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BEGIN:VEVENT
SUMMARY:Daniel Douglas (Yale University)
DTSTART:20220217T220000Z
DTEND:20220217T233000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/1
DESCRIPTION:Title: Tropical Fock-Goncharov coordinates for SL_3-webs on surfaces\nby Dan
iel Douglas (Yale University) as part of PIMS Geometry / Algebra / Physics
(GAP) Seminar\n\n\nAbstract\nFor a finite-type surface $\\mathfrak{S}$\,
we study a preferred basis for the commutative algebra $\\mathbb{C}[\\math
cal{R}_{\\mathrm{SL}_3}(\\mathfrak{S})]$ of regular functions on the $\\te
xt{SL}_3(\\mathbb C)$-character variety\, introduced by Sikora-Westbury. T
hese basis elements come from the trace functions associated to certain tr
i-valent graphs embedded in the surface $\\mathfrak{S}$. We show that this
basis can be naturally indexed by positive integer coordinates\, defined
by Knutson-Tao rhombus inequalities and modulo $3$ congruence conditions.
These coordinates are related\, by the geometric theory of Fock-Goncharov\
, to the tropical points at infinity of the dual version of the character
variety. This is joint work with Zhe Sun.\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Dranowski (University of Southern California)
DTSTART:20220324T220000Z
DTEND:20220324T233000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/2
DESCRIPTION:Title: Computing fusion products of MV cycles using the Mirkovic–Vybornov isom
orphism\nby Anne Dranowski (University of Southern California) as part
of PIMS Geometry / Algebra / Physics (GAP) Seminar\n\n\nAbstract\nThe fus
ion of two subvarieties in the affine Grassmannian is a degeneration of th
eir product\, defined using the Beilinson-Drinfeld Grassmannian. In this t
alk\, we present a conceptually elementary approach to computing this prod
uct in type A when the varieties are MV cycles. As an application\, we can
compute all cluster exchange relations in the coordinate ring of the uppe
r-triangular subgroup of $\\text{GL}_4$\, confirming that all the cluster
variables are contained in the basis of MV cycles.\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bryan Kettle (University of Alberta)
DTSTART:20220512T220000Z
DTEND:20220512T233000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/3
DESCRIPTION:Title: Super Yangians: where we are today\nby Bryan Kettle (University of Al
berta) as part of PIMS Geometry / Algebra / Physics (GAP) Seminar\n\nLectu
re held in THORV 124.\n\nAbstract\nGiven any finite-dimensional simple Lie
algebra $\\mathfrak a$ over $\\mathbb C$\, the Yangian $\\mathbf{Y}(\\mat
hfrak a)$ is a certain unital associative $\\mathbb C$-algebra. In particu
lar\, Yangians form a family of so-called quantum groups. The main propert
y these algebras is the foundational fact that their representations produ
ce rational solutions to the quantum Yang-Baxter equation. The structure a
nd representation theory of Yangians has become a study in and of itself a
nd has expanded to the study of super Yangians based on Lie superalgebras\
; however\, the theory of super Yangians is comparatively less developed t
han its non-super counterpart. In this talk\, we will survey what recent a
dvancements have been made in the study of super Yangians and view what el
se remains to do.\n\nHybrid delivery (in person on University of Saskatche
wan campus and via Zoom).\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Rupert (Utah State)
DTSTART:20220526T220000Z
DTEND:20220526T233000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/4
DESCRIPTION:Title: Constructing braided categories associated to logarithmic vertex algebras
\nby Matthew Rupert (Utah State) as part of PIMS Geometry / Algebra /
Physics (GAP) Seminar\n\nLecture held in THORV 124.\n\nAbstract\nUnrolled
quantum groups are a family of quantum algebras closely related to the non
-restricted specialization of Drinfeld-Jimbo algebras at roots of unity. T
hese quantum groups have played a pivotal role in the study of the Kazhdan
-Lusztig correspondence\, that is\, the study of equivalences between modu
le categories over quantum groups and logarithmic vertex operator algebras
. In this talk I will introduce unrolled quantum groups\, describe their r
ole in the Kazhdan-Lusztig correspondence\, and state some recent results.
\n\nHybrid delivery (in person on University of Saskatchewan campus and vi
a Zoom).\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sasha Tsymbaliuk (Purdue)
DTSTART:20220530T220000Z
DTEND:20220530T233000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/5
DESCRIPTION:Title: BGG-type relations for transfer matrices of rational spin chains and the
shifted Yangians\nby Sasha Tsymbaliuk (Purdue) as part of PIMS Geometr
y / Algebra / Physics (GAP) Seminar\n\nLecture held in THORV 124.\n\nAbstr
act\nIn this talk\, I will discuss: (1) the new BGG-type resolutions of fi
nite dimensional representations of simple Lie algebras that lead to BGG-r
elations expressing finite-dimensional transfer matrices via infinite-dime
nsional ones\, (2) the factorization of infinite-dimensional ones into the
product of two Q-operators\, (3) the construction of a large family of ra
tional Lax matrices from antidominantly shifted Yangians. This talk is bas
ed on the joint works with R. Frassek\, I. Karpov\, and V. Pestun.\n\nHybr
id delivery (in person on University of Saskatchewan campus and via Zoom).
\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphaël Belliard (University of Alberta)
DTSTART:20220714T220000Z
DTEND:20220714T233000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/6
DESCRIPTION:Title: Pushing around loop equations\nby Raphaël Belliard (University of Al
berta) as part of PIMS Geometry / Algebra / Physics (GAP) Seminar\n\nLectu
re held in THORV 124.\n\nAbstract\nThe term “loop equations” was coine
d by Migdal in the early 90's in the context of quark confinement to refer
to certain sets of equations describing the propagation of test particles
in quantum field theory.\n\nThey have since appeared many times at the bo
undary between mathematics and physics. From statistical spectroscopy to e
numerative geometry via integrable hierarchies\, they encode conformal fea
tures of various problems in an analytic way.\n\nThe prototypical situatio
n where loop equations are valuable is that of matrix integrals\, with app
lications ranging from all the aforementioned topics to number theory and
even artificial neural networks.\n\nA seemingly antipodal approach to matr
ix integrals is that of orthogonal polynomials\, unveiling a subtle relati
onship between loop equations and the geometry of meromorphic connections.
This bridge can be abstracted in terms of $W$-algebra constraints and we
shall cross it back and forth.\n\nHybrid delivery (in person on University
of Saskatchewan campus and via Zoom).\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Jinwoo Kang (Caltech)
DTSTART:20220818T220000Z
DTEND:20220818T233000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/7
DESCRIPTION:Title: A universal formula for the density of states with global symmetry\nb
y Monica Jinwoo Kang (Caltech) as part of PIMS Geometry / Algebra / Physic
s (GAP) Seminar\n\nLecture held in THORV 124.\n\nAbstract\nIt has long bee
n the case that representation theory played an important role in understa
nding the spectrum of states in physics. I will describe how it can be use
d to describe some universal aspect of $d$-dimensional unitary conformal f
ield theories with a global symmetry group\, which can be a discrete group
or a compact Lie group.\n\nHybrid delivery (in person on University of Sa
skatchewan campus and via Zoom).\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maggie Miller (Stanford University)
DTSTART:20221013T220000Z
DTEND:20221013T233000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/8
DESCRIPTION:Title: Obstructing isotopy with an extra dimension\nby Maggie Miller (Stanfo
rd University) as part of PIMS Geometry / Algebra / Physics (GAP) Seminar\
n\nLecture held in THORV 124.\n\nAbstract\nIn 1982\, Livingston showed tha
t several examples of Seifert surfaces that are not isotopic in the $3$-sp
here become isotopic when pushed into the $4$-ball. This is consistent wit
h a common intuition in topology: objects that are somehow similar should
become the same when stabilized. We recently constructed families exhibiti
ng that this is not always the case — that is\, surfaces in the $3$-sphe
re that remain non-isotopic even when pushed into the $4$-ball. This is jo
int work with Kyle Hayden\, Seungwon Kim\, JungHwan Park\, and Isaac Sundb
erg.\n\nHybrid delivery (in person on University of Saskatchewan campus an
d via Zoom).\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Groechenig (University of Toronto)
DTSTART:20221124T220000Z
DTEND:20221124T233000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/9
DESCRIPTION:Title: Complex K-theory of dual Hitchin systems\nby Michael Groechenig (Univ
ersity of Toronto) as part of PIMS Geometry / Algebra / Physics (GAP) Semi
nar\n\nLecture held in THORV 124.\n\nAbstract\nI will report on joint work
with Shiyu Shen. Moduli spaces of $\\text{SL}(n)$ and $\\text{PGL}(n)$-Hi
ggs bundles are conjecturally related by a derived equivalence and (up to
HK rotation) mirror symmetry. This talk will be devoted to a shadow of the
se equivalences in complex K-theory.\n\nHybrid delivery (in person on Univ
ersity of Saskatchewan campus and via Zoom).\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksei Ilin (University of Toronto)
DTSTART:20221215T223000Z
DTEND:20221216T000000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/10
DESCRIPTION:Title: Bethe subalgebras of Yangians\nby Aleksei Ilin (University of Toront
o) as part of PIMS Geometry / Algebra / Physics (GAP) Seminar\n\nLecture h
eld in THORV 124.\n\nAbstract\nThe main object of this talk is the family
of commutative Bethe subaglebras in the Yangian. It is a natural family of
commutative subalgebras of the Yangian parameterized by the simple adjoin
t Lie group. In my talk I will discuss how this family is connected with v
arious wonderful compactifications. I also plan to discuss applications of
this family to the theory of crystals.\n\nHybrid delivery (in person on U
niversity of Saskatchewan campus and via Zoom).\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Young (Utah State University)
DTSTART:20230202T223000Z
DTEND:20230203T000000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/11
DESCRIPTION:Title: $U_q(\\mathfrak{gl}(1 \\vert 1))$ and $U(1 \\vert 1)$ Chern--Simons theo
ry\nby Matthew Young (Utah State University) as part of PIMS Geometry
/ Algebra / Physics (GAP) Seminar\n\n\nAbstract\nChern--Simons theory\, as
introduced by Witten\, is a three dimensional quantum gauge theory associ
ated to a compact simple Lie group and a level. The mathematical model of
this theory as a topological quantum field theory was introduced by Reshet
ikhin and Turaev and is at the core of modern quantum topology. The goal o
f this talk is to explain a non-semisimple modification of the constructio
n of Reshetikhin and Turaev which realizes Chern--Simons theory with gauge
supergroup $U(1 \\vert 1)$\, as studied in the physics literature by Roza
nsky--Saleur and Mikhaylov. In particular\, I'll motivate and explain vari
ous relative modular structures on the category of representations of the
quantum group of $\\mathfrak{gl}(1 \\vert 1)$ which should be seen as non-
semisimple analogues of modular tensor categories associated to the quantu
m representation theory of a simple Lie algebra at a root of unity. Based
on joint work with Nathan Geer.\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Islambouli (UC Davis)
DTSTART:20230503T220000Z
DTEND:20230503T233000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/12
DESCRIPTION:Title: Multisections and Bridge multisections\nby Gabriel Islambouli (UC Da
vis) as part of PIMS Geometry / Algebra / Physics (GAP) Seminar\n\n\nAbstr
act\nIn 2016\, Gay and Kirby showed that every compact smooth 4-manifold c
an be decomposed into three standard pieces. A particularly nice feature o
f this decomposition is that the smooth topology of the 4-manifold can be
encoded by curves on a surface. In this talk\, we explore the consequences
of allowing more pieces in this decomposition\, and show that many intere
sting cut and paste procedures can be carried out by natural mapping class
es on the surface. We also explore a related decomposition for knotted sur
faces in a 4-manifold.\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Puttipong Pongtanapaisan (University of Saskatchewan)
DTSTART:20230512T220000Z
DTEND:20230512T233000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/13
DESCRIPTION:Title: Random knotting and linking\nby Puttipong Pongtanapaisan (University
of Saskatchewan) as part of PIMS Geometry / Algebra / Physics (GAP) Semin
ar\n\nLecture held in THORV 124.\n\nAbstract\nBack in the old days\, befor
e the invention of Apple Wireless Airpods\, people were more familiar with
the tendency of the headphones in their pockets to become knotted. It see
ms natural to expect that the probability that a random curve is tangled i
ncreases with its length. In fact\, Frisch\, Wasserman\, and Delbrück con
jectured that sufficiently long ring polymers will be knotted with high pr
obability. In this talk\, I will discuss some models where the conjecture
is known to be true\, including a setting that I investigated with Jeremy
Eng\, Chris Soteros\, and Rob Scharein. Topological techniques used in the
proofs such as finite-type invariants will also be discussed.\n\nHybrid d
elivery (in person on University of Saskatchewan campus and via Zoom).\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sachin Gautam (Ohio State University)
DTSTART:20230803T220000Z
DTEND:20230803T233000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/14
DESCRIPTION:Title: R-matrices of affine Yangians\nby Sachin Gautam (Ohio State Universi
ty) as part of PIMS Geometry / Algebra / Physics (GAP) Seminar\n\nLecture
held in THORV 124.\n\nAbstract\nYangians are certain remarkable Hopf algeb
ras\, associated to finite-dimensional simple Lie algebras\, introduced by
Drinfeld in the 1980's. Drinfeld proved\, in a non-constructive manner\,
that each Yangian comes equipped with a formal solution to the famous Yang
-Baxter equation\, known as Drinfeld's universal R-matrix.\n\nIn this talk
\, I will present a very concrete method to construct Drinfeld's universal
R-matrix using additive difference equations. I will explain how our meth
od generalizes to other situations where no analogue of Drinfeld's result
is known\, such as Yangians associated to affine Kac-Moody algebras. I wil
l highlight the significant differences between the finite and affine situ
ations\, and the new challenges present in the latter.\n\nThis talk is bas
ed on earlier works joint with Valerio Toledano Laredo and Curtis Wendland
t\, and a recent one in collaboration with Andrea Appel and Curtis Wendlan
dt.\n\nHybrid delivery (in person on University of Saskatchewan campus and
via Zoom).\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abid Ali (University of Saskatchewan)
DTSTART:20231012T223000Z
DTEND:20231013T000000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/15
DESCRIPTION:Title: Strong integrality of inversion subgroups of Kac-Moody groups\nby Ab
id Ali (University of Saskatchewan) as part of PIMS Geometry / Algebra / P
hysics (GAP) Seminar\n\nLecture held in THORV 124.\n\nAbstract\nThe questi
on of integrality for semi-simple algebraic groups over the field of ratio
nal numbers was established by Chevalley in the 1950s as part of his work
on associating affine group schemes with groups over integers. For infinit
e-dimensional Kac-Moody groups\, it remains an open problem. To state this
problem more precisely\, let $\\mathfrak g$ be a symmetrizable Kac–Mood
y algebra over $\\mathbb Q$\, $V$ be an integrable highest weight $\\mathf
rak g$-module\, and $V_{\\mathbb Z}$ be a $\\mathbb Z$-form of $V$. Let $G
=G(\\mathbb{Q})$ be an associated minimal representation-theoretic Kac–M
oody group and let $G(\\mathbb{Z})$ be its integral subgroup. Suppose $\\G
amma(\\mathbb{Z})$ is the Chevalley subgroup of $G$\, that is\, the subgro
up that stabilizes the lattice $V_{\\mathbb Z}$ in $V$. The integrality fo
r $G$ is to determine if $G(\\mathbb{Z})=\\Gamma(\\mathbb{Z})$. We will di
scuss some progress on this problem\, which we made in a joint work with L
isa Carbone\, Dongwen Liu\, and Scott H. Murray. Our results have various
applications\, including the integrality of subgroups of the unipotent sub
group $U$ of $G$ that are generated by commuting real root groups.\n\nHybr
id delivery (in person on University of Saskatchewan campus and via Zoom).
\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Casey Blacker (George Mason University)
DTSTART:20231122T220000Z
DTEND:20231122T233000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/16
DESCRIPTION:Title: Geometric and algebraic reduction of multisymplectic manifolds\nby C
asey Blacker (George Mason University) as part of PIMS Geometry / Algebra
/ Physics (GAP) Seminar\n\nLecture held in PHYSICS 128.\n\nAbstract\nA sym
plectic Hamiltonian manifold consists of a Lie group action on a symplecti
c manifold\, together with the additional structure of a moment map\, whic
h encodes the group action in terms of the assignment of Hamiltonian vecto
r fields. In special cases\, the moment map determines a smooth submanifol
d to which the Lie group action restricts and the resulting quotient inher
its the structure of symplectic manifold. In every case\, it is possible t
o construct a reduced Poisson algebra that plays the role of the space of
smooth functions on the reduced symplectic manifold.\n\nIn this talk\, we
will discuss an adaptation of these ideas to the multisymplectic setting.
Specifically\, we will exhibit a geometric reduction procedure for multisy
mplectic manifolds in the presence of a Hamiltonian action\, an algebraic
reduction procedure for the associated $L$-infinity algebras of classical
observables\, and a comparison of these two construction. This is joint wo
rk with Antonio Miti and Leonid Ryvkin.\n\nHybrid delivery (in person on U
niversity of Saskatchewan campus and via Zoom).\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuly Billig (Carleton University)
DTSTART:20240111T220000Z
DTEND:20240111T233000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/17
DESCRIPTION:Title: Sheaves of AV-modules over projective varieties\nby Yuly Billig (Car
leton University) as part of PIMS Geometry / Algebra / Physics (GAP) Semin
ar\n\nLecture held in THORV 124.\n\nAbstract\nAV-modules are representatio
ns of the Lie algebra $V$ of vector fields that admit a compatible action
of the commutative algebra $A$ of functions. This notion is a natural gene
ralization of $\\mathcal D$-modules. In this talk we shall start by review
ing the theory of AV-modules over smooth irreducible affine varieties $X$.
When the variety $X$ is projective\, it is necessary to consider sheaves
of AV-modules. We describe associative algebras that control the category
of AV-modules\, and construct a functor from the category of strong repres
entations of Lie algebra of jets of vector fields to the category of AV-mo
dules. This talk is based on the joint work with Colin Ingalls\, as well
as the work of Emile Bouaziz and Henrique Rocha.\n\nHybrid delivery (in pe
rson on University of Saskatchewan campus and via Zoom).\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julius Grimminger (University of Oxford)
DTSTART:20240207T223000Z
DTEND:20240207T233000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/18
DESCRIPTION:Title: Quivers and their 3d Coulomb branches\nby Julius Grimminger (Univers
ity of Oxford) as part of PIMS Geometry / Algebra / Physics (GAP) Seminar\
n\nLecture held in THORV 124.\n\nAbstract\nI will aim to give a pedagogica
l introduction to 3d Coulomb branches of quiver gauge theories\, which are
certain holomorphic symplectic varieties with symplectic singularities. A
fter briefly explaining why I care about such spaces as a physicist\, I wi
ll focus on the mathematical aspects of Coulomb branches\, and discuss in
particular how to count their holomorphic functions. I will then show how
discrete modifications of a quiver induces a discrete quotient on its Coul
omb branch.\n\nHybrid delivery (in person on University of Saskatchewan ca
mpus and via Zoom).\n\n\n(This is part of a series with https://researchse
minars.org/talk/PIMS_GAP/19/ occurring immediately after this talk.)\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Bourget (CEA Paris-Saclay)
DTSTART:20240207T233000Z
DTEND:20240208T003000Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/19
DESCRIPTION:Title: Decay and fission of magnetic quivers\nby Antoine Bourget (CEA Paris
-Saclay) as part of PIMS Geometry / Algebra / Physics (GAP) Seminar\n\nLec
ture held in THORV 124.\n\nAbstract\nOver the past 5 years\, the stratific
ation of 3d Coulomb branches into symplectic leaves has been the subject o
f intense work in the physics community. Mathematically\, this corresponds
to understanding the nested singularity structure of conical symplectic s
ingularities. This class includes Nakajima quiver varieties\, slices in af
fine grassmannians\, instanton moduli spaces\, and much more. In this talk
\, I will review the methods that have been developed\, centered on the co
ncept of magnetic quivers. I will show how insights from string theory pro
vide easy algorithms that can be implemented on a computer.\n\nHybrid deli
very (in person on University of Saskatchewan campus and via Zoom).\n\n(Th
is is part of a series with https://researchseminars.org/talk/PIMS_GAP/18/
occurring immediately before this talk.)\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siwei Xu (The Ohio State University)
DTSTART:20260312T230000Z
DTEND:20260313T001500Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/20
DESCRIPTION:Title: Affine Yangians and quantum toroidal algebras in type A\nby Siwei Xu
(The Ohio State University) as part of PIMS Geometry / Algebra / Physics
(GAP) Seminar\n\nLecture held in PHYSIC 130.\n\nAbstract\nThe main objects
of my talk are the affine Yangian and the quantum toroidal algebra of typ
e A with two deformation parameters\, as introduced in the work of Bershte
in and Tsymbaliuk (2019). These algebras first appeared in Maulik and Okou
nkov’s 2012 work\, where they were realized in a purely geometric form t
hrough the equivariant cohomology of quiver varieties. In this talk\, I co
nstruct an explicit functor from an appropriate category of representation
s of the affine Yangian associated with $\\mathfrak{sl}(mn)$ to that of th
e quantum toroidal algebra associated with $\\mathfrak{sl}(m)$ for all pos
itive integers m and n\, which extends the construction of Gautam and Tole
dano Laredo (2016).\n\nHybrid delivery (in person on University of Saskatc
hewan campus and via Zoom).\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Raymond (University of Hamburg)
DTSTART:20260326T230000Z
DTEND:20260327T001500Z
DTSTAMP:20260422T212729Z
UID:PIMS_GAP/21
DESCRIPTION:Title: Inverting Hamiltonian Reduction - A Rep Theory Perspective\nby Chris
Raymond (University of Hamburg) as part of PIMS Geometry / Algebra / Phys
ics (GAP) Seminar\n\nLecture held in PHYSIC 130.\n\nAbstract\nQuantum Hami
ltonian reduction is an algebraic procedure that produces new vertex algeb
ras from known ones\, with the best understood examples being the W-algebr
as that arise from affine vertex algebras. Recent work has focused on mora
lly inverting this construction\, which has important implications for rep
resentation theory. Moreover\, since affine vertex algebras are intimately
tied to their underlying Lie algebras\, this inverse construction also pr
ovides new tools for constructing and studying weight modules over both fi
nite and affine Lie algebras\, which are of broader interest in algebra an
d mathematical physics. In this talk\, I'll give an introduction to the id
eas involved and illustrate the construction by showing how it naturally p
roduces simple weight modules with infinite-dimensional weight spaces ever
ywhere.\n\nHybrid delivery (in person on University of Saskatchewan campus
and via Zoom).\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/21/
END:VEVENT
END:VCALENDAR