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BEGIN:VEVENT
SUMMARY:Maxence Mayrand (University of Toronto)
DTSTART;VALUE=DATE-TIME:20200903T185000Z
DTEND;VALUE=DATE-TIME:20200903T195000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20200910T185000Z
DTEND;VALUE=DATE-TIME:20200910T195000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20200917T185000Z
DTEND;VALUE=DATE-TIME:20200917T195000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20201001T185000Z
DTEND;VALUE=DATE-TIME:20201001T195000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20201015T185000Z
DTEND;VALUE=DATE-TIME:20201015T195000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20201022T185000Z
DTEND;VALUE=DATE-TIME:20201022T195000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20200924T185000Z
DTEND;VALUE=DATE-TIME:20200924T195000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20201008T185000Z
DTEND;VALUE=DATE-TIME:20201008T195000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20201029T185000Z
DTEND;VALUE=DATE-TIME:20201029T195000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20201105T195000Z
DTEND;VALUE=DATE-TIME:20201105T205000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20201112T195000Z
DTEND;VALUE=DATE-TIME:20201112T205000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20201119T195000Z
DTEND;VALUE=DATE-TIME:20201119T205000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20201203T195000Z
DTEND;VALUE=DATE-TIME:20201203T205000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20210128T195000Z
DTEND;VALUE=DATE-TIME:20210128T205000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20210204T195000Z
DTEND;VALUE=DATE-TIME:20210204T205000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20210211T195000Z
DTEND;VALUE=DATE-TIME:20210211T205000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20210218T195000Z
DTEND;VALUE=DATE-TIME:20210218T205000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20210304T195000Z
DTEND;VALUE=DATE-TIME:20210304T205000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20210225T195000Z
DTEND;VALUE=DATE-TIME:20210225T205000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20210311T195000Z
DTEND;VALUE=DATE-TIME:20210311T205000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20210318T185000Z
DTEND;VALUE=DATE-TIME:20210318T195000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20210325T185000Z
DTEND;VALUE=DATE-TIME:20210325T195000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20210415T185000Z
DTEND;VALUE=DATE-TIME:20210415T195000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20210422T185000Z
DTEND;VALUE=DATE-TIME:20210422T195000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20210408T185000Z
DTEND;VALUE=DATE-TIME:20210408T195000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20210401T185000Z
DTEND;VALUE=DATE-TIME:20210401T195000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
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;VALUE=DATE-TIME:20210422T201000Z
DTEND;VALUE=DATE-TIME:20210422T211000Z
DTSTAMP;VALUE=DATE-TIME:20210419T085943Z
UID:GPRTatNU/27
DESCRIPTION:by Matan Harel (Northeastern University) as part of Geometry\,
Physics\, and Representation Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/27/
END:VEVENT
END:VCALENDAR