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BEGIN:VEVENT
SUMMARY:Frobenius splitting of semi-infinite flag manifolds
DTSTART;VALUE=DATE-TIME:20190206T020000Z
DTEND;VALUE=DATE-TIME:20190206T030000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-2639@indico.ipmu.jp
DESCRIPTION:Speakers: Syu Kato ()\nWe explain that extremal weight modules
of quantum loop algebras give rise to the projective coordinate ring of t
he formal model of the semi-infinite flag manifolds over the ring of integ
ers with two inverted. Then\, we exhibit how this gives rise to the Froben
ius splitting of such an (ind-)scheme. This particularly implies that the
Schubert varieties of the quasi-map spaces from a projective line to a (pa
rtial) flag manifold admits a Frobenius splitting compatible with the boun
daries\, and consequently such varieties are normal and has rational singu
larity in characteristic zero. This extends the case of the genuine quasi-
map spaces by Braverman-Finkelberg and the asymptotic case by myself.\n\nI
f time allows\, we explain how to use such results to understand the struc
ture of equivariant small quantum $K$-theory of a (partial) flag manifold.
\n\nhttps://indico.ipmu.jp/event/168/contributions/2639/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2639/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cohomological construction of quantum symmetric pairs
DTSTART;VALUE=DATE-TIME:20190208T043000Z
DTEND;VALUE=DATE-TIME:20190208T053000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-2627@indico.ipmu.jp
DESCRIPTION:Speakers: Andrea Appel ()\nBraided module categories provide a
conceptual framework for universal solutions of the (twisted) reflection
equation\, in analogy of what braided monoidal categories are for the quan
tum Yang-Baxter equation. In the theory of quantum groups\, natural exampl
es of braided module categories arise from the category of representations
of a quantum symmetric pair coideal subalgebra as recently proved by M. B
alagovic and S. Kolb. In this talk\, I will describe the semi-classical in
terpretation of their construction and how this leads to a cohomological c
onstruction of quantized symmetric pairs in the context of deformation the
ory.\n\nhttps://indico.ipmu.jp/event/168/contributions/2627/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2627/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hall algebra of sheaves on abelian surfaces
DTSTART;VALUE=DATE-TIME:20190206T063000Z
DTEND;VALUE=DATE-TIME:20190206T073000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-2637@indico.ipmu.jp
DESCRIPTION:Speakers: Shintaro Yanagida ()\nI will give some explicit calc
ulations on the Hall algebra of sheaves on abelian surfaces\, and will exp
lain their relationship to the elliptic integrable system of Macdonald-Rui
jsenaars operators.\n\nhttps://indico.ipmu.jp/event/168/contributions/2637
/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2637/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Homology of affine Grassmannian and quantum cohomology
DTSTART;VALUE=DATE-TIME:20190208T003000Z
DTEND;VALUE=DATE-TIME:20190208T013000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-2634@indico.ipmu.jp
DESCRIPTION:Speakers: Changjian Su ()\nLet $G$ be a complex reductive grou
p\, and $X$ be a smooth projective $G$-variety. We will construct an algeb
ra homomorphism from the homology of the affine Grassmannian $Gr_G$ to the
G-equivariant quantum cohomology of $X$. The construction uses shift oper
ators in quantum cohomolgies. Joint work with Alexander Braverman.\n\nhttp
s://indico.ipmu.jp/event/168/contributions/2634/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2634/
END:VEVENT
BEGIN:VEVENT
SUMMARY:New TQFTs from DAHA
DTSTART;VALUE=DATE-TIME:20190208T053000Z
DTEND;VALUE=DATE-TIME:20190208T063000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-2646@indico.ipmu.jp
DESCRIPTION:Speakers: Sergei Gukov ()\nhttps://indico.ipmu.jp/event/168/co
ntributions/2646/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2646/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discrete Painlevé Equation and Four-dimensional Gauge Theories
DTSTART;VALUE=DATE-TIME:20190204T050000Z
DTEND;VALUE=DATE-TIME:20190204T060000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-2636@indico.ipmu.jp
DESCRIPTION:Speakers: Masahito Yamazaki ()\nWe discuss special solutions f
or the Hirota-type bilinear identity for the E8 discrete Painlevé equatio
n and its "lens-generalization". The key identity is provided by transform
ation formulas for the lens-elliptic gamma function\, which were first fou
nd via the Seiberg dualities in $4d$ $\\mathcal{N}=1$ theories\, and studi
ed in connection with the super-master solution of the star-triangle relat
ion.\n\nhttps://indico.ipmu.jp/event/168/contributions/2636/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2636/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Some applications of defects in supersymmetric gauge theory
DTSTART;VALUE=DATE-TIME:20190204T003000Z
DTEND;VALUE=DATE-TIME:20190204T013000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-2648@indico.ipmu.jp
DESCRIPTION:Speakers: Nikita Nekrasov ()\nI will explain the formula of Ga
mayun\, Iorgov and Lysovyy relating Painleve VI tau-function to $c=1$ conf
ormal blocks and some of it generalizations\, using the blowup formulas fo
r $N_f = 2N_c$ supersymmetric $N=2$ $d=4$ theory. If time permits I will t
alk about the eigenvalue problem for the elliptic Calogero-Moser system.\n
\nhttps://indico.ipmu.jp/event/168/contributions/2648/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2648/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cohomological Hall algebras\, vertex algebras and instantons
DTSTART;VALUE=DATE-TIME:20190204T020000Z
DTEND;VALUE=DATE-TIME:20190204T030000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-2729@indico.ipmu.jp
DESCRIPTION:Speakers: Yaping Yang ()\nA new class of vertex operator algeb
ras\, vertex algebras at the corner\, are recently introduced by Gaiotto a
nd Rapčák\, generalizing the affine W-algebra of $\\mathfrak{gl}_N$. In
my talk\, I will discuss an action of this new vertex algebra on the cohom
ology of certain spiked instanton moduli spaces on 3CY manifold in the sen
se of Nekrasov. This action is naturally obtained using the cohomological
Hall algebras of Kontsevich-Soibelman. This talk is based on my joint work
with Miroslav Rapčák\, Yan Soibelman\, and Gufang Zhao.\n\nhttps://indi
co.ipmu.jp/event/168/contributions/2729/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2729/
END:VEVENT
BEGIN:VEVENT
SUMMARY:SUSY localization for Coulomb branch operators in 3 and 4 dimensio
ns
DTSTART;VALUE=DATE-TIME:20190206T003000Z
DTEND;VALUE=DATE-TIME:20190206T013000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-2635@indico.ipmu.jp
DESCRIPTION:Speakers: Takuya Okuda ()\nWe calculate\, via SUSY localizatio
n\, the correlators of the operators whose vevs parametrize the Coulomb br
anches. In $4d$\, we review the computation of the correlators of Wilson-
't Hooft line operators in $N=2$ gauge theories on $S^1 \\times \\mathbb{R
}^3$. The results involve $Z_{\\text{mono}}$\, the monopole analog of the
Nekrasov instanton partition function. For a class $\\mathcal{S}$ theory
\, the correlators describe deformation quantization of the Hitchin moduli
space in terms of Fenchel-Nielsen coordinates. In $3d$\, we compute corre
lators of dressed monopole operators in $N=4$ gauge theories on $\\mathbb{
R}^3$ with omega deformation and develop similar stories. We compare our
results with those obtained in other approaches. Based on arXiv:1111.4221
with Ito and Taki\, as well as on a work in progress with Y. Yoshida.\n\nh
ttps://indico.ipmu.jp/event/168/contributions/2635/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2635/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geometry of quiver W-algebra
DTSTART;VALUE=DATE-TIME:20190207T020000Z
DTEND;VALUE=DATE-TIME:20190207T030000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-2630@indico.ipmu.jp
DESCRIPTION:Speakers: Taro Kimura ()\nQuiver W-algebra is the gauge theore
tical construction of q-deformed W-algebra. The generating current of the
algebra is given as the operator analog of the qq-character associated wit
h the representation on the quiver. I'd like to show that a master formula
for such a generating current is obtained through the geometric construct
ion of the qq-character by Nekrasov.\n\nhttps://indico.ipmu.jp/event/168/c
ontributions/2630/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2630/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deatonomization of cluster integrable systems
DTSTART;VALUE=DATE-TIME:20190206T050000Z
DTEND;VALUE=DATE-TIME:20190206T060000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-2628@indico.ipmu.jp
DESCRIPTION:Speakers: Mikhail Bershtein ()\nTo any Newton polygon one can
assign the cluster integrable system. The group $G$ of discrete flows acts
on the phase space\, preserving the integrals of motion of the cluster in
tegrable system. After deautonomization the action $G$ leads to $q$-differ
ence equations\, which are equations of isomonodromic deformations of line
ar $q$-difference equations. Finally\, these equations can be explicitly s
olved using Nekrasov functions of $5d$ supersymmetric gauge theory or part
ition functions of topological strings. The Seiberg-Witten curve for corre
sponding supersymmetric gauge theory and toric Calabi-Yau are constructed
from the initial Newton polygon.\n\nBased on joint works with A. Marshakov
and P. Gavrylenko.\n\nhttps://indico.ipmu.jp/event/168/contributions/2628
/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2628/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Intersection of mirror branes on Higgs moduli spaces
DTSTART;VALUE=DATE-TIME:20190205T003000Z
DTEND;VALUE=DATE-TIME:20190205T013000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-2629@indico.ipmu.jp
DESCRIPTION:Speakers: Tamás Hausel ()\nI will discuss a computational app
roach for the semiclassical limit of mirror symmetry for Higgs moduli spac
es for Langlands dual groups\, by comparing the equivariant indices of int
ersections of mirror branes.\n\nhttps://indico.ipmu.jp/event/168/contribut
ions/2629/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2629/
END:VEVENT
BEGIN:VEVENT
SUMMARY:3d holomorphic blocks from the intertwiner of quantum toroidal alg
ebra
DTSTART;VALUE=DATE-TIME:20190205T020000Z
DTEND;VALUE=DATE-TIME:20190205T030000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-2649@indico.ipmu.jp
DESCRIPTION:Speakers: Hiroaki Kanno ()\nThe intertwiner of the Fock repre
sentation of the quantum toroidal algebra of $\\mathfrak{gl}_1$ type can b
e identified with the refined topological vertex\, which is a building blo
ck of 5d lift of the Nekrasov instanton partition function. In general the
correlation function of the intertwiners satisfies a difference equation
of KZ type\, where the associated R-matrix is featured. In this talk I wil
l explain how we can derive generalized KZ equation for quantum toroidal a
lgebra in a simplified setting and show that 3d holomorphic blocks arise a
s solutions to the equation.\n\nhttps://indico.ipmu.jp/event/168/contribut
ions/2649/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2649/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Symplectic duality and Langlands duality
DTSTART;VALUE=DATE-TIME:20190208T020000Z
DTEND;VALUE=DATE-TIME:20190208T030000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-2641@indico.ipmu.jp
DESCRIPTION:Speakers: Justin Hilburn ()\nIn this talk I would like to sket
ch how one can use the tools of derived symplectic geometry and holomorphi
cally twisted gauge theories to derive a relationship between symplectic d
uality and local Langlands. Our starting point will be an observation due
to Gaiotto-Witten that a $3d$ $\\mathcal{N}=4$ theory with a $G$ flavor sy
mmetry is a boundary condition for $4d$ $\\mathcal{N}=4$ SYM with gauge gr
oup $G$. By examining the relationship between boundary observables and bu
lk lines we will be able to derive constructions originally due to Braverm
an\, Finkelberg\, Nakajima. By examine the relationship between boundary l
ines and bulk surface operators one can derive new connections to local ge
ometric Langlands.\n\nThis is based on joint work with Philsang Yoo\, Tudo
r Dimofte\, and Davide Gaiotto.\n\nhttps://indico.ipmu.jp/event/168/contri
butions/2641/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2641/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Five-dimensional topological indices and Bethe ansatz at large $N$
DTSTART;VALUE=DATE-TIME:20190204T063000Z
DTEND;VALUE=DATE-TIME:20190204T073000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-3129@indico.ipmu.jp
DESCRIPTION:Speakers: Seyed Morteza Hosseini ()\nI will provide a general
formula for the exact partition function of five-dimensional supersymmetr
ic gauge theories on a four-manifold times a circle. The four-manifold is
either toric Kaehler or a product of two Riemann surfaces. Then I will dis
cuss the Bethe ansatz system associated to our partition functions at larg
e $N$.\n\nhttps://indico.ipmu.jp/event/168/contributions/3129/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/3129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toward double affine flag varieties and Grassmannians
DTSTART;VALUE=DATE-TIME:20190207T003000Z
DTEND;VALUE=DATE-TIME:20190207T013000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-3130@indico.ipmu.jp
DESCRIPTION:Speakers: Dinakar Muthiah ()\nRecently there has been a growin
g interest in double affine Grassmannians\, especially because of their re
lationship with Coulomb branches of quiver gauge theories. However\, not m
uch has been said about double affine flag varieties. I will discuss some
results toward understanding double affine flag varieties and Grassmannian
s (and their Schubert subvarieties) from the point of view of $p$-adic Kac
-Moody groups. I will discuss Hecke algebras\, Bruhat order\, and Kazhdan-
Lusztig polynomials in this setting. This includes work joint with Daniel
Orr and joint with Manish Patnaik.\n\nhttps://indico.ipmu.jp/event/168/con
tributions/3130/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/3130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Categorical Hikita duality
DTSTART;VALUE=DATE-TIME:20190205T063000Z
DTEND;VALUE=DATE-TIME:20190205T073000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-2632@indico.ipmu.jp
DESCRIPTION:Speakers: Michael McBreen ()\nSymplectic duality predicts vari
ous relationships (often somewhat mysterious) between the Higgs and Coulom
b branches of certain $3d$ $\\mathcal{N}=4$ supersymmetric gauge theories.
In particular\, Hikita's conjecture relates the cohomology ring of the Hi
ggs branch with the coordinate ring of the fixed scheme of the Coulomb bra
nch\, with respect to a torus action on the latter. I will discuss joint w
ork with Roman Bezrukavnikov\, which proposes a categorical analogue of th
is conjecture for abelian gauge theories. It relates constructible sheaves
on the loop space of the Higgs branch with coherent sheaves on the fixed
scheme of the Coulomb branch. I will give a combinatorial model for for ca
tegories and sketch a proof.\n\nhttps://indico.ipmu.jp/event/168/contribut
ions/2632/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2632/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Non-unitary modular categories from the Coulomb branch
DTSTART;VALUE=DATE-TIME:20190205T050000Z
DTEND;VALUE=DATE-TIME:20190205T060000Z
DTSTAMP;VALUE=DATE-TIME:20240725T121545Z
UID:indico-contribution-168-2647@indico.ipmu.jp
DESCRIPTION:Speakers: Du Pei ()\nWe propose a new link between the geometr
y of moduli spaces and the representation theory of vertex operator algebr
as. The construction goes through a class of four-dimensional quantum fiel
d theories that are said to satisfy "property F". Each such theory gives r
ise to a family of modular tensor categories\, whose algebraic structures
are intimately related to the geometry of the Coulomb branch. This is base
d on joint work with Mykola Dedushenko\, Sergei Gukov\, Hiraku Nakajima an
d Ke Ye.\n\nhttps://indico.ipmu.jp/event/168/contributions/2647/
LOCATION:Lecture Hall(1F)\, Kavli IPMU
URL:https://indico.ipmu.jp/event/168/contributions/2647/
END:VEVENT
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