation Theory Seminar\n\n
\nAbstract\n3d mirror symmetry is a conjectured duality among symplectic v
arieties that expects deep relationships between enumerative invariants of
varieties that may appear to be unrelated. In this talk\, I will describe
the general setup of 3d mirror symmetry and will then explain its nontriv
ial combinatorial implications in the example of the cotangent bundle of t
he Grassmannian and its mirror variety. In this case\, the 3d mirror relat
ionship is governed by a new family of difference operators which characte
rize the Macdonald polynomials.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tina Kanstrup (UMass Amherst)
DTSTART:20210311T195000Z
DTEND:20210311T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/20
DESCRIPTION:Title: Link homologies and Hilbert schemes via representation theory\nby Ti
na Kanstrup (UMass Amherst) as part of Geometry\, Physics\, and Representa
tion Theory Seminar\n\n\nAbstract\nThe aim of this joint work in progress
with Roman Bezrukavnikov is to unite different approaches to Khovanov-Roza
nsky triply graded link homology. The original definition is completely al
gebraic in terms of Soergel bimodules. It has been conjectured by Gorsky\,
Negut and Rasmussen that it can also be calculated geometrically in terms
of cohomolgy of sheaves on Hilbert schemes. Motivated by string theory Ob
lomkov and Rozansky constructed a link invariant in terms of matrix factor
izations on related spaces and later proved that it coincides with Khovano
v-Rozansky homology. In this talk I’ll discuss a direct relation between
the different constructions and how one might invent these spaces startin
g directly from definitions.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Zhao (MIT)
DTSTART:20210318T185000Z
DTEND:20210318T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/21
DESCRIPTION:by Yu Zhao (MIT) as part of Geometry\, Physics\, and Represent
ation Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Shapiro (Notre Dame)
DTSTART:20210325T185000Z
DTEND:20210325T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/22
DESCRIPTION:Title: Cluster realization of spherical DAHA\nby Alexander Shapiro (Notre D
ame) as part of Geometry\, Physics\, and Representation Theory Seminar\n\n
\nAbstract\nSpherical subalgebra of Cherednik's double affine Hecke algebr
a of type A admits a polynomial representation in which its generators act
via elementary symmetric functions and Macdonald operators. Recognizing t
he elementary symmetric functions as eigenfunctions of quantum Toda Hamilt
onians\, and applying (the inverse of) the Toda spectral transform\, one o
btains a new representation of spherical DAHA. In this talk\, I will discu
ss how this new representation gives rise to an injective homomorphism fro
m the spherical DAHA into a quantum cluster algebra in such a way that the
action of the modular group on the former is realized via cluster transfo
rmations. The talk is based on a joint work in progress with Philippe Di F
rancesco\, Rinat Kedem\, and Gus Schrader.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kristin DeVleming (UC San Diego)
DTSTART:20210415T185000Z
DTEND:20210415T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/23
DESCRIPTION:Title: Wall crossing for K-moduli spaces\nby Kristin DeVleming (UC San Dieg
o) as part of Geometry\, Physics\, and Representation Theory Seminar\n\n\n
Abstract\nThere are many different methods to compactly moduli spaces of v
arieties with a rich source of examples from compactifying moduli spaces o
f curves. In this talk\, I will explain a relatively new compactification
coming from K-stability and how it connects to serval other compactificat
ions\, focusing on the case of plane curves of degree $d$. In particular\,
we regard a plane curve as a log Fano pair $(\\mathbb{P}^2\, aC)$ and stu
dy the K-moduli compactifications and establish a wall crossing framework
as a varies. We will describe all wall crossings for low degree plane curv
es and discuss the picture for general $\\mathbb{Q}$-Gorenstein smoothable
log Fano pairs. This is joint work with Kenneth Ascher and Yuchen Liu.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harm Derksen (Northeastern University)
DTSTART:20210422T185000Z
DTEND:20210422T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/24
DESCRIPTION:Title: The G-Stable Rank for Tensors\nby Harm Derksen (Northeastern Univers
ity) as part of Geometry\, Physics\, and Representation Theory Seminar\n\n
\nAbstract\nThe rank of a matrix can be generalized to tensors. In fact\,
there are many different rank notions for tensors that all coincide for ma
trices\, such as the tensor rank\, border rank\, subrank and slice rank (a
nd asymptotic versions of each of these). In this talk I will discuss two
notions of rank that are closely related to Geometric Invariant Theory\, t
he non-commutative rank and the G-stable rank. The non-commutative rank ca
n be used for giving lower bounds for tensor rank and border rank. The G-s
table rank was recently used by my graduate student Zhi Jiang to improve t
he asymptotic upper bounds of Ellenberg and Gijswijt for the Cap Set Probl
em.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milen Yakimov (Northeastern University)
DTSTART:20210408T185000Z
DTEND:20210408T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/25
DESCRIPTION:Title: Root of unity quantum cluster algebras\nby Milen Yakimov (Northeaste
rn University) as part of Geometry\, Physics\, and Representation Theory S
eminar\n\n\nAbstract\nWe will describe a theory of root of unity quantum c
luster algebras\, which cover as special cases the big quantum groups of D
e Concini\, Kac and Process. All such algebras will be shown to be polynom
ial identity (PI) algebras. Inside each of them\, we will construct a cano
nical central subalgebra which is proved to be isomorphic to the underlyin
g cluster algebra. It is a far-reaching generalization of the De Concini-K
ac-Procesi central subalgebras in big quantum groups and presents a genera
l framework for studying the representation theory of quantum algebras at
roots of unity by means of cluster algebras as the relevant data becomes (
PI algebra\, canonical central subalgebra)=(root of unity quantum cluster
algebra\, underlying cluster algebra). We will also present an explicit fo
rmula for the corresponding discriminants in this general setting that can
be applied in many concrete situations of interest\, such as the discrimi
nants of all root of unity quantum unipotent cells for symmetrizable Kac-M
oody algebras. This is a joint work with Bach Nguyen (Xavier Univ) and Kur
t Trampel (Notre Dame Univ).\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inês Rodrigues (University of Lisbon)
DTSTART:20210401T185000Z
DTEND:20210401T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/26
DESCRIPTION:Title: A cactus group action on shifted tableau crystals and a shifted Berenste
in-Kirillov group\nby Inês Rodrigues (University of Lisbon) as part o
f Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nGi
llespie\, Levinson and Purbhoo introduced a crystal-like structure for shi
fted tableaux\, called the shifted tableau crystal. Following a similar ap
proach as Halacheva\, we exhibit a natural internal action of the cactus g
roup on this structure\, realized by the restrictions of the shifted Schü
tzenberger involution to all primed intervals of the underlying crystal al
phabet. This includes the shifted crystal reflection operators\, which agr
ee with the restrictions of the shifted Schützenberger involution to sing
le-coloured connected components\, but unlike the case for type A crystals
\, these do not need to satisfy the braid relations of the symmetric group
.\n\nIn addition\, we define a shifted version of the Berenstein-Kirillov
group\, by considering shifted Bender-Knuth involutions. Paralleling the w
orks of Halacheva and Chmutov\, Glick and Pylyavskyy for type A semistanda
rd tableaux of straight shape\, we exhibit another occurrence of the cactu
s group action on shifted tableau crystals of straight shape via the actio
n of the shifted Berenstein-Kirillov group. We conclude that the shifted B
erenstein-Kirillov group is isomorphic to a quotient of the cactus group.
Not all known relations that hold in the classic Berenstein-Kirillov group
need to be satisfied by the shifted Bender-Knuth involutions\, namely the
one equivalent to the braid relations of the type A crystal reflection op
erators\, but the ones implying the relations of the cactus group are veri
fied\, thus we have another presentation for the cactus group in terms of
shifted Bender-Knuth involutions.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matan Harel (Northeastern University)
DTSTART:20210422T201000Z
DTEND:20210422T211000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/27
DESCRIPTION:Title: The loop O(n) model and the XOR trick\nby Matan Harel (Northeastern
University) as part of Geometry\, Physics\, and Representation Theory Semi
nar\n\n\nAbstract\nThe loop O(n) model is a model for random configuration
s of non-overlapping loops on the hexagonal lattice\, which contains many
models of interest (such as the Ising model\, self-avoiding walks\, and ra
ndom Lipshitz functions) as special cases. The physics literature conjectu
res that the model undergoes several different phase transitions\, leading
to a dazzling phase diagram\; over the last several years\, several featu
res of the phase diagram have been proven rigorously. In this talk\, I wil
l describe the predicted behavior of the model and show some recent progre
ss towards proving that typical samples of perturbations of the uniform me
asure on loop configurations have long loops. This is joint work with Nick
Crawford\, Alexander Glazman\, and Ron Peled.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Jin (Boston College)
DTSTART:20210909T185000Z
DTEND:20210909T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/28
DESCRIPTION:Title: Homological mirror symmetry for the universal centralizers\nby Xin J
in (Boston College) as part of Geometry\, Physics\, and Representation The
ory Seminar\n\n\nAbstract\nI will present my recent result on homological
mirror symmetry for the universal centralizer (a.k.a Toda space) associate
d to a complex semisimple Lie group.\n\nThe A-side is a partially wrapped
Fukaya category on the universal centralizer\, and the B-side is the categ
ory of coherent sheaves on the categorical quotient of the dual maximal to
rus by the Weyl group (with some modifications if the group has nontrivial
center). I will illustrate many of the geometry and ideas of the proof us
ing the example of SL_2 or PGL_2.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Ruehle (Northeastern University)
DTSTART:20210916T185000Z
DTEND:20210916T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/29
DESCRIPTION:Title: Geodesics and topological transitions in Calabi-Yau manifolds of Picard
rank two\nby Fabian Ruehle (Northeastern University) as part of Geomet
ry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nWe discuss
the structure of the Kähler moduli space of Picard rank two Calabi-Yau t
hreefolds\, which are given in terms of complete intersections in projecti
ve ambient spaces\, or as hypersurfaces in toric ambient spaces. As it tur
ns out\, flop transitions are ubiquitous in such setups. The triple inters
ection form of the Kähler cone generators can be brought into four differ
ent normal forms\, and we use this to solve the geodesic equations in the
moduli space for each one of them. Moreover\, we will discuss that flops c
an lead to isomorphic or non-isomorphic Calabi-Yau manifolds. We find that
there exist infinite flop chains of isomorphic geometries\, but only a fi
nite number of flops to inequivalent manifolds. Physically\, the latter re
sult is expected based on the swampland distance conjecture\, and mathemat
ically fits to a conjecture due to Kawamata and Morrison for Calabi-Yau th
reefolds.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ignacio Barros-Reyes (Paris-Saclay University)
DTSTART:20210923T185000Z
DTEND:20210923T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/30
DESCRIPTION:Title: Irrationality of moduli spaces\nby Ignacio Barros-Reyes (Paris-Sacla
y University) as part of Geometry\, Physics\, and Representation Theory Se
minar\n\n\nAbstract\nI will talk about the problem of determining the bira
tional complexity of moduli spaces of curves and K3 surfaces. I will recal
l some recently introduced invariants that measure irrationality and talk
about what is known for these moduli spaces. In the second half I will rep
ort on joint work with D. Agostini and K.-W. Lai\, where we study how the
degrees of irrationality of the moduli spaces of polarized K3 surfaces gro
w with respect to the genus g. We provide polynomial bounds. The proof rel
ies on Kudla's modularity conjecture for Shimura varieties of orthogonal t
ype. For special genera we exploit the deep Hodge theoretic relation betwe
en K3 surfaces and special hyperkähler fourfolds to obtain much sharper b
ounds.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (University of Toronto)
DTSTART:20210930T185000Z
DTEND:20210930T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/31
DESCRIPTION:Title: Monodromy of eigenvectors for trigonometric Gaudin algebras\nby Joel
Kamnitzer (University of Toronto) as part of Geometry\, Physics\, and Rep
resentation Theory Seminar\n\n\nAbstract\nConsider a tensor product of rep
resentations of a semisimple Lie algebra g. The Gaudin algebra is a commut
ative algebra which acts on this tensor product\, commuting with the actio
n of g. This algebra depends on a parameter which lives in the moduli spac
e of marked genus 0 curves. In previous work\, we studied the monodromy of
eigenvectors for this algebra as the parameter varies in the real locus o
f this space. In new work in-progress\, we consider trigonometric Gaudin a
lgebras\, which act on the same vector space (but do not commute with the
g-action). We see that this leads to the action of the affine cactus group
\, and we describe the action of this group combinatorially using crystals
. I will also describe the (conjectural) relation between trigonometric Ga
udin algebras and the quantum cohomology of affine Grassmannian slices.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renzo Cavalieri (Colorado State University)
DTSTART:20211202T195000Z
DTEND:20211202T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/32
DESCRIPTION:Title: The integral Chow ring of $M_0(\\mathbb{P}^r\,d)$\nby Renzo Cavalier
i (Colorado State University) as part of Geometry\, Physics\, and Represen
tation Theory Seminar\n\n\nAbstract\nWe give an efficient presentation of
the Chow ring with integral coefficients of the open part of the \n
moduli space of rational maps of odd degree to projective space. A less fa
ncy description of this space \n has its closed points correspond to
equivalence classes of $(r+1)$-tuples of degree $d$ polynomials in one \n
variable with no common positive degree factor. We identify this sp
ace as a $GL(2)$ quotient of an open \n set in a projective space\,
and then obtain a (highly redundant) presentation by considering an envelo
pe \n of the complement. A combinatorial analysis then leads us to e
liminating a large number of relations\, \n and to express the remai
ning ones in generating function form for all dimensions. The upshot of th
is \n work is to observe the rich combinatorial structure contained
in the Chow rings of these moduli spaces \n as the degree and the ta
rget dimension vary. This is joint work with Damiano Fulghesu.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julianna Tymoczko (Smith College)
DTSTART:20211104T185000Z
DTEND:20211104T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/34
DESCRIPTION:Title: Comparing different bases for irreducible symmetric group representation
s\nby Julianna Tymoczko (Smith College) as part of Geometry\, Physics\
, and Representation Theory Seminar\n\n\nAbstract\nWe describe two differe
nt bases for irreducible symmetric group representations: the tableaux bas
is from combinatorics (and from the geometry of a class of varieties calle
d Springer fibers)\; and the web basis from knot theory (and from the quan
tum representations of Lie algebras). We then describe new results compar
ing the bases\, e.g. showing that the change-of-basis matrix is upper-tria
ngular\, and sketch some applications to geometry and representation theor
y. This work is joint with H. Russell\, as well as with T. Goldwasser and
G. Sun.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karina Batistelli (University of Chile)
DTSTART:20211118T195000Z
DTEND:20211118T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/35
DESCRIPTION:Title: Kazhdan-Lusztig polynomials for $\\tilde{B}_2$\nby Karina Batistelli
(University of Chile) as part of Geometry\, Physics\, and Representation
Theory Seminar\n\n\nAbstract\nKazhdan-Lusztig polynomials lie at the inter
section of representation theory\, geometry and algebraic combinatorics. D
espite their relevance and elementary definition (through a recursive algo
rithm involving only elementary operations)\, the explicit computation of
these polynomials is still one of the hardest open problems in algebraic c
ombinatorics. In this talk we will present the explicit formulas of the Ka
zhdan-Lusztig polynomials for a Coxeter system of type $\\tilde{B}_2$.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Kang (California Institute of Technology)
DTSTART:20211209T195000Z
DTEND:20211209T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/36
DESCRIPTION:Title: Characteristic numbers of elliptic fourfolds\nby Monica Kang (Califo
rnia Institute of Technology) as part of Geometry\, Physics\, and Represen
tation Theory Seminar\n\n\nAbstract\nI will first consider crepant resolut
ions of Weierstrass models corresponding to elliptically-fibered fourfolds
with simple Lie algebras. I will further discuss the fibrations with mult
isections or nontrivial Mordell-Weil groups. In contrast to the case of f
ivefolds\, Chern and Pontryagin numbers of fourfolds are invariant under c
repant birational maps. This fact enables us to be able to compute Chern a
nd Pontryagin numbers\, independently from a choice of a crepant resolutio
n\, along with various other characteristic numbers such as the Euler char
acteristic\, the holomorphic genera\, the Todd-genus\, the L-genus\, the A
-genus\, and the eight-form curvature invariant from M-theory. For the cas
e of Calabi-Yau fourfolds\, F-theory compactification provides the resulti
ng 4d N=1 gauge theories.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Gammage (Harvard University)
DTSTART:20211014T185000Z
DTEND:20211014T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/37
DESCRIPTION:Title: Abelian 3d mirror symmetry\nby Ben Gammage (Harvard University) as p
art of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstrac
t\n3d mirror symmetry is a proposed physical duality relating a pair of 3d
N=4 field theories. Various mathematical shadows of this result have been
studied\, but ultimately (after a topological twisting)\, 3dMS should ent
ail an equivalence between a pair of 2-categories associated to the algebr
aic (respectively\, symplectic) geometry of a pair of holomorphic symplect
ic stacks. In general\, the definitions of these 2-categories are not know
n\, but in this talk we explain how one can define the relevant 2-categori
es and construct an equivalence between them in the case where the spaces
involved are linear quotients by a torus. Potential applications include a
Betti geometric version of Tate's thesis and a recovery of earlier result
s on Koszul duality for hypertoric categories O. This is joint work with J
ustin Hilburn and Aaron Mazel-Gee.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mandy Cheung (Harvard University)
DTSTART:20211021T185000Z
DTEND:20211021T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/38
DESCRIPTION:Title: Family Floer mirror and mirror symmetry for rank 2 cluster varieties
\nby Mandy Cheung (Harvard University) as part of Geometry\, Physics\, and
Representation Theory Seminar\n\n\nAbstract\nThe Gross-Hacking-Keel mirro
r is constructed in terms of scattering diagrams and theta functions. The
ground of the construction is that scattering diagrams inherit the algebro
-geometric analogue of the holomorphic disks counting. With Yu-shen Lin\,
we made use this idea and gave first non-trivial examples of family Floer
mirror. Then with Sam Bardwell-Evans\, Hansol Hong\, and Yu-shen LIn\, we
construct a special Lagrangian fibration on the non-toric blowups of toric
surfaces that contains nodal fibres\, and prove that the fibres bounding
Maslov 0 discs reproduce the scattering diagrams. As a consequence\, we ca
n then illustrate the mirror duality between the A and X cluster varieties
.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Payman Eskandari (University of Toronto)
DTSTART:20211028T185000Z
DTEND:20211028T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/39
DESCRIPTION:Title: The unipotent radical of the Mumford-Tate group of a very general mixed
Hodge structure with a fixed associated graded\nby Payman Eskandari (U
niversity of Toronto) as part of Geometry\, Physics\, and Representation T
heory Seminar\n\n\nAbstract\nThe Mumford-Tate group $G(M)$ of a mixed Hodg
e structure $M$ is a subgroup of $GL(M)$ which satisfies the following pro
perty: any rational subspace of any tensor power of $M$ underlies a mixed
Hodge substructure if and only if it is invariant under the natural action
of $G(M)$. Assuming $M$ is graded-polarizable\, the unipotent radical $U(
M)$ of $G(M)$ is a subgroup of the unipotent radical $U_0(M)$ of the parab
olic subgroup of $GL(M)$ associated to the weight filtration on $M$. Let u
s say $U(M)$ is large if it is equal to $U_0(M)$.\n\nThis talk is a report
on a recent joint work with Kumar Murty\, where we consider the set of al
l mixed Hodge structures on a given rational vector space\, with a fixed w
eight filtration and a fixed polarizable associated graded Hodge structure
. It is easy to see that this set is in a canonical bijection with the set
of complex points of an affine complex variety $S$. The main result is th
at assuming some conditions on the (fixed) associated graded hold\, outsid
e a union of countably many proper Zariski closed subsets of $S$ the unipo
tent radical of the Mumford-Tate group is large.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter McNamara (University of Melbourne)
DTSTART:20220120T195000Z
DTEND:20220120T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/40
DESCRIPTION:Title: Sheaves behaving badly\nby Peter McNamara (University of Melbourne)
as part of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbs
tract\nThis talk is about singularities of Schubert varieties\,\nstudied v
ia sheaf-theoretic invariants like intersection cohomology\nand parity she
aves. The motivation comes from the use of these sheaves\nin representatio
n theory\, which began with the celebrated proof of the\nKazhdan-Lusztig c
onjectures by Beilinson-Bernstein localisation. We\nwill present examples
of poor behaviour (in particular exhibit\nnon-perverse parity sheaves)\, w
hich thwart historic overly-optimistic\nconjectures on the singularities o
f Schubert varieties.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Souheila Hassoun (Northeastern University)
DTSTART:20220127T195000Z
DTEND:20220127T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/41
DESCRIPTION:Title: The admissible sub-objects\nby Souheila Hassoun (Northeastern Univer
sity) as part of Geometry\, Physics\, and Representation Theory Seminar\n\
n\nAbstract\nThe study of admissible sub-objects of a certain object in an
additive category relatively to a Quillen exact structure is an exciting
subject that leads to some unaccepted characterizations. We propose new ge
neral notions of intersections and some of sub-objects to study the Jordan
-Holder property of an exact category. We then generalize the length funct
ion and the Gabriel-Roiter measure to the realm of exact categories. \nWe
also initiate the study of weakly exact structures\, a generalization of b
oth Quillen exact structures and the important and widely used notion of A
belian categories. We investigate when these structures form lattices.\nTh
is talk is based on several joint works: arxiv numbers 2009.10024\, 2006.0
3505\, and 1809.01282.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Loizides (Cornell University)
DTSTART:20220203T195000Z
DTEND:20220203T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/42
DESCRIPTION:Title: Moduli of flat connections on a surface and the Atiyah-Bott classes\
nby Yiannis Loizides (Cornell University) as part of Geometry\, Physics\,
and Representation Theory Seminar\n\n\nAbstract\nLet $\\Sigma$ be a compac
t oriented surface (possibly with boundary)\, and let $G$ be a compact con
nected simply connected Lie group. I will describe classes in the K-theory
of a moduli space of flat $G$-connections on $\\Sigma$. In the case of a
closed surface\, these classes were introduced by Atiyah and Bott. When th
e boundary of the surface is non-empty\, further investigation leads to a
gauge theoretic version of a theorem of Teleman and Woodward.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Megumi Harada (McMaster University)
DTSTART:20220428T185000Z
DTEND:20220428T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/43
DESCRIPTION:Title: Hessenberg patch ideals\, geometric vertex decomposition\, and Grobner b
ases\nby Megumi Harada (McMaster University) as part of Geometry\, Phy
sics\, and Representation Theory Seminar\n\n\nAbstract\nHessenberg varieti
es are subvarieties of the flag variety $Flags(\\mathbb{C}^n)$\, the study
of which have rich interactions with symplectic geometry\, representation
theory\, and equivariant topology\, among other research areas\, with par
ticular recent attention arising from its connections to the famous Stanle
y-Stembridge conjecture in combinatorics. The special case of regular nilp
otent Hessenberg varieties has been much studied\, and in this talk I will
describe some work in progress analyzing the local defining ideals of the
se varieties. In particular\, using some techniques relating liason theory
\, geometric vertex decomposition\, and the theory of Grobner bases (follo
wing work of Klein and Rajchgot)\, we are able to show that\, for the coor
dinate patch corresponding to the longest word $w_0$\, the local defining
ideal for any indecomposable Hessenberg variety is geometrically vertex de
composable\, and we find an explicit Grobner basis for a certain monomial
order. This is a report on joint work in progress with Sergio Da Silva.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marianna Russkikh (MIT)
DTSTART:20220210T195000Z
DTEND:20220210T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/44
DESCRIPTION:Title: Dimers and embeddings\nby Marianna Russkikh (MIT) as part of Geometr
y\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nWe introduc
e a concept of ‘t-embeddings’ of weighted bipartite planar graphs. We
believe that these t-embeddings always exist and that they are good candid
ates to recover the complex structure of big bipartite planar graphs carry
ing a dimer model. We also develop a relevant theory of discrete holomorph
ic functions on t-embeddings\; this theory unifies Kenyon’s holomorphic
functions on T-graphs and s-holomorphic functions coming from the Ising mo
del. We provide a meta-theorem on convergence of the height fluctuations t
o the Gaussian Free Field.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Cannizzo (Stony Brook)
DTSTART:20220310T195000Z
DTEND:20220310T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/45
DESCRIPTION:Title: Global homological mirror symmetry for genus 2 curves\nby Catherine
Cannizzo (Stony Brook) as part of Geometry\, Physics\, and Representation
Theory Seminar\n\n\nAbstract\nA smooth genus 2 curve has a 6 dimensional f
amily of possible complex structures\, parametrized by the genus-2 Siegel
space. We describe a generalized SYZ mirror family of symplectic manifolds
\, and the mirror correspondence of Kähler cones with the Siegel space. W
e also describe the Fukaya category of the symplectic manifold (a Landau-G
inzburg model)\, with structure maps deformed by the B-field. This involve
s adapting Guillemin’s Kähler potential to a toric variety of infinite
type and computing monodromy of a symplectic fibration with critical locus
given by the “banana manifold” of three P^1’s attached at two point
s. Finally\, we end with a homological mirror symmetry result between the
genus 2 curves and their mirrors. This is joint work with H. Azam\, C-C. M
. Liu\, and H. Lee.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Arbesfeld (Imperial College London)
DTSTART:20220303T195000Z
DTEND:20220303T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/46
DESCRIPTION:Title: Descendent series for Hilbert schemes of points on surfaces\nby Noah
Arbesfeld (Imperial College London) as part of Geometry\, Physics\, and R
epresentation Theory Seminar\n\n\nAbstract\nStructure often emerges from H
ilbert schemes of points on surfaces when the underlying surface is fixed
but the number of points parametrized is allowed to vary. One example of s
uch structure comes from integrals of tautological bundles\, which appear
in physical and geometric computations. When compiled into generating seri
es\, these integrals display interesting functional properties. \n\nI will
focus on the example of K-theoretic descendent series\, certain series fo
rmed from holomorphic Euler characteristics of tautological bundles. Namel
y\, I will explain how to use a Macdonald polynomial symmetry of Mellit to
deduce that the K-theoretic descendent series are expansions of rational
functions.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Weinstein (Berkeley/Stanford)
DTSTART:20220421T185000Z
DTEND:20220421T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/47
DESCRIPTION:Title: A Lie-Rinehart algebra in general relativity\nby Alan Weinstein (Ber
keley/Stanford) as part of Geometry\, Physics\, and Representation Theory
Seminar\n\n\nAbstract\nBlohmann\, Schiavina\, and I have found a Lie-Rineh
art algebra on a graded extension of the space of initial values for the E
instein equations whose bracket relations match those of the constraints o
n the initial values.\n\nThis will be a follow-up to last year's talk\, bu
t I will not assume that anyone has heard it.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asilata Bapat (ANU)
DTSTART:20220224T195000Z
DTEND:20220224T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/48
DESCRIPTION:by Asilata Bapat (ANU) as part of Geometry\, Physics\, and Rep
resentation Theory Seminar\n\n\nAbstract\nConsider the space of Bridgeland
stability conditions of a suitably nice triangulated category. Autoequiva
lences of the triangulated category act on the space of stability conditio
ns. Fixing a stability condition imposes extra combinatorial structure on
the category that can be used to study the group of autoequivalences in va
rious different ways. This talk will showcase some of the fascinating stru
cture that emerges via this idea\, particularly for 2-Calabi-Yau categorie
s associated to quivers. This is based on joint work with Anand Deopurkar
and Anthony Licata.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Cristofaro-Gardiner (Maryland)
DTSTART:20220407T185000Z
DTEND:20220407T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/49
DESCRIPTION:Title: The simplicity conjecture\nby Dan Cristofaro-Gardiner (Maryland) as
part of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstra
ct\nIn the 60s and 70s\, there was a flurry of activity concerning the que
stion of whether or not various subgroups of homeomorphism groups of manif
olds are simple\, with beautiful contributions by Fathi\, Kirby\, Mather\,
Thurston\, and many others. A funnily stubborn case that remained open wa
s the case of area-preserving homeomorphisms of surfaces. For example\, fo
r balls of dimension at least 3\, the relevant group was shown to be simpl
e by work of Fathi from the 1970s\, but the answer in the two-dimensional
case was not known. I will explain recent joint work proving that the gro
up of compactly supported area preserving homeomorphisms of the two-disc i
s in fact not a simple group\, which answers the ``Simplicity Conjecture
” in the affirmative. Our proof uses a new tool for studying area-prese
rving surface homeomorphisms\, called periodic Floer homology (PFH) spectr
al invariants\; these recover the classical Calabi invariant via a kind of
Weyl law. I will also briefly mention a generalization of our result to
compact surfaces of any genus.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oded Yacobi (Sydney)
DTSTART:20220324T185000Z
DTEND:20220324T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/50
DESCRIPTION:Title: On the action of Weyl groups on canonical bases and categorical braid gr
oup actions\nby Oded Yacobi (Sydney) as part of Geometry\, Physics\, a
nd Representation Theory Seminar\n\n\nAbstract\nIn this talk we'll be cons
idering the following situation: suppose we have a representation $(V\,\\p
i)$ of a Weyl group equipped with a canonical basis. Given an element $g$
of the group\, can we extract interesting information about the matrix of
$\\pi(g)$ with respect to the basis? In general this is extremely diffic
ult but in some situations there are beautiful answers to this question.
The first results in this direction are due to Berenstein-Zelevinsky and S
tembridge\, who proved that the long element of the symmetric group acts o
n the Kazhdan-Lusztig basis by the Schutzenberger involution on tableau.
I will explain vast generalizations of this theorem. The underlying ideas
driving these results come from braid group actions on derived categories
. This is based on joint work with Martin Gossow.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Filip Dul (UMass Amherst)
DTSTART:20220217T195000Z
DTEND:20220217T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/51
DESCRIPTION:Title: General Covariance with Stacks\nby Filip Dul (UMass Amherst) as part
of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\n
General covariance is a crucial notion in the study of field theories on c
urved spacetimes. In our context\, a generally covariant field theory is o
ne whose dependence on a Riemannian (or Lorentzian) metric is equivariant
with respect to the diffeomorphism group of the underlying manifold/spacet
ime. In this talk\, we will make these notions precise by using stacks and
the Batalin-Vilkovisky formalism\, and will moreover recover the associat
ed equivariant classical observables in the perturbative case.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Utiralova (MIT)
DTSTART:20220414T185000Z
DTEND:20220414T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/52
DESCRIPTION:Title: Harish-Chandra bimodules in complex rank\nby Alexandra Utiralova (MI
T) as part of Geometry\, Physics\, and Representation Theory Seminar\n\n\n
Abstract\nThe Deligne tensor categories are defined as an interpolation of
the categories of representations of groups $GL_n$\, $O_n$\, $Sp_{2n}$\,
or $S_n$ to the complex values of the parameter $n$. One can extend many c
lassical representation-theoretic notions and constructions to this contex
t. These complex rank analogs of classical objects provide insights into t
heir stable behavior patterns as n goes to infinity.\n\nI will talk about
some of my results on Harish-Chandra bimodules in the Deligne cateogories.
It is known that in the classical case simple Harish-Chandra bimodules ad
mit a classification in terms of W-orbits of certain pairs of weights. How
ever\, the notion of weight is not well-defined in the setting of the Deli
gne categories. I will explain how in complex rank the above-mentioned cla
ssification translates to a condition on the corresponding (left and right
) central characters.\n\nAnother interesting phenomenon arising in complex
rank is that there are two ways to define harish-Chandra bimodules. That
is\, one can either require that the center acts locally finitely on a bim
odule $M$ or that $M$ has a finite K-type. The two conditions are known to
be equivalent for a semi-simple Lie algebra in the classical setting\, ho
wever in the Deligne categories\, it is no longer the case. I will talk ab
out a way to construct examples of Harish-Chandra bimodules of finite K-ty
pe using the ultraproduct realization of the Deligne categories.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Kirchhoff-Lukat (MIT)
DTSTART:20220331T185000Z
DTEND:20220331T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/53
DESCRIPTION:Title: Lagrangian intersection Floer cohomology for log symplectic surfaces
\nby Charlotte Kirchhoff-Lukat (MIT) as part of Geometry\, Physics\, and R
epresentation Theory Seminar\n\n\nAbstract\nI will begin by giving an intr
oduction to a special and widely studied class of Poisson manifolds: log s
ymplectic manifolds. While these have degeneracies\, they are sufficiently
close to being symplectic that many properties and techniques from symple
ctic geometry extend. The main result I will present is my recent generali
zation of Lagrangian intersection Floer cohomology to log symplectic surfa
ces.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Webster (Waterloo)
DTSTART:20220428T200000Z
DTEND:20220428T210000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/54
DESCRIPTION:Title: Representation theory and a little bit of quantum field theory\nby B
en Webster (Waterloo) as part of Geometry\, Physics\, and Representation T
heory Seminar\n\n\nAbstract\nOne of the central foci of representation the
ory in the 20th century was the representation theory of Lie algebras\, st
arting with finite dimensional algebras and expanding to a rich\, but stil
l mysterious infinite dimensional theory. In this century\, we realized th
at this was only one special case of a bigger theory\, with new sources of
interesting non-commutative algebras whose representations we'd like to s
tudy\, such as Cherednik algebras. In mathematical terms\, we could connec
t these to symplectic resolutions of singularities\, but a more intriguing
explanation is that they arise from 3d quantum field theories. I'll try t
o provide an overview about what's known about this topic and what we're s
till confused about.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Jeishing Wen (Northeastern)
DTSTART:20220908T185000Z
DTEND:20220908T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/55
DESCRIPTION:Title: Wreath Macdonald operators\nby Joshua Jeishing Wen (Northeastern) as
part of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstr
act\nDefined by Haiman\, wreath Macdonald polynomials are generalizations
of Macdonald polynomials to wreath products of symmetric groups with a fix
ed cyclic group. Using a wreath analogue of the Frobenius characteristic\,
they can be viewed as partially-symmetric functions. Relatively little is
known about them. In this talk\, we present novel difference operators th
at are diagonalized on the wreath Macdonald polynomials. Their formulas ar
e quite complicated\, but they give strong evidence that bispectral dualit
y holds in the wreath case. This is joint work with Daniel Orr and Mark Sh
imozono.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minh-Tâm Trinh (MIT)
DTSTART:20221006T185000Z
DTEND:20221006T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/56
DESCRIPTION:Title: Catalan combinatorics versus nonabelian Hodge theory\nby Minh-Tâm T
rinh (MIT) as part of Geometry\, Physics\, and Representation Theory Semin
ar\n\n\nAbstract\nThe Oblomkov–Rasmussen–Shende conjecture relates the
homologies of the Hilbert schemes of a plane curve singularity to the tri
ply-graded Khovanov–Rozansky (i.e.\, HOMFLYPT) homology of its link\, vi
a an identity in variables a\, q\, t. Two major cases are known: (1) the t
= -1 limit\, settled a decade ago by Maulik\; (2) the lowest-a-degree\, q
= 1 limit of the "torus link" case\, settled jointly by Elias–Hogancamp
\, Mellit\, and Gorsky–Mazin\, using (q\, t)-Catalan combinatorics as an
essential bridge. An unpublished research statement of Shende speculated
that the ORS conjecture could be proved in a third\, totally different way
\, via a wild analogue of the P = W phenomenon in nonabelian Hodge theory.
He and his coauthors carried out most of this approach for the "torus-kno
t" subcase of case (1). We extend their work\, and also refine it enough t
o handle the (more difficult) torus-knot subcase of case (2). The key is o
ur new geometric model for Khovanov–Rozansky homology\, which realizes t
he t variable as cohomological degree. If there is time\, we will explain
how this flavor of nonabelian Hodge theory is related to the noncrossing-n
onnesting dichotomy in Catalan combinatorics.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elie Casbi (Northeastern)
DTSTART:20220915T185000Z
DTEND:20220915T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/57
DESCRIPTION:Title: Hall algebras and quantum cluster algebras\nby Elie Casbi (Northeast
ern) as part of Geometry\, Physics\, and Representation Theory Seminar\n\n
\nAbstract\nThe theory of Hall algebras has known many spectacular develop
ments and applications since the discovery by Ringel of their connection w
ith quantum groups. One important object arising naturally in the study of
Hall algebras is the integration map defined by Reineke\, which allows to
produce certain celebrated wall-crossing identities. In this talk I will
first focus on the Dynkin case and show how the integration map can be int
erpreted in a natural way via the representation theory of quantum affine
algebras. I will then explain how this opens perspectives towards an analo
gous interpretation for more general quivers\, relying on the framework of
quantum cluster algebras. This is ongoing joint work with Lang Mou.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Neguţ (MIT)
DTSTART:20220929T173000Z
DTEND:20220929T183000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/58
DESCRIPTION:Title: Quantum loop groups for generalized Cartan matrices\nby Andrei Negu
ţ (MIT) as part of Geometry\, Physics\, and Representation Theory Seminar
\n\n\nAbstract\nWe construct a quantum loop group associated to an arbitra
ry symmetric generalized Cartan matrix by defining appropriate versions of
the Drinfeld-Serre relations. Explaining the meaning of the word "appropr
iate" and specifying the relations will be the main purpose of the talk.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Sherman-Bennett (MIT)
DTSTART:20221020T185000Z
DTEND:20221020T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/59
DESCRIPTION:Title: Cluster structures on type A braid varieties and 3D plabic graphs\nb
y Melissa Sherman-Bennett (MIT) as part of Geometry\, Physics\, and Repres
entation Theory Seminar\n\n\nAbstract\nBraid varieties are smooth affine v
arieties associated to any positive braid. Special cases of braid varietie
s include Richardson varieties\, double Bruhat cells\, and double Bott-Sam
elson cells. Cluster algebras are a class of commutative rings with a rich
combinatorial structure\, introduced by Fomin and Zelevinsky. I'll discus
s joint work with P. Galashin\, T. Lam and D. Speyer in which we show the
coordinate rings of braid varieties are cluster algebras\, proving and gen
eralizing a conjecture of Leclerc in the case of Richardson varieties. See
ds for these cluster algebras come from "3D plabic graphs"\, which are bic
olored graphs embedded in a 3-dimensional ball that generalize Postnikov's
plabic graphs for positroid varieties.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Dinkins (Northeastern)
DTSTART:20220922T185000Z
DTEND:20220922T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/60
DESCRIPTION:Title: Curve counts\, representation theory\, and 3d mirror symmetry\nby Hu
nter Dinkins (Northeastern) as part of Geometry\, Physics\, and Representa
tion Theory Seminar\n\n\nAbstract\nThe last two decades have seen great su
ccess in studying representation theoretic objects through geometric techn
iques. One small part of this story involves Nakajima quiver varieties\, c
urve counting\, and a mysterious string-theoretic duality. More specifical
ly\, curve counting in Nakajima varieties turns out to be governed by cert
ain q-difference equations that\, after a nontrivial amount of work\, can
be seen to coincide with the some well-known equations from representation
theory. Moreover\, these curve counts are expected to possess deep nontri
vial symmetries that have only been understood in very specific examples.
I will provide an overview of the main concepts and results related to the
se ideas\, discuss my own contributions\, and mention some future directio
ns.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davesh Maulik (MIT)
DTSTART:20221013T185000Z
DTEND:20221013T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/61
DESCRIPTION:Title: P=W conjecture for GL_n\nby Davesh Maulik (MIT) as part of Geometry\
, Physics\, and Representation Theory Seminar\n\n\nAbstract\nThe P=W conje
cture\, first proposed by de Cataldo-Hausel-Migliorini in 2010\, gives a l
ink between the topology of the moduli space of Higgs bundles on a curve a
nd the Hodge theory of the corresponding character variety\, using non-abe
lian Hodge theory. In this talk\, I will explain this circle of ideas and
discuss a recent proof of the conjecture for GL_n (joint with Junliang Sh
en).\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Smirnov (UNC Chapel Hill)
DTSTART:20221027T185000Z
DTEND:20221027T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/62
DESCRIPTION:Title: Vertex functions modulo p\nby Andrey Smirnov (UNC Chapel Hill) as pa
rt of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract
\nThe vertex functions are generating functions counting rational curves i
n a quiver variety.\nThey also give a basis of solutions to quantum differ
ential equation associated with the quiver variety. \nIn my talk I discuss
a construction of certain polynomial solutions of quantum differential eq
uation modulo a prime p.\nI also describe a number of conjectures relating
the p-adic limit of these solutions to the vertex functions. \nThe talk i
s based on a joint investigation in progress with A. Varchenko.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolás Andruskiewitsch (Universidad Nacional de Córdoba)
DTSTART:20221117T195000Z
DTEND:20221117T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/63
DESCRIPTION:Title: Nichols algebras over abelian groups\nby Nicolás Andruskiewitsch (U
niversidad Nacional de Córdoba) as part of Geometry\, Physics\, and Repre
sentation Theory Seminar\n\n\nAbstract\nNichols algebras are fundamental i
nvariants of large classes of Hopf algebras. I will survey from scratch t
hose arising from abelian groups\, focusing on the methods of computation
.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Mautner (UC Riverside)
DTSTART:20221208T195000Z
DTEND:20221208T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/64
DESCRIPTION:Title: Perverse sheaves on symmetric products of the plane\nby Carl Mautner
(UC Riverside) as part of Geometry\, Physics\, and Representation Theory
Seminar\n\n\nAbstract\nIn joint work with Tom Braden we give a purely alge
braic description of the category of perverse sheaves (with coefficients i
n any field) on $S^n(C^2)$\, the n-fold symmetric product of the plane. I
n particular\, using the geometry of the Hilbert scheme of points\, we rel
ate this category to the symmetric group and its representation ring. Our
work is motivated by analogous structure appearing in the Springer resolu
tion and Hilbert-Chow morphism.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yan Zhou (Northeastern)
DTSTART:20221103T185000Z
DTEND:20221103T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/65
DESCRIPTION:Title: Irregular opers\, Stokes geometry and WKB analysis\nby Yan Zhou (Nor
theastern) as part of Geometry\, Physics\, and Representation Theory Semin
ar\n\n\nAbstract\nWe study\, using the extended isomonodromy deformation\,
the WKB approximation of Stokes matrices of a class of meromorphic linear
ODE systems of Poincare rank 1 on the projective line that appear in vari
ous contexts of geometry. We show that\, via the degenerate Riemann-Hilber
t map\, the WKB approximation of Stokes matrices recovers the Gelfand-Tset
lin integrable systems whose action variables match with period on spectra
l curves. If time permits\, we will also briefly discuss the potential ram
ifications to cluster theory\, spectral networks and gl(n)-crystals (in t
he quantum setting). The talk is based on joint work with Anton Alekseev a
nd Xiaomeng Xu and ongoing discussions with Andrew Neitzke.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abigail Ward (MIT)
DTSTART:20221201T195000Z
DTEND:20221201T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/66
DESCRIPTION:Title: Symplectomorphisms mirror to birational transformations of the projectiv
e plane\nby Abigail Ward (MIT) as part of Geometry\, Physics\, and Rep
resentation Theory Seminar\n\n\nAbstract\nWe construct a non-finite type f
our-dimensional Weinstein domain $M_{univ}$ and describe a HMS corresponde
nce between distinguished birational transformations of the projective pla
ne preserving a standard holomorphic volume form and symplectomorphisms of
$M_{univ}$. The space $M_{univ}$ is universal in the sense that it contai
ns every Liouville manifold mirror to a log Calabi-Yau surface as a Weinst
ein subdomain\; after restricting to these subdomains\, we recover a mirro
r correspondence between the automorphism group of any open log Calabi-Yau
surface and the symplectomorphism group of its mirror. This is joint work
with Ailsa Keating.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ahmad Reza Haj Saeedi Sadegh (Northeastern)
DTSTART:20221110T195000Z
DTEND:20221110T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/67
DESCRIPTION:Title: Deformation spaces\, rescaled bundles\, and their applications in geomet
ry and analysis\nby Ahmad Reza Haj Saeedi Sadegh (Northeastern) as par
t of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\
nWe construct an algebraic vector bundle over the deformation to the norma
l cone for an embedding of manifolds through a rescaling of a vector bundl
e over the ambient space. This method generalizes the construction of the
spinor rescaled bundle over the tangent groupoid by Nigel Higson and Zelin
Yi. Applications of this construction include local index formula\, equiv
ariant index formula\, Kirillov formula and Witten and Novikov deformation
of de Rham operator.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weiqiang Wang (UVA)
DTSTART:20230302T195000Z
DTEND:20230302T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/68
DESCRIPTION:Title: Quantum Schur dualities ABC\nby Weiqiang Wang (UVA) as part of Geome
try\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nThe class
ical Schur duality admits a q-deformation due to Jimbo\, which is a dualit
y between a quantum group and Hecke algebra of type A. A new quantum Schur
duality between an i-quantum group (arising from quantum symmetric pairs)
and Hecke algebra of type B was formulated by Huanchen Bao and myself. In
this talk\, I will explain these dualities\, their geometric incarnation\
, and applications to super Kazhdan-Lusztig theories of type ABC.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu-Shen Lin (BU)
DTSTART:20230316T185000Z
DTEND:20230316T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/69
DESCRIPTION:Title: Symplectic scattering diagrams for Log Calabi-Yau Surfaces\nby Yu-Sh
en Lin (BU) as part of Geometry\, Physics\, and Representation Theory Semi
nar\n\n\nAbstract\nThe pioneering work of Gross-Hacking-Keel studied the m
irror symmetry for log Calabi-Yau surfaces proved that there exists a natu
ral superpotential defined on the mirrors. The key intermediate product of
the mirror construction are some combinatorial data called scattering dia
grams. In this talk\, I will explain the symplectic heuristic of the const
ruction and mathematically how we retrieve the superpotentials and the sca
ttering diagram from Lagrangian Floer theory. As corollaries\, we prove a
version of cluster mirror symmetry of rank two\, a real analogue of 27 lin
es on cubic surfaces and a folklore conjecture "open Gromov-Witten invaria
nts=log Gromov-Witten invariants. This is a joint work with Bardwell-Evans
\, Cheung and Hong.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Larson (Harvard)
DTSTART:20230126T195000Z
DTEND:20230126T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/70
DESCRIPTION:Title: Cohomology of moduli spaces of stable curves\nby Hannah Larson (Harv
ard) as part of Geometry\, Physics\, and Representation Theory Seminar\n\n
\nAbstract\nThe cohomology rings of moduli spaces often have distinguished
classes called tautological classes. This talk is about the special situa
tion when all cohomology classes on a moduli space are tautological. I wil
l start with the example of projective space. Then I'll introduce the modu
li spaces M_{g\,n}-bar of n-poined\, stable genus g curves\, using the exa
mple M_{2\,0}-bar as a guide. At the end\, I'll present several new small
values (g\, n) where we have proven that all classes on M_{g\,n}-bar are t
autological. This is joint work with Samir Canning.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claire Frechette (BC)
DTSTART:20230406T185000Z
DTEND:20230406T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/71
DESCRIPTION:Title: Metaplectic ice: using statistical mechanics in representation theory\nby Claire Frechette (BC) as part of Geometry\, Physics\, and Representa
tion Theory Seminar\n\n\nAbstract\nLocal Whittaker functions for reductive
groups play an integral role in number theory and representation theory\,
and many of their applications extend to the metaplectic case\, where red
uctive groups are replaced by their metaplectic covering groups. We will e
xamine these functions for covers of $GL_r$ through the lens of a solvable
lattice model\, or ice model: a construction from statistical mechanics t
hat provides a surprising bridge between spaces of Whittaker functions and
representations of quantum groups. This story has been well studied befor
e for the case of one particularly nice cover of $GL_r$\, which eliminates
all complications arising from the center of the group. In this talk\, we
will see that the same types of connections hold for any metaplectic cove
r of $GL_r$\, as well as examine how different choices of covering group i
nteract with the center of $GL_r$ to change the story.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Rybnikov (Harvard)
DTSTART:20230202T195000Z
DTEND:20230202T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/73
DESCRIPTION:Title: Kashiwara crystals from maximal commutative subalgebras\nby Leonid R
ybnikov (Harvard) as part of Geometry\, Physics\, and Representation Theor
y Seminar\n\n\nAbstract\nShift of argument subalgebras is a family of maxi
mal commutative subalgebras in the universal enveloping algebra U(g) param
etrized by regular elements of the Cartan subalgebra of a reductive Lie al
gebra g. According to Vinberg\, the Gelfand-Tsetlin subalgebra in U(gl_n)
is a limit case of such family\, so one can regard the eigenbases for such
commutative subalgebras in finite-dimensional g-modules as a deformation
of the Gelfand-Tsetlin basis (which is more general than Gelfand-Tsetlin b
ases themselves because exists for arbitrary semisimple Lie algebra g). I
will define a natural structure of a Kashiwara crystal on the spectra of t
he shift of argument subalgebras of U(g) in finite-dimensional g-modules.
This gives a topological description of the inner cactus group action on a
g-crystal\, as a monodromy of an appropriate covering of the De Concini-P
rocesi closure of the complement of the root hyperplane arrangement in the
Cartan subalgebra. In particular\, this gives a topological description o
f the Berenstein-Kirillov group (generated by Bender-Knuth involutions on
the Gelfand-Tsetlin polytope) and of its relation to the cactus group due
to Chmutov\, Glick and Pylyavskyy.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Hogancamp (Northeastern)
DTSTART:20230330T185000Z
DTEND:20230330T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/74
DESCRIPTION:Title: The nilpotent cone for sl2 and annular link homology\nby Matt Hoganc
amp (Northeastern) as part of Geometry\, Physics\, and Representation Theo
ry Seminar\n\n\nAbstract\nIn this talk I will discuss an equivalence of ca
tegories relating SL(2)-equivariant vector bundles on the nilpotent cone f
or sl(2) and the annular Bar-Natan category (this latter category appears
in the context of Khovanov homology for links in a thickened annulus). In
deed\, both categories admit a diagrammatic description in terms of the sa
me "dotted" Temperley-Lieb diagrammatics\, as I will explain. Under this
equivalence\, Bezrukavnikov's quasi-exceptional collection on the nilcone
(in the SL2 case) has an elegant description in terms of some special annu
lar links. In recent joint work with Dave Rose and Paul Wedrich\, we cons
tructed a very special Ind-object in the annular Bar-Natan category which
is a categorical analogue of a "Kirby element" from quantum topology\; I w
ill conclude by sketching a neat "BGG resolution" afforded by our categor
ified Kirby element. This is based on joint work with Rose and Wedrich.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Travis Mandel (OU)
DTSTART:20230223T195000Z
DTEND:20230223T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/75
DESCRIPTION:Title: Bracelet bases are theta bases\nby Travis Mandel (OU) as part of Geo
metry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nCluster
algebras from marked surfaces can be interpreted as skein algebras\, as f
unctions on decorated Teichmüller space\, or as functions on certain modu
li of SL2-local systems. These algebras and their quantizations have well
-known collections of special elements called "bracelets" (due to Fock-Gon
charov and Musiker-Schiffler-Williams\, and due to D. Thurston in the quan
tum setting). On the other hand\, Gross-Hacking-Keel-Kontsevich used idea
s from mirror symmetry to construct canonical bases of "theta functions" f
or cluster algebras\, and this was extended to the quantum setting in my w
ork with Ben Davison. I will review these constructions and describe rece
nt work with Fan Qin in which we prove that the (quantum) bracelets bases
coincide with the corresponding (quantum) theta bases.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pham Tiep (Rutgers/MIT/Princeton)
DTSTART:20230216T195000Z
DTEND:20230216T205000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/76
DESCRIPTION:Title: Character bounds for finite simple groups\nby Pham Tiep (Rutgers/MIT
/Princeton) as part of Geometry\, Physics\, and Representation Theory Semi
nar\n\n\nAbstract\nGiven the current knowledge of complex representations
of finite simple groups\, obtaining good upper bounds for their characters
values is still a difficult problem\, a satisfactory solution of which wo
uld have significant implications in a number of applications. We will rep
ort on recent results that produce such character bounds\, and discuss som
e applications of them\, in and outside of group theory.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cesar Cuenca (Harvard)
DTSTART:20230420T185000Z
DTEND:20230420T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/77
DESCRIPTION:Title: Invariant measures of infinite-dimensional groups over finite fields
\nby Cesar Cuenca (Harvard) as part of Geometry\, Physics\, and Representa
tion Theory Seminar\n\n\nAbstract\nIn this talk\, we study the problem of
characterizing the set of G-invariant measures on a space of infinite-dime
nsional matrices over a finite field. The groups G being considered are in
ductive limits of the finite general linear groups GL(n\, q) and the finit
e even unitary groups $U(2n\, q^2)$ over a finite field\; our proposed pro
blem is still open in the latter even unitary case and the talk focuses on
it. One partial result translates the problem to the classification of po
sitive harmonic functions on branching graphs that are Hall-Littlewood ver
sions of the Young graph. A second partial result is the construction of a
large class of invariant measures by means of the Hopf-algebra structure
on the ring of symmetric functions. The talk is based on joint work with G
rigori Olshanski.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (McGill)
DTSTART:20230427T185000Z
DTEND:20230427T195000Z
DTSTAMP:20260422T225841Z
UID:GPRTatNU/78
DESCRIPTION:Title: Virtual cactus group: combinatorics and topology\nby Joel Kamnitzer
(McGill) as part of Geometry\, Physics\, and Representation Theory Seminar
\n\n\nAbstract\nThe cactus group is a finitely presented group analogous t
o the braid group. It acts on combinatorial objects\, especially tensor pr
oducts of crystals. It is also the fundamental group of the moduli space o
f marked real genus 0 stable curves. The virtual cactus group contains bot
h the cactus group and the symmetric group with some natural relations (he
re "virtual" is in the sense of virtual knot theory). I will explain how t
he virtual cactus group appears combinatorially and topologically.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/78/
END:VEVENT
END:VCALENDAR