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BEGIN:VEVENT
SUMMARY:Dylan Allegretti (Yau Mathematical Sciences Center at Tsinghua Uni
versity)
DTSTART:20221017T050000Z
DTEND:20221017T063000Z
DTSTAMP:20260404T094702Z
UID:gapkias/1
DESCRIPTION:Title: Teichmüller spaces\, quadratic differentials\, and cluster coordin
ates\nby Dylan Allegretti (Yau Mathematical Sciences Center at Tsinghu
a University) as part of Geometry\, Algebra and Physics at KIAS\n\n\nAbstr
act\nIn the late 1980s\, Nigel Hitchin and Michael Wolf independently disc
overed a parametrization of the Teichmüller space of a compact surface by
holomorphic quadratic differentials. In this talk\, I will describe a gen
eralization of their result. I will explain how\, by replacing holomorphic
differentials by meromorphic differentials\, one is naturally led to cons
ider an object called the enhanced Teichmüller space. The latter is an ex
tension of the classical Teichmüller space which is important in mathemat
ical physics and the theory of cluster algebras.\n
LOCATION:https://stable.researchseminars.org/talk/gapkias/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Douglas (Yale University)
DTSTART:20221024T010000Z
DTEND:20221024T023000Z
DTSTAMP:20260404T094702Z
UID:gapkias/2
DESCRIPTION:Title: Dimers\, webs\, and local systems\nby Daniel Douglas (Yale Univ
ersity) as part of Geometry\, Algebra and Physics at KIAS\n\n\nAbstract\nF
or a planar bipartite graph G equipped with a SLn-local system\, we show t
hat the determinant of the associated Kasteleyn matrix counts “n-multiwe
bs” (generalizations of n-webs) in G\, weighted by their web-traces. We
use this fact to study random n-multiwebs in graphs on some simple surface
s. Time permitting\, we will discuss some relations to Fock-Goncharov theo
ry. This is joint work with Rick Kenyon and Haolin Shi.\n
LOCATION:https://stable.researchseminars.org/talk/gapkias/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hironori Oya (Tokyo Institute of Technology)
DTSTART:20221222T010000Z
DTEND:20221222T023000Z
DTSTAMP:20260404T094702Z
UID:gapkias/3
DESCRIPTION:Title: Wilson lines on the moduli space of $G$-local systems on a marked s
urface\nby Hironori Oya (Tokyo Institute of Technology) as part of Geo
metry\, Algebra and Physics at KIAS\n\n\nAbstract\nFor a marked surface $\
\Sigma$\, there are two kinds of extensions of moduli spaces of local syst
ems on $\\Sigma$\, written as $\\mathcal{A}_{\\widetilde{G}\, \\Sigma}$ an
d $\\mathcal{P}_{G\, \\Sigma}$\, where $\\widetilde{G}$ is a connected sim
ply-connected complex simple algebraic group and $G=\\widetilde{G}/Z(\\wid
etilde{G})$ its adjoint group. These are introduced by Fock--Goncharov and
Goncharov--Shen respectively\, and it is known that the pair $(\\mathcal{
A}_{\\widetilde{G}\, \\Sigma}\, \\mathcal{P}_{G\, \\Sigma})$ forms a clust
er ensemble.\n In this talk\, we formulate a class of $\\widetilde{G}$ or
$G$-valued morphisms defined on these moduli spaces\, which we call Wilso
n lines. I explain their basic properties and application. In particular\,
we give an affirmative answer to the $\\mathrm{A}=\\mathrm{U}$ problem fo
r the cluster algebras arising from the cluster $K_2$-structures on $\\mat
hcal{A}_{\\widetilde{G}\, \\Sigma}$ under some assumptions on $G$ and $\\S
igma$.\n This talk is based on a joint work with Tsukasa Ishibashi and Li
nhui Shen.\n
LOCATION:https://stable.researchseminars.org/talk/gapkias/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunsuke Kano (Research Alliance Center for Mathematical Sciences\
, Tohoku University)
DTSTART:20230112T050000Z
DTEND:20230112T063000Z
DTSTAMP:20260404T094702Z
UID:gapkias/4
DESCRIPTION:Title: Unbounded sl(3)-laminations and their shear coordinates\nby Shu
nsuke Kano (Research Alliance Center for Mathematical Sciences\, Tohoku Un
iversity) as part of Geometry\, Algebra and Physics at KIAS\n\n\nAbstract\
nFock--Goncharov pointed out the space of unbounded laminations on a marke
d surface gives the set of tropical valued points of the moduli space of t
he framed PGL_2 local systems on the surface. The key point of this identi
fication is that the shear coordinate of the space of unbounded lamination
s gives the tropicalized cluster structure of the moduli space.\nIn this t
alk\, we introduce the space of unbounded sl(3) laminations (with pinnings
) and define the "shear coordinate" on it as a generalization of the sl(2)
case.\nIf time permits\, we discuss the graphical basis of the Ishibashi-
-Yuasa sl(3) skein algebra.\nThis talk is based on a joint work with Tsuka
sa Ishibashi.\n
LOCATION:https://stable.researchseminars.org/talk/gapkias/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsukasa Ishibashi (Mathematical Institute\, Tohoku University)
DTSTART:20230511T013000Z
DTEND:20230511T030000Z
DTSTAMP:20260404T094702Z
UID:gapkias/5
DESCRIPTION:Title: Moduli space of decorated G-local systems and skein algebras\nb
y Tsukasa Ishibashi (Mathematical Institute\, Tohoku University) as part o
f Geometry\, Algebra and Physics at KIAS\n\n\nAbstract\nThe moduli space o
f decorated (twisted) G-local systems on a marked surface\, originally int
roduced by Fock–Goncharov\, is known to have a natural cluster K_2 struc
ture. In particular\, it admits a quantization via the framework of quantu
m cluster algebras\, due to Berenstein—Zelevinsky and Goncharov—Shen.\
nIn this talk\, I will explain its (in general conjectural) relation to th
e skein algebras. This talk is based on joint works with Hironori Oya\, Li
nhui Shen and Wataru Yuasa.\n
LOCATION:https://stable.researchseminars.org/talk/gapkias/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wataru Yuasa (Graduate School of Science\, Division of Mathematics
and Mathematical Sciences\, Kyoto University)
DTSTART:20230629T013000Z
DTEND:20230629T030000Z
DTSTAMP:20260404T094702Z
UID:gapkias/6
DESCRIPTION:Title: State-clasp correspondence for skein algebras\nby Wataru Yuasa
(Graduate School of Science\, Division of Mathematics and Mathematical Sci
ences\, Kyoto University) as part of Geometry\, Algebra and Physics at KIA
S\n\n\nAbstract\nWe introduce the stated and the clasped sp_4-skein algebr
as for an oriented surface with marked points on the boundary. Moreover\,
we show that the reduced version of the stated g-skein algebra is isomorph
ic to the boundary-localization of the clasped g-skein algebra for g=sl_2\
, sl_3\, or sp_4. This isomorphism is a quantum counterpart of the two des
criptions of the cluster algebra of the surface associated with g in terms
of the matrix coefficients of Wilson lines and cluster variables\, respec
tively. This talk is based on a joint work with Tsukasa Ishibashi (Tohoku
Univ.).\n
LOCATION:https://stable.researchseminars.org/talk/gapkias/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sin-Myung Lee (Korea Institute for Advanced Study)
DTSTART:20231023T020000Z
DTEND:20231023T033000Z
DTSTAMP:20260404T094702Z
UID:gapkias/7
DESCRIPTION:Title: Representations of quantum affine (super)algebras from the R-matrix
's point of view\nby Sin-Myung Lee (Korea Institute for Advanced Study
) as part of Geometry\, Algebra and Physics at KIAS\n\nLecture held in Roo
m 1424\, Korea Institute for Advanced Study.\n\nAbstract\nOne of the major
problems in representation theory of quantum affine algebras is to unders
tand the tensor product structure\, for which it has been recognized that
(normalized) R-matrices and their poles play a crucial role. In this talk\
, we first give a brief survey on representations of quantum affine (super
)algebras from this perspective. Then we will explain a new approach motiv
ated from the super duality for Lie superalgebras\, which is an ongoing pr
oject with Jae-Hoon Kwon and Masato Okado.\n
LOCATION:https://stable.researchseminars.org/talk/gapkias/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Davison (The University of Edinburgh)
DTSTART:20231205T050000Z
DTEND:20231205T063000Z
DTSTAMP:20260404T094702Z
UID:gapkias/8
DESCRIPTION:Title: Strong positivity for quantum cluster algebras\nby Ben Davison
(The University of Edinburgh) as part of Geometry\, Algebra and Physics at
KIAS\n\nLecture held in Room 1424\, Korea Institute for Advanced Study.\n
\nAbstract\nQuantum cluster algebras are quantizations of cluster algebras
\, which are a class of algebras interpolating between integrable systems
and combinatorics. These algebras were originally introduced to study posi
tivity phenomena arising in the study of quantum groups\, and so one of th
e key questions regarding them (and their quantum analogues) is whether th
ey admit a basis for which the structure constants are positive. The class
ical version of this question was settled in the affirmative by Gross\, Ha
cking\, Keel and Kontsevich. I will present a proof of the quantum version
of this positivity for skew-symmetric quantum cluster algebras\, due to j
oint work with Travis Mandel\, based on results in categorified Donaldson-
Thomas theory and scattering diagrams.\n
LOCATION:https://stable.researchseminars.org/talk/gapkias/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Buciumas (Pohang University of Science and Technology (PO
STECH))
DTSTART:20240425T013000Z
DTEND:20240425T030000Z
DTSTAMP:20260404T094702Z
UID:gapkias/9
DESCRIPTION:Title: Hecke algebras\, Whittaker functions and quantum groups\nby Val
entin Buciumas (Pohang University of Science and Technology (POSTECH)) as
part of Geometry\, Algebra and Physics at KIAS\n\nLecture held in KIAS 142
4.\n\nAbstract\nI will give a brief overview of the Satake isomorphism and
the Casselman-Shalika formula\, which are basic tools in the representati
on theory of p-adic groups. These two results essentially state that the s
pherical Hecke algebra and the spherical Whittaker functions on a p-adic g
roup can be understood in terms of the representation theory of the dual g
roup.\nWhen passing from p-adic groups to their metaplectic covers\, it wa
s conjectured by Gaitsgory and Lurie (recently proved in different setting
s by Campbell-Dhillon-Raskin and Buciumas-Patnaik) that the dual group get
s replaced by a certain quantum group at a root of unity. I will try to ex
plain the conjecture of Gaitsgory-Lurie and if time permits some of the id
eas of the proof in the algebraic setting\, as well as some interactions t
o combinatorics and number theory.\n
LOCATION:https://stable.researchseminars.org/talk/gapkias/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sunghyuk Park (Harvard University)
DTSTART:20240430T010000Z
DTEND:20240430T023000Z
DTSTAMP:20260404T094702Z
UID:gapkias/10
DESCRIPTION:Title: 3d quantum trace map\nby Sunghyuk Park (Harvard University) as
part of Geometry\, Algebra and Physics at KIAS\n\n\nAbstract\nI will spea
k about my recent joint work with Sam Panitch constructing the 3d quantum
trace map\, a homomorphism from the Kauffman bracket skein module of an id
eally triangulated 3-manifold to its (square root) quantum gluing module\,
thereby giving a precise relationship between the two quantizations of th
e character variety of ideally triangulated 3-manifolds. Our construction
is based on the study of stated skein modules and their behavior under spl
itting\, especially into face suspensions.\n
LOCATION:https://stable.researchseminars.org/talk/gapkias/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitriy Voloshyn (IBS Center for Geometry and Physics)
DTSTART:20240503T013000Z
DTEND:20240503T030000Z
DTSTAMP:20260404T094702Z
UID:gapkias/11
DESCRIPTION:Title: Cluster algebras and Poisson geometry\nby Dmitriy Voloshyn (IB
S Center for Geometry and Physics) as part of Geometry\, Algebra and Physi
cs at KIAS\n\nLecture held in Room 1423\, Korea Institute for Advanced Stu
dy.\n\nAbstract\nCluster algebras are commutative rings with distinguished
sets of generators characterized by a remarkable combinatorial structure.
Discovered by S. Fomin and A. Zelevinsky in the early 2000s\, these algeb
raic structures have found applications across diverse mathematical fields
\, including integrable systems\, total positivity\, Teichmüller theory\,
Poisson geometry\, knot theory and mathematical physics.\n Fomin and Zel
evinsky conjectured that numerous varieties in Lie theory are equipped wit
h a cluster structure. Early examples include double Bruhat cells\, Grassm
annians and simple complex algebraic groups. M. Gekhtman\, M. Shapiro and
A. Vainshtein observed that cluster algebras in these examples are compati
ble with certain Poisson brackets. Specifically\, for any given cluster $
𝑥_1\,𝑥_2\,...\,𝑥_n$\, there exist constants 𝟂ij such that $\\{
𝑥_i\,𝑥_j\\} = \\omega_{ij} 𝑥_i 𝑥_j$. This observation led to a
program aiming to construct cluster algebras by addressing the inverse pr
oblem: given a Poisson bracket in the coordinate ring of an algebraic vari
ety and a collection of regular functions $(𝑥_1\,𝑥_2\,...\,𝑥_n)$
satisfying $\\{𝑥_i\,𝑥_j\\} = \\omega_{ij} 𝑥_i 𝑥_j$\, does ther
e exist a compatible cluster algebra? The research initiative led to the f
ormulation of the GSV conjecture: for a given simple complex algebraic gro
up and a Poisson bracket from the Belavin-Drinfeld class\, there exists a
compatible cluster structure.\n The plan for the talk is as follows. Firs
t\, we will discuss an example of a cluster structure on ${\\rm GL}_3(\\ma
thbb{C})$. Then we will explore the connection between cluster algebras an
d Poisson geometry\, as well as discuss how to construct a cluster structu
re compatible with a Poisson bracket. After that\, we will discuss the rec
ent results on the three main families of objects: simple connected simple
complex algebraic groups\, their Drinfeld doubles and their Poisson duals
.\n
LOCATION:https://stable.researchseminars.org/talk/gapkias/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volker Genz (IBS Center for Geometry and Physics)
DTSTART:20240627T013000Z
DTEND:20240627T030000Z
DTSTAMP:20260404T094702Z
UID:gapkias/12
DESCRIPTION:Title: Crystals and Cluster Algebras\nby Volker Genz (IBS Center for
Geometry and Physics) as part of Geometry\, Algebra and Physics at KIAS\n\
nLecture held in Room 1423\, Korea Institute for Advanced Study.\n\nAbstra
ct\nCrystal operators on canonical bases as introduced by Kashiwara/Luszti
g provide in particular a toolbox to compute within the category of finite
dimensional representations of finite dimensional simple Lie algebras. Mo
tivated by this we introduce certain operators on the lattice of tropical
points of mirror dual A- and X-cluster spaces. In particular\, this yields
a crystal-like structure on the canonical basis due to Gross-Hacking-Keel
-Kontsevich.\n
LOCATION:https://stable.researchseminars.org/talk/gapkias/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhihao Wang (Korea Institute for Advanced Study)
DTSTART:20250919T013000Z
DTEND:20250919T030000Z
DTSTAMP:20260404T094702Z
UID:gapkias/13
DESCRIPTION:Title: Centers and Representations of the SL(n) quantum Teichmüller Spac
e\nby Zhihao Wang (Korea Institute for Advanced Study) as part of Geom
etry\, Algebra and Physics at KIAS\n\nLecture held in Room 8101\, KIAS.\n\
nAbstract\nThe SL(n)-skein algebra of a surface can be thought of as a qua
ntization of the surface’s character variety. When n=2\, it agrees with
the familiar Kauffman bracket skein algebra\, so the \\mathrm{SL}(n) SL(n)
-skein theory can be viewed as a natural generalization. Thanks to the wor
k of Lê and Yu\, we know that the SL(n)-skein algebra is closely related
to the SL(n) quantum Teichmüller space through the quantum trace map. In
this talk\, we will look at the centers and representations of both balanc
ed Fock–Goncharov algebras and SL(n)-skein algebras.\n
LOCATION:https://stable.researchseminars.org/talk/gapkias/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Davison (The Univ. of Edinburgh)
DTSTART:20251205T020000Z
DTEND:20251205T033000Z
DTSTAMP:20260404T094702Z
UID:gapkias/14
DESCRIPTION:Title: Tutte polynomials of graphs and symplectic duality\nby Ben Dav
ison (The Univ. of Edinburgh) as part of Geometry\, Algebra and Physics at
KIAS\n\nLecture held in Room 8101\, KIAS.\n\nAbstract\nThe Tutte polynomi
al of a graph is a two-variable polynomial\, which is the universal polyno
mial satisfying the deletion contraction recursion. In this talk I will ex
plain how this polynomial arises as a special case of a bicharacteristic p
olynomial defined for pairs of symplectic dual conical resolutions of sing
ularities. More precisely\, the Tutte polynomial records the dimensions of
the graded pieces of the cohomology of hypertoric varieties (which I’ll
introduce) along with the two filtrations by cohomological degree\, comin
g from symplectic duality and Maulik-Okounkov stable envelopes (which I wi
ll also introduce). As well as recovering Tutte polynomials\, there are ot
her bicharacteristic polynomials of symplectic resolutions to explore\, wh
ich I will describe if there is time. These results produce new inequaliti
es of coefficients of Tutte polynomials of matroids. This talk is based on
joint work with Michael McBreen.\n
LOCATION:https://stable.researchseminars.org/talk/gapkias/14/
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