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BEGIN:VEVENT
SUMMARY:Honghao Gao (Michigan State University)
DTSTART:20210104T000000Z
DTEND:20210104T010000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/1
DESCRIPTION:Title: Sheaves in contact topology I\nby Honghao Gao (Michigan State U
niversity) as part of Legendrians\, Cluster algebras\, and Mirror symmetry
\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nMic
rolocal sheaf theory was introduced by Kashiwara-Schapira around 80s. With
the notion of micro-support\, one can use sheaves on smooth manifolds to
access the geometry of their cotangent bundles. In recent years\, microloc
al sheaf theory entered contact and symplectic topology\, and has been use
d to solve open problems. In this lecture series\, we will introduce micro
local sheaf theory in the context of low-dimensional contact topology\, an
d supply the audience with background for its applications such as produci
ng non-classical invariants for Legendrian knots and distinguishing exact
Lagrangian fillings.\n\nLecture 1: Legendrian knots and sheaves $\\newline
$\nBasics of Legendrain knots\, sheaves and microsupport\, local condition
s at arcs\, cusps\, crossings.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Honghao Gao (Michigan State University)
DTSTART:20210104T010000Z
DTEND:20210104T020000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/2
DESCRIPTION:Title: Sheaves in contact topology II\nby Honghao Gao (Michigan State
University) as part of Legendrians\, Cluster algebras\, and Mirror symmetr
y\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nMi
crolocal sheaf theory was introduced by Kashiwara-Schapira around 80s. Wit
h the notion of micro-support\, one can use sheaves on smooth manifolds to
access the geometry of their cotangent bundles. In recent years\, microlo
cal sheaf theory entered contact and symplectic topology\, and has been us
ed to solve open problems. In this lecture series\, we will introduce micr
olocal sheaf theory in the context of low-dimensional contact topology\, a
nd supply the audience with background for its applications such as produc
ing non-classical invariants for Legendrian knots and distinguishing exact
Lagrangian fillings.\n\nLecture 2: invariance $\\newline$\nCategory of sh
eaves\, non-classical invariants for Legendrian submanifolds (theorem by G
uillermou-Kashiwara-Schapira)\, combinatorial verification under Reidemeis
ter moves.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheol-Hyun Cho (Seoul National University)
DTSTART:20210104T040000Z
DTEND:20210104T050000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/3
DESCRIPTION:Title: Homological mirror symmetry via Lagrangian Floer theory I\nby C
heol-Hyun Cho (Seoul National University) as part of Legendrians\, Cluster
algebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Repu
blic of Korea.\n\nAbstract\nA version of homological mirror symmetry(HMS)
conjecture relates the Fukaya category of a symplectic manifold and matrix
factorization category of a mirror Landau-Ginzburg model. In this introdu
ctory lecture series\, we illustrate geometric ideas behind such correspon
dences from a biased point of view of the theory of localized mirror funct
or in Lagrangian Floer theory.\n\nLecture 1 : A-infinity category\, HMS an
d localized mirror functor\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheol-Hyun Cho (Seoul National University)
DTSTART:20210104T050000Z
DTEND:20210104T060000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/4
DESCRIPTION:Title: Homological mirror symmetry via Lagrangian Floer theory II\nby
Cheol-Hyun Cho (Seoul National University) as part of Legendrians\, Cluste
r algebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Rep
ublic of Korea.\n\nAbstract\nA version of homological mirror symmetry(HMS)
conjecture relates the Fukaya category of a symplectic manifold and matri
x factorization category of a mirror Landau-Ginzburg model. In this introd
uctory lecture series\, we illustrate geometric ideas behind such correspo
ndences from a biased point of view of the theory of localized mirror func
tor in Lagrangian Floer theory.\n\nLecture 2 : Monotone Floer theory and i
ts HMS\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhyung Cho (Sungkyunkwan University)
DTSTART:20210104T063000Z
DTEND:20210104T073000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/5
DESCRIPTION:Title: Mutations and toric degenerations I\nby Yunhyung Cho (Sungkyunk
wan University) as part of Legendrians\, Cluster algebras\, and Mirror sym
metry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract
\nThe aim of this lecture is to understand a relation between the wall cro
ssing phenomenon of Lagrangians and the mutations in cluster theory via to
ric degenerations.\n\nLecture 1: Fano toric varieties and potentials $\\ne
wline$\n- A brief introduction to toric varieties $\\newline$\n- Potential
functions of smooth Fano toric varieties\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhyung Cho (Sungkyunkwan University)
DTSTART:20210104T073000Z
DTEND:20210104T083000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/6
DESCRIPTION:Title: Mutations and toric degenerations II\nby Yunhyung Cho (Sungkyun
kwan University) as part of Legendrians\, Cluster algebras\, and Mirror sy
mmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstrac
t\nThe aim of this lecture is to understand a relation between the wall cr
ossing phenomenon of Lagrangians and the mutations in cluster theory via t
oric degenerations.\n\nLecture 2: Toric degenerations\, examples and const
ruction $\\newline$\n- Toric degenerations\; definitions and examples $\\n
ewline$\n- Construction of toric degenerations $\\newline$\n- Potential fu
nctions via toric degenerations $\\newline$\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Honghao Gao (Michigan State University)
DTSTART:20210105T000000Z
DTEND:20210105T010000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/7
DESCRIPTION:Title: Sheaves in contact topology III\nby Honghao Gao (Michigan State
University) as part of Legendrians\, Cluster algebras\, and Mirror symmet
ry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nM
icrolocal sheaf theory was introduced by Kashiwara-Schapira around 80s. Wi
th the notion of micro-support\, one can use sheaves on smooth manifolds t
o access the geometry of their cotangent bundles. In recent years\, microl
ocal sheaf theory entered contact and symplectic topology\, and has been u
sed to solve open problems. In this lecture series\, we will introduce mic
rolocal sheaf theory in the context of low-dimensional contact topology\,
and supply the audience with background for its applications such as produ
cing non-classical invariants for Legendrian knots and distinguishing exac
t Lagrangian fillings.\n\nLecture 3: moduli space of sheaves $\\newline$\n
moduli space of sheaves for elementary tangles\, microlocal rank 1 sheaves
\, positive braid Legendrian knots\, flags and Bott-Samelson cells.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Honghao Gao (Michigan State University)
DTSTART:20210105T010000Z
DTEND:20210105T020000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/8
DESCRIPTION:Title: Sheaves in contact topology IV\nby Honghao Gao (Michigan State
University) as part of Legendrians\, Cluster algebras\, and Mirror symmetr
y\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nMi
crolocal sheaf theory was introduced by Kashiwara-Schapira around 80s. Wit
h the notion of micro-support\, one can use sheaves on smooth manifolds to
access the geometry of their cotangent bundles. In recent years\, microlo
cal sheaf theory entered contact and symplectic topology\, and has been us
ed to solve open problems. In this lecture series\, we will introduce micr
olocal sheaf theory in the context of low-dimensional contact topology\, a
nd supply the audience with background for its applications such as produc
ing non-classical invariants for Legendrian knots and distinguishing exact
Lagrangian fillings.\n\nLecture 4: Lagrangian fillings $\\newline$\nSingu
larities of Legendrian fronts\, exact Lagrangian fillings and Legendrian w
eaves\, sheaf quantization of Lagrangian fillings.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheol-Hyun Cho (Seoul National University)
DTSTART:20210105T040000Z
DTEND:20210105T050000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/9
DESCRIPTION:Title: Homological mirror symmetry via Lagrangian Floer theory III\nby
Cheol-Hyun Cho (Seoul National University) as part of Legendrians\, Clust
er algebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Re
public of Korea.\n\nAbstract\nA version of homological mirror symmetry(HMS
) conjecture relates the Fukaya category of a symplectic manifold and matr
ix factorization category of a mirror Landau-Ginzburg model. In this intro
ductory lecture series\, we illustrate geometric ideas behind such corresp
ondences from a biased point of view of the theory of localized mirror fun
ctor in Lagrangian Floer theory.\n\nLecture 3 : Fukaya category of surface
s and its HMS\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheol-Hyun Cho (Seoul National University)
DTSTART:20210105T050000Z
DTEND:20210105T060000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/10
DESCRIPTION:Title: Homological mirror symmetry via Lagrangian Floer theory IV\nby
Cheol-Hyun Cho (Seoul National University) as part of Legendrians\, Clust
er algebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Re
public of Korea.\n\nAbstract\nA version of homological mirror symmetry(HMS
) conjecture relates the Fukaya category of a symplectic manifold and matr
ix factorization category of a mirror Landau-Ginzburg model. In this intro
ductory lecture series\, we illustrate geometric ideas behind such corresp
ondences from a biased point of view of the theory of localized mirror fun
ctor in Lagrangian Floer theory.\n\nLecture 4 : Singularities and its HMS\
n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhyung Cho (Sungkyunkwan University)
DTSTART:20210105T063000Z
DTEND:20210105T073000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/11
DESCRIPTION:Title: Mutations and toric degenerations III\nby Yunhyung Cho (Sungky
unkwan University) as part of Legendrians\, Cluster algebras\, and Mirror
symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstr
act\nThe aim of this lecture is to understand a relation between the wall
crossing phenomenon of Lagrangians and the mutations in cluster theory via
toric degenerations.\n\nLecture 3: Mutations of potentials $\\newline$\n-
Mutations of Laurent polynomials\, polytopes\, and Lagrangian tori\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhyung Cho (Sungkyunkwan University)
DTSTART:20210105T073000Z
DTEND:20210105T083000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/12
DESCRIPTION:Title: Mutations and toric degenerations IV\nby Yunhyung Cho (Sungkyu
nkwan University) as part of Legendrians\, Cluster algebras\, and Mirror s
ymmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstra
ct\nThe aim of this lecture is to understand a relation between the wall c
rossing phenomenon of Lagrangians and the mutations in cluster theory via
toric degenerations.\n\nLecture 4: Examples: flag variety $\\newline$\n- T
oric degenerations of flag varieties $\\newline$\n- Cluster structures of
G/B and potential functions\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART:20210106T000000Z
DTEND:20210106T010000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/13
DESCRIPTION:Title: An introduction to cluster algebras I\nby Linhui Shen (Michiga
n State University) as part of Legendrians\, Cluster algebras\, and Mirror
symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbst
ract\nCluster algebras are commutative algebras equipped with remarkable c
ombinatorial structures. Since its inception in 2000\, the theory of clust
er algebras has found numerous exciting applications in mathematics and ph
ysics. This series of lectures aim to provide an accessible introduction t
o cluster algebras for a general mathematical audience. In particular\, we
will investigate the following topics.\n\nLecture 1: Cluster algebras of
rank 2: positive Laurent Phenomenon and greedy bases $\\newline$\nThis lec
ture will focus on cluster algebras of rank 2. Using elementary combinator
ial tools\, we will prove the positive Laurent Phenomenon and construct gr
eedy bases for cluster algebras of rank 2.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART:20210106T010000Z
DTEND:20210106T020000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/14
DESCRIPTION:Title: An introduction to cluster algebras II\nby Linhui Shen (Michig
an State University) as part of Legendrians\, Cluster algebras\, and Mirro
r symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbs
tract\nCluster algebras are commutative algebras equipped with remarkable
combinatorial structures. Since its inception in 2000\, the theory of clus
ter algebras has found numerous exciting applications in mathematics and p
hysics. This series of lectures aim to provide an accessible introduction
to cluster algebras for a general mathematical audience. In particular\, w
e will investigate the following topics.\n\nLecture 2: Cluster algebras an
d Finite type classifications$\\newline$\nWe begin with a rigorous definit
ion of cluster algebras in terms of quiver mutations. We present a classif
ication of cluster algebras of finite types by ADE quivers and explain the
ir connections to generalized associahedra.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART:20210107T000000Z
DTEND:20210107T010000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/15
DESCRIPTION:Title: An introduction to cluster algebras III\nby Linhui Shen (Michi
gan State University) as part of Legendrians\, Cluster algebras\, and Mirr
or symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAb
stract\nCluster algebras are commutative algebras equipped with remarkable
combinatorial structures. Since its inception in 2000\, the theory of clu
ster algebras has found numerous exciting applications in mathematics and
physics. This series of lectures aim to provide an accessible introduction
to cluster algebras for a general mathematical audience. In particular\,
we will investigate the following topics.\n\nLecture 3: Poisson geometry a
nd quantization$\\newline$\nCluster varieties carry intrinsic Poisson stru
ctures. We present a quantization of cluster varieties and explore their c
onnections with the theory of quantum groups.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART:20210108T000000Z
DTEND:20210108T010000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/16
DESCRIPTION:Title: An introduction to cluster algebras IV\nby Linhui Shen (Michig
an State University) as part of Legendrians\, Cluster algebras\, and Mirro
r symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbs
tract\nCluster algebras are commutative algebras equipped with remarkable
combinatorial structures. Since its inception in 2000\, the theory of clus
ter algebras has found numerous exciting applications in mathematics and p
hysics. This series of lectures aim to provide an accessible introduction
to cluster algebras for a general mathematical audience. In particular\, w
e will investigate the following topics.\n\nLecture 4: Categorification an
d Donaldson-Thomas theory$\\newline$\nEvery cluster variety can be categor
ized and gives rise to a 3d Calabi-Yau category with a generic stability c
ondition. In this lecture\, we will investigate their connections to the
motivic Donaldson-Thomas theory.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (Michigan State University)
DTSTART:20210107T010000Z
DTEND:20210107T020000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/17
DESCRIPTION:Title: Examples of cluster varieties from plabic graphs I\nby Daping
Weng (Michigan State University) as part of Legendrians\, Cluster algebras
\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of K
orea.\n\nAbstract\nCluster varieties were introduced by Fock and Goncharov
as geometric counterparts of Fomin and Zelevinsky’s cluster algebras. S
imply speaking\, cluster varieties are algebraic varieties with an atlas o
f torus charts\, whose transition maps are captured by certain combinatori
al process called cluster mutations. Many interesting geometric objects tu
rn out to be examples of cluster varieties\, and one can then use cluster
theoretical techniques to study these geometric objects. In this lecture s
eries\, we will discuss various examples of cluster varieties whose combin
atorics can be captured by plabic graphs\, including Grassmannians and dou
ble Bruhat/Bott-Samelson cells of $SL_n$. This lecture series will be comp
lementary to Linhui Shen’s lecture series on cluster theory.\n\nLecture
1: $Gr(2\,n)$ and $M(0\,n)$ $\\newline$\nWe discuss the cluster structures
on Grassmannian $Gr(2\,n)$ and on the moduli space of $n$ points in $\\ma
thbb{P}^1$. These are examples of cluster varieties of Dynkin $A_{n-3}$ mu
tation type and their combinatorics are captured by triangulations of an $
n$-gon.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (Osaka University)
DTSTART:20210107T050000Z
DTEND:20210107T060000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/18
DESCRIPTION:Title: Symplectic geometry in algebraic analysis I\nby Tatsuki Kuwaga
ki (Osaka University) as part of Legendrians\, Cluster algebras\, and Mirr
or symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAb
stract\nIn these lectures\, I will explain two ideas in algebraic analysis
: sheaf quantization and exact WKB analysis\, with emphasis on relations t
o symplectic geometry. The ideas presented in the lectures will be used in
my talk in the workshop.\n\nLecture 1: Sheaf quantization: basic ideas an
d examples\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (Osaka University)
DTSTART:20210107T060000Z
DTEND:20210107T070000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/19
DESCRIPTION:Title: Symplectic geometry in algebraic analysis II\nby Tatsuki Kuwag
aki (Osaka University) as part of Legendrians\, Cluster algebras\, and Mir
ror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nA
bstract\nIn these lectures\, I will explain two ideas in algebraic analysi
s: sheaf quantization and exact WKB analysis\, with emphasis on relations
to symplectic geometry. The ideas presented in the lectures will be used i
n my talk in the workshop.\n\nLecture 2: Sheaf quantization: continued\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (Michigan State University)
DTSTART:20210107T020000Z
DTEND:20210107T030000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/20
DESCRIPTION:Title: Examples of cluster varieties from plabic graphs II\nby Daping
Weng (Michigan State University) as part of Legendrians\, Cluster algebra
s\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of
Korea.\n\nAbstract\nCluster varieties were introduced by Fock and Goncharo
v as geometric counterparts of Fomin and Zelevinsky’s cluster algebras.
Simply speaking\, cluster varieties are algebraic varieties with an atlas
of torus charts\, whose transition maps are captured by certain combinator
ial process called cluster mutations. Many interesting geometric objects t
urn out to be examples of cluster varieties\, and one can then use cluster
theoretical techniques to study these geometric objects. In this lecture
series\, we will discuss various examples of cluster varieties whose combi
natorics can be captured by plabic graphs\, including Grassmannians and do
uble Bruhat/Bott-Samelson cells of $SL_n$. This lecture series will be com
plementary to Linhui Shen’s lecture series on cluster theory.\n\nLecture
2: plabic graphs and $Gr(k\,n)$ $\\newline$\nWe introduce plabic (planar
bicolor) graphs and use them to describe the cluster structures on Grassma
nnian $Gr(k\,n)$ and on the moduli space of $n$ points on $\\mathbb{P}^{k-
1}$.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (Michigan State University)
DTSTART:20210108T010000Z
DTEND:20210108T020000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/21
DESCRIPTION:Title: Examples of cluster varieties from plabic graphs III\nby Dapin
g Weng (Michigan State University) as part of Legendrians\, Cluster algebr
as\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of
Korea.\n\nAbstract\nCluster varieties were introduced by Fock and Gonchar
ov as geometric counterparts of Fomin and Zelevinsky’s cluster algebras.
Simply speaking\, cluster varieties are algebraic varieties with an atlas
of torus charts\, whose transition maps are captured by certain combinato
rial process called cluster mutations. Many interesting geometric objects
turn out to be examples of cluster varieties\, and one can then use cluste
r theoretical techniques to study these geometric objects. In this lecture
series\, we will discuss various examples of cluster varieties whose comb
inatorics can be captured by plabic graphs\, including Grassmannians and d
ouble Bruhat/Bott-Samelson cells of $SL_n$. This lecture series will be co
mplementary to Linhui Shen’s lecture series on cluster theory.\n\nLectur
e 3: double Bruhat cells of $SL_n$ $\\newline$\nWe introduce double Bruhat
cells of a semisimple Lie group and discuss the cluster structures on dou
ble Bruhat cells of $SL_n$ in terms of plabic graphs.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (Michigan State University)
DTSTART:20210108T020000Z
DTEND:20210108T030000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/22
DESCRIPTION:Title: Examples of cluster varieties from plabic graphs IV\nby Daping
Weng (Michigan State University) as part of Legendrians\, Cluster algebra
s\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of
Korea.\n\nAbstract\nCluster varieties were introduced by Fock and Goncharo
v as geometric counterparts of Fomin and Zelevinsky’s cluster algebras.
Simply speaking\, cluster varieties are algebraic varieties with an atlas
of torus charts\, whose transition maps are captured by certain combinator
ial process called cluster mutations. Many interesting geometric objects t
urn out to be examples of cluster varieties\, and one can then use cluster
theoretical techniques to study these geometric objects. In this lecture
series\, we will discuss various examples of cluster varieties whose combi
natorics can be captured by plabic graphs\, including Grassmannians and do
uble Bruhat/Bott-Samelson cells of $SL_n$. This lecture series will be com
plementary to Linhui Shen’s lecture series on cluster theory.\n\nLecture
4: double Bott-Samelson cells of $SL_n$ and positive braid closures $\\ne
wline$\nWe introduce double Bott-Samelson cells of $SL_n$ as a generalizat
ion of double Bruhat cells. We will describe their cluster structures and
the connection to positive braid closures.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (Osaka University)
DTSTART:20210108T050000Z
DTEND:20210108T060000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/23
DESCRIPTION:Title: Symplectic geometry in algebraic analysis III\nby Tatsuki Kuwa
gaki (Osaka University) as part of Legendrians\, Cluster algebras\, and Mi
rror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\n
Abstract\nIn these lectures\, I will explain two ideas in algebraic analys
is: sheaf quantization and exact WKB analysis\, with emphasis on relations
to symplectic geometry. The ideas presented in the lectures will be used
in my talk in the workshop.\n\nLecture 3: Exact WKB analysis: basics\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (Osaka University)
DTSTART:20210108T060000Z
DTEND:20210108T070000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/24
DESCRIPTION:Title: Symplectic geometry in algebraic analysis IV\nby Tatsuki Kuwag
aki (Osaka University) as part of Legendrians\, Cluster algebras\, and Mir
ror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nA
bstract\nIn these lectures\, I will explain two ideas in algebraic analysi
s: sheaf quantization and exact WKB analysis\, with emphasis on relations
to symplectic geometry. The ideas presented in the lectures will be used i
n my talk in the workshop.\n\nLecture 4: Exact WKB analysis: cluster algeb
ra and local systems\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lenhard L. Ng (Duke University)
DTSTART:20210111T010000Z
DTEND:20210111T015000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/25
DESCRIPTION:Title: Infinitely many fillings through augmentations\nby Lenhard L.
Ng (Duke University) as part of Legendrians\, Cluster algebras\, and Mirro
r symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbs
tract\nIn 2020\, a few groups of people proved that certain Legendrian lin
ks in R^3 have infinitely many exact Lagrangian fillings that are distinct
under Hamiltonian isotopy. These groups (Casals-Gao\, Gao-Shen-Wang\, Cas
als-Zaslow) used a variety of approaches involving microlocal sheaf theory
and cluster structures. I'll describe a different\, Floer-theoretic appro
ach to the same sort of result\, using integer-valued augmentations of Leg
endrian contact homology\, and I'll discuss some examples that are amenabl
e to the Floerapproach but not (yet?) the other approaches. This is joint
work with Roger Casals.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Casals (University of California\, Davis)
DTSTART:20210111T000000Z
DTEND:20210111T005000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/26
DESCRIPTION:Title: Legendrian knots and their Lagrangian fillings: A conspectus on re
cent developments\nby Roger Casals (University of California\, Davis)
as part of Legendrians\, Cluster algebras\, and Mirror symmetry\n\nLecture
held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nIn this talk I
will survey some of the recent developments in the study of Lagrangian fi
llings of Legendrian knots. First\, I will introduce and motivate the lead
ing questions. Then\, we will discuss the current methods and techniques a
vailable to tackle them. Finally\, I will suggest some open problems that
now seem at reach\, along with some strategies to approach them.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Honghao Gao (Michigan State University)
DTSTART:20210111T020000Z
DTEND:20210111T025000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/27
DESCRIPTION:Title: Infinitely many fillings through sheaves\nby Honghao Gao (Mich
igan State University) as part of Legendrians\, Cluster algebras\, and Mir
ror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nA
bstract\nThis talk will complement other talks in the day and present conc
rete examples. Specifically\, I will construct infinitely many Lagrangian
fillings for the Legendrian torus link (3\,6)\, and explain how to disting
uish them using sheaves and cluster algebras. Time permitting\, I will dis
cuss other torus links (joint work with R. Casals) and positive braid link
s (joint work with L. Shen and D. Weng).\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byung Hee An (Kyungpook National University)
DTSTART:20210112T000000Z
DTEND:20210112T005000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/28
DESCRIPTION:Title: Lagrangian fillings of Legendrian links of finite type\nby Byu
ng Hee An (Kyungpook National University) as part of Legendrians\, Cluster
algebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Repu
blic of Korea.\n\nAbstract\nIn this talk\, we will focus on Legendrian lin
ks admitting cluster structures of finite type (via N-graph ways) and prov
e that those Legendrian links of type ADE have embedded exact Lagrangian f
illings as many as the number of seeds in their cluster structures. $\\new
line$\nFurthermore\, we will describe the cluster structures of BCFG-type
among Lagrangian fillings of ADE-type Legendrian links\, which have certai
n partial symmetries. $\\newline$\nThis is joint work with Youngjin Bae (I
ncheon National University) and Eunjeong Lee (IBS-CGP).\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART:20210112T010000Z
DTEND:20210112T015000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/29
DESCRIPTION:Title: Quantum geometry of moduli spaces of local systems\nby Linhui
Shen (Michigan State University) as part of Legendrians\, Cluster algebras
\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of K
orea.\n\nAbstract\nLet $G$ be a split semi-simple algebraic group over $\\
mathbb{Q}$. We introduce a natural cluster structure on moduli spaces of $
G$-local systems over surfaces with marked points. As a consequence\, the
moduli spaces of $G$-local systems admit natural Poisson structures\, and
can be further quantized. We will study the principal series representatio
ns of such quantum spaces. It will recover many classical topics\, such as
the $q$-deformed Toda systems\, quantum groups\, and the modular functor
conjecture for such representations. This talk will mainly be based on joi
nt work with A.B. Goncharov.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (Michigan State University)
DTSTART:20210112T020000Z
DTEND:20210112T025000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/30
DESCRIPTION:Title: Symplectic Structure on Augmentation Varieties\nby Daping Weng
(Michigan State University) as part of Legendrians\, Cluster algebras\, a
nd Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea
.\n\nAbstract\nIn a recent joint project with H. Gao and L. Shen\, we intr
oduce a cluster K2 structure on the augmentation variety of the Chekanov-E
liashberg dga for the rainbow closure of any positive braid with marked po
int decorations. This cluster K2 structure defines a holomorphic presymple
ctic structure on the complex augmentation variety. Using a result of Gonc
harov and Kenyon on surface bipartite graphs\, we prove that this holomorp
hic presymplectic structure becomes symplectic after we reduce the number
of marked points to a single marked per link component.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Lam (University of Michigan)
DTSTART:20210113T000000Z
DTEND:20210113T005000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/31
DESCRIPTION:Title: Positroid varieties and $q\,t$ -Catalan numbers\nby Thomas La
m (University of Michigan) as part of Legendrians\, Cluster algebras\, and
Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\
n\nAbstract\nPositroid varieties are subvarieties of the Grassmannian defi
ned as intersections of rotations of Schubert varieties in my work with Kn
utson and Speyer. They also appear in the work of Shende-Treumann-Williams
-Zaslow as moduli spaces of constructible sheaves with microsupport in a L
egendrian link. $\\newline$\nWe show that the "top open positroid variety"
has mixed Hodge polynomial given by the $q\,t$-rational Catalan numbers
(up to a simple factor). The $q\,t$-rational Catalan numbers satisfy remar
kable symmetry and unimodality properties\, and we show that these follow
from the curious Lefschetz phenomenon for cluster varieties. The cohomolog
ies of open positroid varieties are shown to be related to Khovanov-Rosanz
ky knot homology.$\\newline$\nThis talk is based on joint work with Pavel
Galashin.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naoki Fujita (The University of Tokyo)
DTSTART:20210113T010000Z
DTEND:20210113T015000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/32
DESCRIPTION:Title: Newton-Okounkov bodies arising from cluster structures and mutatio
ns on polytopes\nby Naoki Fujita (The University of Tokyo) as part of
Legendrians\, Cluster algebras\, and Mirror symmetry\n\nLecture held in PO
STECH\, Pohang\, Republic of Korea.\n\nAbstract\nA toric degeneration is a
flat degeneration from a projective variety to a toric variety\, which ca
n be used to apply the theory of toric varieties to other projective varie
ties. In this talk\, we discuss relations among the following three constr
uctions of toric degenerations: representation theory\, Newton-Okounkov bo
dies\, and cluster algebras. More precisely\, we construct Newton-Okounkov
bodies using cluster structures\, and realize representation-theoretic an
d cluster-theoretic toric degenerations using this framework. We also disc
uss its relation with combinatorial mutations which was introduced in the
context of mirror symmetry for Fano varieties. More precisely\, we relate
Newton-Okounkov bodies of flag varieties arising from cluster structures b
y combinatorial mutations. This talk is based on joint works with Hironori
Oya and Akihiro Higashitani.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyun Kyu Kim (Ewha Womans University)
DTSTART:20210113T020000Z
DTEND:20210113T025000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/33
DESCRIPTION:Title: $SL_3$-laminations as bases for $PGL_3$ cluster varieties for surf
aces\nby Hyun Kyu Kim (Ewha Womans University) as part of Legendrians\
, Cluster algebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Poha
ng\, Republic of Korea.\n\nAbstract\nI will recall Fock-Goncharov's dualit
y conjecture for cluster $A$- and $X$-varieties\, and Fock-Goncharov's sol
ution for the case of certain enhanced moduli spaces of $G$-local systems
on a punctured surface when $G$ is $SL_2$ and $PGL_2$. Then I will explain
how Kuperberg's web can be used to extend this result to the case when $G
$ is $SL_3$ and $PGL_3$.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Gammage (Harvard)
DTSTART:20210114T000000Z
DTEND:20210114T005000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/34
DESCRIPTION:Title: Mirror symmetry through perverse schobers\nby Benjamin Gammage
(Harvard) as part of Legendrians\, Cluster algebras\, and Mirror symmetry
\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nWe
explain how the language of perverse schobers gives a natural tool for des
cribing a generalization of the Seidel-Sheridan strategy for computing Fuk
aya categories to the non-Lefschetz situation. We apply this technique to
calculate the Fukaya category of the Milnor fiber of a Berglund-Hübsch si
ngularity\, building on some earlier computations of David Nadler. This ca
lculation proves a conjecture of Lekili-Ueda.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yat-Hin Suen (IBS-CGP)
DTSTART:20210114T010000Z
DTEND:20210114T015000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/35
DESCRIPTION:Title: Tropical Lagrangian multi-sections and smoothing of locally free s
heaves on log Calabi-Yau surfaces\nby Yat-Hin Suen (IBS-CGP) as part o
f Legendrians\, Cluster algebras\, and Mirror symmetry\n\nLecture held in
POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nHomological mirror symm
etry suggests that Lagrangian multi-sections over an integral affine manif
old with singularities $B$ should mirror to holomorphic vector bundles. In
this talk\, I will introduce the tropical version of Lagrangian multi-sec
tions\, called tropical Lagrangian multi-sections. I will mainly focus on
dimension 2. To certain tropical Lagrangian multi-sections over $B$\, I w
ill construct a locally free sheaf $E_0$ on the log Calabi-Yau surface $X_
0(B)$ associated to $B$ and study the smoothability of the pair $(X_0(B)\,
E_0)$. This is a joint work with Kwokwai Chan and Ziming Ma.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sangwook Lee (Soongsil University)
DTSTART:20210114T020000Z
DTEND:20210114T025000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/36
DESCRIPTION:Title: Orbifold Jacobian algebras and generalized Kodaira-Spencer maps\nby Sangwook Lee (Soongsil University) as part of Legendrians\, Cluster
algebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Repub
lic of Korea.\n\nAbstract\nGiven an algebraic function\, its Jacobian alge
bra encodes the information of the singularity. There is also a notion of
orbifold Jacobian algebras for functions which admit finite (abelian) grou
p actions. We give a construction of an orbifold Jacobian algebra as Floer
cohomology of a Lagrangian submanifold which represents homological mirro
r functor. We also discuss generalized Kodaira-Spencer maps whose image is
not necessarily an ordinary Jacobian algebra. This talk is based on the j
oint work with C.-H. Cho.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (Osaka University)
DTSTART:20210115T000000Z
DTEND:20210115T005000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/37
DESCRIPTION:Title: Cluster coordinates from sheaf quantization of spectral curve\
nby Tatsuki Kuwagaki (Osaka University) as part of Legendrians\, Cluster a
lgebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republ
ic of Korea.\n\nAbstract\nA sheaf quantization is a sheaf associated to a
Lagrangian brane. In this talk\, I will explain my construction of sheaf q
uantization of the spectral curves of Schrodinger equations\, which is a p
art of conjectural $\\hbar$-Riemann—Hilbert correspondence. The construc
tion is based on exact WKB analysis. I will also explain an application to
cluster theory. Iwaki—Nakanishi have found cluster variables in exact W
KB analysis. The construction of sheaf quantization gives a geometric expl
anation of Iwaki—Nakanishi’s cluster variables and their variants. A p
art of this talk is based on my joint work in progress with T. Ishibashi.\
n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Zaslow (Northwestern University)
DTSTART:20210115T010000Z
DTEND:20210115T015000Z
DTSTAMP:20260404T131158Z
UID:LCM2021/38
DESCRIPTION:Title: Dimers and Mirror Moduli\nby Eric Zaslow (Northwestern Univers
ity) as part of Legendrians\, Cluster algebras\, and Mirror symmetry\n\nLe
cture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nI will tr
y to describe a counting problem that arises from considering mirror appro
aches to dimer integrable systems. Some of this talk is based on joint wor
k with David Treumann and Harold Williams\, and some is an ongoing project
with Helge Ruddatand others.\n
LOCATION:https://stable.researchseminars.org/talk/LCM2021/38/
END:VEVENT
END:VCALENDAR