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BEGIN:VEVENT
SUMMARY:Honghao Gao (Michigan State University)
DTSTART:20210104T000000Z
DTEND:20210104T010000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/1
DESCRIPTION:Title:
Sheaves in contact topology I\nby Honghao Gao (Michigan State Universi
ty) as part of Legendrians\, Cluster algebras\, and Mirror symmetry\n\nLec
ture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nMicrolocal
sheaf theory was introduced by Kashiwara-Schapira around 80s. With the no
tion of micro-support\, one can use sheaves on smooth manifolds to access
the geometry of their cotangent bundles. In recent years\, microlocal shea
f theory entered contact and symplectic topology\, and has been used to so
lve open problems. In this lecture series\, we will introduce microlocal s
heaf theory in the context of low-dimensional contact topology\, and suppl
y the audience with background for its applications such as producing non-
classical invariants for Legendrian knots and distinguishing exact Lagrang
ian fillings.\n\nLecture 1: Legendrian knots and sheaves $\\newline$\nBasi
cs of Legendrain knots\, sheaves and microsupport\, local conditions at ar
cs\, cusps\, crossings.\n
LOCATION:https://researchseminars.org/talk/LCM2021/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Honghao Gao (Michigan State University)
DTSTART:20210104T010000Z
DTEND:20210104T020000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/2
DESCRIPTION:Title:
Sheaves in contact topology II\nby Honghao Gao (Michigan State Univers
ity) as part of Legendrians\, Cluster algebras\, and Mirror symmetry\n\nLe
cture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nMicroloca
l sheaf theory was introduced by Kashiwara-Schapira around 80s. With the n
otion of micro-support\, one can use sheaves on smooth manifolds to access
the geometry of their cotangent bundles. In recent years\, microlocal she
af theory entered contact and symplectic topology\, and has been used to s
olve open problems. In this lecture series\, we will introduce microlocal
sheaf theory in the context of low-dimensional contact topology\, and supp
ly the audience with background for its applications such as producing non
-classical invariants for Legendrian knots and distinguishing exact Lagran
gian fillings.\n\nLecture 2: invariance $\\newline$\nCategory of sheaves\,
non-classical invariants for Legendrian submanifolds (theorem by Guillerm
ou-Kashiwara-Schapira)\, combinatorial verification under Reidemeister mov
es.\n
LOCATION:https://researchseminars.org/talk/LCM2021/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheol-Hyun Cho (Seoul National University)
DTSTART:20210104T040000Z
DTEND:20210104T050000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/3
DESCRIPTION:Title:
Homological mirror symmetry via Lagrangian Floer theory I\nby Cheol-Hy
un Cho (Seoul National University) as part of Legendrians\, Cluster algebr
as\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of
Korea.\n\nAbstract\nA version of homological mirror symmetry(HMS) conject
ure relates the Fukaya category of a symplectic manifold and matrix factor
ization category of a mirror Landau-Ginzburg model. In this introductory l
ecture series\, we illustrate geometric ideas behind such correspondences
from a biased point of view of the theory of localized mirror functor in L
agrangian Floer theory.\n\nLecture 1 : A-infinity category\, HMS and local
ized mirror functor\n
LOCATION:https://researchseminars.org/talk/LCM2021/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheol-Hyun Cho (Seoul National University)
DTSTART:20210104T050000Z
DTEND:20210104T060000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/4
DESCRIPTION:Title:
Homological mirror symmetry via Lagrangian Floer theory II\nby Cheol-H
yun Cho (Seoul National University) as part of Legendrians\, Cluster algeb
ras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic o
f Korea.\n\nAbstract\nA version of homological mirror symmetry(HMS) conjec
ture relates the Fukaya category of a symplectic manifold and matrix facto
rization category of a mirror Landau-Ginzburg model. In this introductory
lecture series\, we illustrate geometric ideas behind such correspondences
from a biased point of view of the theory of localized mirror functor in
Lagrangian Floer theory.\n\nLecture 2 : Monotone Floer theory and its HMS\
n
LOCATION:https://researchseminars.org/talk/LCM2021/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhyung Cho (Sungkyunkwan University)
DTSTART:20210104T063000Z
DTEND:20210104T073000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/5
DESCRIPTION:Title:
Mutations and toric degenerations I\nby Yunhyung Cho (Sungkyunkwan Uni
versity) as part of Legendrians\, Cluster algebras\, and Mirror symmetry\n
\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nThe a
im of this lecture is to understand a relation between the wall crossing p
henomenon of Lagrangians and the mutations in cluster theory via toric deg
enerations.\n\nLecture 1: Fano toric varieties and potentials $\\newline$\
n- A brief introduction to toric varieties $\\newline$\n- Potential functi
ons of smooth Fano toric varieties\n
LOCATION:https://researchseminars.org/talk/LCM2021/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhyung Cho (Sungkyunkwan University)
DTSTART:20210104T073000Z
DTEND:20210104T083000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/6
DESCRIPTION:Title:
Mutations and toric degenerations II\nby Yunhyung Cho (Sungkyunkwan Un
iversity) as part of Legendrians\, Cluster algebras\, and Mirror symmetry\
n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\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 de
generations.\n\nLecture 2: Toric degenerations\, examples and construction
$\\newline$\n- Toric degenerations\; definitions and examples $\\newline$
\n- Construction of toric degenerations $\\newline$\n- Potential functions
via toric degenerations $\\newline$\n
LOCATION:https://researchseminars.org/talk/LCM2021/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Honghao Gao (Michigan State University)
DTSTART:20210105T000000Z
DTEND:20210105T010000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/7
DESCRIPTION:Title:
Sheaves in contact topology III\nby Honghao Gao (Michigan State Univer
sity) as part of Legendrians\, Cluster algebras\, and Mirror symmetry\n\nL
ecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nMicroloc
al sheaf theory was introduced by Kashiwara-Schapira around 80s. With the
notion of micro-support\, one can use sheaves on smooth manifolds to acces
s the geometry of their cotangent bundles. In recent years\, microlocal sh
eaf theory entered contact and symplectic topology\, and has been used to
solve open problems. In this lecture series\, we will introduce microlocal
sheaf theory in the context of low-dimensional contact topology\, and sup
ply the audience with background for its applications such as producing no
n-classical invariants for Legendrian knots and distinguishing exact Lagra
ngian fillings.\n\nLecture 3: moduli space of sheaves $\\newline$\nmoduli
space of sheaves for elementary tangles\, microlocal rank 1 sheaves\, posi
tive braid Legendrian knots\, flags and Bott-Samelson cells.\n
LOCATION:https://researchseminars.org/talk/LCM2021/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Honghao Gao (Michigan State University)
DTSTART:20210105T010000Z
DTEND:20210105T020000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/8
DESCRIPTION:Title:
Sheaves in contact topology IV\nby Honghao Gao (Michigan State Univers
ity) as part of Legendrians\, Cluster algebras\, and Mirror symmetry\n\nLe
cture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nMicroloca
l sheaf theory was introduced by Kashiwara-Schapira around 80s. With the n
otion of micro-support\, one can use sheaves on smooth manifolds to access
the geometry of their cotangent bundles. In recent years\, microlocal she
af theory entered contact and symplectic topology\, and has been used to s
olve open problems. In this lecture series\, we will introduce microlocal
sheaf theory in the context of low-dimensional contact topology\, and supp
ly the audience with background for its applications such as producing non
-classical invariants for Legendrian knots and distinguishing exact Lagran
gian fillings.\n\nLecture 4: Lagrangian fillings $\\newline$\nSingularitie
s of Legendrian fronts\, exact Lagrangian fillings and Legendrian weaves\,
sheaf quantization of Lagrangian fillings.\n
LOCATION:https://researchseminars.org/talk/LCM2021/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheol-Hyun Cho (Seoul National University)
DTSTART:20210105T040000Z
DTEND:20210105T050000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/9
DESCRIPTION:Title:
Homological mirror symmetry via Lagrangian Floer theory III\nby Cheol-
Hyun Cho (Seoul National University) as part of Legendrians\, Cluster alge
bras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic
of Korea.\n\nAbstract\nA version of homological mirror symmetry(HMS) conje
cture relates the Fukaya category of a symplectic manifold and matrix fact
orization category of a mirror Landau-Ginzburg model. In this introductory
lecture series\, we illustrate geometric ideas behind such correspondence
s from a biased point of view of the theory of localized mirror functor in
Lagrangian Floer theory.\n\nLecture 3 : Fukaya category of surfaces and i
ts HMS\n
LOCATION:https://researchseminars.org/talk/LCM2021/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheol-Hyun Cho (Seoul National University)
DTSTART:20210105T050000Z
DTEND:20210105T060000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/10
DESCRIPTION:Title: Homological mirror symmetry via Lagrangian Floer theory IV\nby Cheol-
Hyun Cho (Seoul National University) as part of Legendrians\, Cluster alge
bras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic
of Korea.\n\nAbstract\nA version of homological mirror symmetry(HMS) conje
cture relates the Fukaya category of a symplectic manifold and matrix fact
orization category of a mirror Landau-Ginzburg model. In this introductory
lecture series\, we illustrate geometric ideas behind such correspondence
s from a biased point of view of the theory of localized mirror functor in
Lagrangian Floer theory.\n\nLecture 4 : Singularities and its HMS\n
LOCATION:https://researchseminars.org/talk/LCM2021/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhyung Cho (Sungkyunkwan University)
DTSTART:20210105T063000Z
DTEND:20210105T073000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/11
DESCRIPTION:Title: Mutations and toric degenerations III\nby Yunhyung Cho (Sungkyunkwan
University) as part of Legendrians\, Cluster algebras\, and Mirror symmetr
y\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nTh
e aim of this lecture is to understand a relation between the wall crossin
g phenomenon of Lagrangians and the mutations in cluster theory via toric
degenerations.\n\nLecture 3: Mutations of potentials $\\newline$\n- Mutati
ons of Laurent polynomials\, polytopes\, and Lagrangian tori\n
LOCATION:https://researchseminars.org/talk/LCM2021/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhyung Cho (Sungkyunkwan University)
DTSTART:20210105T073000Z
DTEND:20210105T083000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/12
DESCRIPTION:Title: Mutations and toric degenerations IV\nby Yunhyung Cho (Sungkyunkwan U
niversity) as part of Legendrians\, Cluster algebras\, and Mirror symmetry
\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\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 d
egenerations.\n\nLecture 4: Examples: flag variety $\\newline$\n- Toric de
generations of flag varieties $\\newline$\n- Cluster structures of G/B and
potential functions\n
LOCATION:https://researchseminars.org/talk/LCM2021/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART:20210106T000000Z
DTEND:20210106T010000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/13
DESCRIPTION:Title: An introduction to cluster algebras I\nby Linhui Shen (Michigan State
University) as part of Legendrians\, Cluster algebras\, and Mirror symmet
ry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nC
luster algebras are commutative algebras equipped with remarkable combinat
orial structures. Since its inception in 2000\, the theory of cluster alge
bras has found numerous exciting applications in mathematics and physics.
This series of lectures aim to provide an accessible introduction to clust
er algebras for a general mathematical audience. In particular\, we will i
nvestigate the following topics.\n\nLecture 1: Cluster algebras of rank 2:
positive Laurent Phenomenon and greedy bases $\\newline$\nThis lecture wi
ll focus on cluster algebras of rank 2. Using elementary combinatorial too
ls\, we will prove the positive Laurent Phenomenon and construct greedy ba
ses for cluster algebras of rank 2.\n
LOCATION:https://researchseminars.org/talk/LCM2021/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART:20210106T010000Z
DTEND:20210106T020000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/14
DESCRIPTION:Title: An introduction to cluster algebras II\nby Linhui Shen (Michigan Stat
e University) as part of Legendrians\, Cluster algebras\, and Mirror symme
try\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\n
Cluster algebras are commutative algebras equipped with remarkable combina
torial structures. Since its inception in 2000\, the theory of cluster alg
ebras has found numerous exciting applications in mathematics and physics.
This series of lectures aim to provide an accessible introduction to clus
ter algebras for a general mathematical audience. In particular\, we will
investigate the following topics.\n\nLecture 2: Cluster algebras and Finit
e type classifications$\\newline$\nWe begin with a rigorous definition of
cluster algebras in terms of quiver mutations. We present a classification
of cluster algebras of finite types by ADE quivers and explain their conn
ections to generalized associahedra.\n
LOCATION:https://researchseminars.org/talk/LCM2021/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART:20210107T000000Z
DTEND:20210107T010000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/15
DESCRIPTION:Title: An introduction to cluster algebras III\nby Linhui Shen (Michigan Sta
te University) as part of Legendrians\, Cluster algebras\, and Mirror symm
etry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\
nCluster algebras are commutative algebras equipped with remarkable combin
atorial structures. Since its inception in 2000\, the theory of cluster al
gebras has found numerous exciting applications in mathematics and physics
. This series of lectures aim to provide an accessible introduction to clu
ster algebras for a general mathematical audience. In particular\, we will
investigate the following topics.\n\nLecture 3: Poisson geometry and quan
tization$\\newline$\nCluster varieties carry intrinsic Poisson structures.
We present a quantization of cluster varieties and explore their connecti
ons with the theory of quantum groups.\n
LOCATION:https://researchseminars.org/talk/LCM2021/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART:20210108T000000Z
DTEND:20210108T010000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/16
DESCRIPTION:Title: An introduction to cluster algebras IV\nby Linhui Shen (Michigan Stat
e University) as part of Legendrians\, Cluster algebras\, and Mirror symme
try\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\n
Cluster algebras are commutative algebras equipped with remarkable combina
torial structures. Since its inception in 2000\, the theory of cluster alg
ebras has found numerous exciting applications in mathematics and physics.
This series of lectures aim to provide an accessible introduction to clus
ter algebras for a general mathematical audience. In particular\, we will
investigate the following topics.\n\nLecture 4: Categorification and Donal
dson-Thomas theory$\\newline$\nEvery cluster variety can be categorized an
d gives rise to a 3d Calabi-Yau category with a generic stability conditio
n. In this lecture\, we will investigate their connections to the motivic
Donaldson-Thomas theory.\n
LOCATION:https://researchseminars.org/talk/LCM2021/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (Michigan State University)
DTSTART:20210107T010000Z
DTEND:20210107T020000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/17
DESCRIPTION:Title: Examples of cluster varieties from plabic graphs I\nby Daping Weng (M
ichigan State University) as part of Legendrians\, Cluster algebras\, and
Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n
\nAbstract\nCluster varieties were introduced by Fock and Goncharov as geo
metric counterparts of Fomin and Zelevinsky’s cluster algebras. Simply s
peaking\, cluster varieties are algebraic varieties with an atlas of torus
charts\, whose transition maps are captured by certain combinatorial proc
ess called cluster mutations. Many interesting geometric objects turn out
to be examples of cluster varieties\, and one can then use cluster theoret
ical techniques to study these geometric objects. In this lecture series\,
we will discuss various examples of cluster varieties whose combinatorics
can be captured by plabic graphs\, including Grassmannians and double Bru
hat/Bott-Samelson cells of $SL_n$. This lecture series will be complementa
ry 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 Gra
ssmannian $Gr(2\,n)$ and on the moduli space of $n$ points in $\\mathbb{P}
^1$. These are examples of cluster varieties of Dynkin $A_{n-3}$ mutation
type and their combinatorics are captured by triangulations of an $n$-gon.
\n
LOCATION:https://researchseminars.org/talk/LCM2021/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (Osaka University)
DTSTART:20210107T050000Z
DTEND:20210107T060000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/18
DESCRIPTION:Title: Symplectic geometry in algebraic analysis I\nby Tatsuki Kuwagaki (Osa
ka University) as part of Legendrians\, Cluster algebras\, and Mirror symm
etry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\
nIn these lectures\, I will explain two ideas in algebraic analysis: sheaf
quantization and exact WKB analysis\, with emphasis on relations to sympl
ectic geometry. The ideas presented in the lectures will be used in my tal
k in the workshop.\n\nLecture 1: Sheaf quantization: basic ideas and examp
les\n
LOCATION:https://researchseminars.org/talk/LCM2021/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (Osaka University)
DTSTART:20210107T060000Z
DTEND:20210107T070000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/19
DESCRIPTION:Title: Symplectic geometry in algebraic analysis II\nby Tatsuki Kuwagaki (Os
aka University) as part of Legendrians\, Cluster algebras\, and Mirror sym
metry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract
\nIn these lectures\, I will explain two ideas in algebraic analysis: shea
f quantization and exact WKB analysis\, with emphasis on relations to symp
lectic geometry. The ideas presented in the lectures will be used in my ta
lk in the workshop.\n\nLecture 2: Sheaf quantization: continued\n
LOCATION:https://researchseminars.org/talk/LCM2021/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (Michigan State University)
DTSTART:20210107T020000Z
DTEND:20210107T030000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/20
DESCRIPTION:Title: Examples of cluster varieties from plabic graphs II\nby Daping Weng (
Michigan State University) as part of Legendrians\, Cluster algebras\, and
Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\
n\nAbstract\nCluster varieties were introduced by Fock and Goncharov as ge
ometric counterparts of Fomin and Zelevinsky’s cluster algebras. Simply
speaking\, cluster varieties are algebraic varieties with an atlas of toru
s charts\, whose transition maps are captured by certain combinatorial pro
cess called cluster mutations. Many interesting geometric objects turn out
to be examples of cluster varieties\, and one can then use cluster theore
tical techniques to study these geometric objects. In this lecture series\
, we will discuss various examples of cluster varieties whose combinatoric
s can be captured by plabic graphs\, including Grassmannians and double Br
uhat/Bott-Samelson cells of $SL_n$. This lecture series will be complement
ary to Linhui Shen’s lecture series on cluster theory.\n\nLecture 2: pla
bic graphs and $Gr(k\,n)$ $\\newline$\nWe introduce plabic (planar bicolor
) graphs and use them to describe the cluster structures on Grassmannian $
Gr(k\,n)$ and on the moduli space of $n$ points on $\\mathbb{P}^{k-1}$.\n
LOCATION:https://researchseminars.org/talk/LCM2021/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (Michigan State University)
DTSTART:20210108T010000Z
DTEND:20210108T020000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/21
DESCRIPTION:Title: Examples of cluster varieties from plabic graphs III\nby Daping Weng
(Michigan State University) as part of Legendrians\, Cluster algebras\, an
d Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.
\n\nAbstract\nCluster varieties were introduced by Fock and Goncharov as g
eometric counterparts of Fomin and Zelevinsky’s cluster algebras. Simply
speaking\, cluster varieties are algebraic varieties with an atlas of tor
us charts\, whose transition maps are captured by certain combinatorial pr
ocess called cluster mutations. Many interesting geometric objects turn ou
t to be examples of cluster varieties\, and one can then use cluster theor
etical techniques to study these geometric objects. In this lecture series
\, we will discuss various examples of cluster varieties whose combinatori
cs can be captured by plabic graphs\, including Grassmannians and double B
ruhat/Bott-Samelson cells of $SL_n$. This lecture series will be complemen
tary to Linhui Shen’s lecture series on cluster theory.\n\nLecture 3: do
uble Bruhat cells of $SL_n$ $\\newline$\nWe introduce double Bruhat cells
of a semisimple Lie group and discuss the cluster structures on double Bru
hat cells of $SL_n$ in terms of plabic graphs.\n
LOCATION:https://researchseminars.org/talk/LCM2021/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (Michigan State University)
DTSTART:20210108T020000Z
DTEND:20210108T030000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/22
DESCRIPTION:Title: Examples of cluster varieties from plabic graphs IV\nby Daping Weng (
Michigan State University) as part of Legendrians\, Cluster algebras\, and
Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\
n\nAbstract\nCluster varieties were introduced by Fock and Goncharov as ge
ometric counterparts of Fomin and Zelevinsky’s cluster algebras. Simply
speaking\, cluster varieties are algebraic varieties with an atlas of toru
s charts\, whose transition maps are captured by certain combinatorial pro
cess called cluster mutations. Many interesting geometric objects turn out
to be examples of cluster varieties\, and one can then use cluster theore
tical techniques to study these geometric objects. In this lecture series\
, we will discuss various examples of cluster varieties whose combinatoric
s can be captured by plabic graphs\, including Grassmannians and double Br
uhat/Bott-Samelson cells of $SL_n$. This lecture series will be complement
ary to Linhui Shen’s lecture series on cluster theory.\n\nLecture 4: dou
ble Bott-Samelson cells of $SL_n$ and positive braid closures $\\newline$\
nWe introduce double Bott-Samelson cells of $SL_n$ as a generalization of
double Bruhat cells. We will describe their cluster structures and the con
nection to positive braid closures.\n
LOCATION:https://researchseminars.org/talk/LCM2021/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (Osaka University)
DTSTART:20210108T050000Z
DTEND:20210108T060000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/23
DESCRIPTION:Title: Symplectic geometry in algebraic analysis III\nby Tatsuki Kuwagaki (O
saka University) as part of Legendrians\, Cluster algebras\, and Mirror sy
mmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstrac
t\nIn these lectures\, I will explain two ideas in algebraic analysis: she
af quantization and exact WKB analysis\, with emphasis on relations to sym
plectic geometry. The ideas presented in the lectures will be used in my t
alk in the workshop.\n\nLecture 3: Exact WKB analysis: basics\n
LOCATION:https://researchseminars.org/talk/LCM2021/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (Osaka University)
DTSTART:20210108T060000Z
DTEND:20210108T070000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/24
DESCRIPTION:Title: Symplectic geometry in algebraic analysis IV\nby Tatsuki Kuwagaki (Os
aka University) as part of Legendrians\, Cluster algebras\, and Mirror sym
metry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract
\nIn these lectures\, I will explain two ideas in algebraic analysis: shea
f quantization and exact WKB analysis\, with emphasis on relations to symp
lectic geometry. The ideas presented in the lectures will be used in my ta
lk in the workshop.\n\nLecture 4: Exact WKB analysis: cluster algebra and
local systems\n
LOCATION:https://researchseminars.org/talk/LCM2021/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lenhard L. Ng (Duke University)
DTSTART:20210111T010000Z
DTEND:20210111T015000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/25
DESCRIPTION:Title: Infinitely many fillings through augmentations\nby Lenhard L. Ng (Duk
e University) as part of Legendrians\, Cluster algebras\, and Mirror symme
try\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\n
In 2020\, a few groups of people proved that certain Legendrian links in R
^3 have infinitely many exact Lagrangian fillings that are distinct under
Hamiltonian isotopy. These groups (Casals-Gao\, Gao-Shen-Wang\, Casals-Zas
low) used a variety of approaches involving microlocal sheaf theory and cl
uster structures. I'll describe a different\, Floer-theoretic approach to
the same sort of result\, using integer-valued augmentations of Legendrian
contact homology\, and I'll discuss some examples that are amenable to th
e Floerapproach but not (yet?) the other approaches. This is joint work wi
th Roger Casals.\n
LOCATION:https://researchseminars.org/talk/LCM2021/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Casals (University of California\, Davis)
DTSTART:20210111T000000Z
DTEND:20210111T005000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/26
DESCRIPTION:Title: Legendrian knots and their Lagrangian fillings: A conspectus on recent de
velopments\nby Roger Casals (University of California\, Davis) as part
of Legendrians\, Cluster algebras\, and Mirror symmetry\n\nLecture held i
n POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nIn this talk I will s
urvey some of the recent developments in the study of Lagrangian fillings
of Legendrian knots. First\, I will introduce and motivate the leading que
stions. Then\, we will discuss the current methods and techniques availabl
e to tackle them. Finally\, I will suggest some open problems that now see
m at reach\, along with some strategies to approach them.\n
LOCATION:https://researchseminars.org/talk/LCM2021/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Honghao Gao (Michigan State University)
DTSTART:20210111T020000Z
DTEND:20210111T025000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/27
DESCRIPTION:Title: Infinitely many fillings through sheaves\nby Honghao Gao (Michigan St
ate University) as part of Legendrians\, Cluster algebras\, and Mirror sym
metry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract
\nThis talk will complement other talks in the day and present concrete ex
amples. Specifically\, I will construct infinitely many Lagrangian filling
s for the Legendrian torus link (3\,6)\, and explain how to distinguish th
em using sheaves and cluster algebras. Time permitting\, I will discuss ot
her torus links (joint work with R. Casals) and positive braid links (join
t work with L. Shen and D. Weng).\n
LOCATION:https://researchseminars.org/talk/LCM2021/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byung Hee An (Kyungpook National University)
DTSTART:20210112T000000Z
DTEND:20210112T005000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/28
DESCRIPTION:Title: Lagrangian fillings of Legendrian links of finite type\nby Byung Hee
An (Kyungpook National University) as part of Legendrians\, Cluster algebr
as\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of
Korea.\n\nAbstract\nIn this talk\, we will focus on Legendrian links admi
tting cluster structures of finite type (via N-graph ways) and prove that
those Legendrian links of type ADE have embedded exact Lagrangian fillings
as many as the number of seeds in their cluster structures. $\\newline$\n
Furthermore\, we will describe the cluster structures of BCFG-type among L
agrangian fillings of ADE-type Legendrian links\, which have certain parti
al symmetries. $\\newline$\nThis is joint work with Youngjin Bae (Incheon
National University) and Eunjeong Lee (IBS-CGP).\n
LOCATION:https://researchseminars.org/talk/LCM2021/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART:20210112T010000Z
DTEND:20210112T015000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/29
DESCRIPTION:Title: Quantum geometry of moduli spaces of local systems\nby Linhui Shen (M
ichigan State University) as part of Legendrians\, Cluster algebras\, and
Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n
\nAbstract\nLet $G$ be a split semi-simple algebraic group over $\\mathbb{
Q}$. We introduce a natural cluster structure on moduli spaces of $G$-loca
l 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 representations of s
uch quantum spaces. It will recover many classical topics\, such as the $q
$-deformed Toda systems\, quantum groups\, and the modular functor conject
ure for such representations. This talk will mainly be based on joint work
with A.B. Goncharov.\n
LOCATION:https://researchseminars.org/talk/LCM2021/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (Michigan State University)
DTSTART:20210112T020000Z
DTEND:20210112T025000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/30
DESCRIPTION:Title: Symplectic Structure on Augmentation Varieties\nby Daping Weng (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\nIn a recent joint project with H. Gao and L. Shen\, we introduce a
cluster K2 structure on the augmentation variety of the Chekanov-Eliashbe
rg dga for the rainbow closure of any positive braid with marked point dec
orations. This cluster K2 structure defines a holomorphic presymplectic st
ructure on the complex augmentation variety. Using a result of Goncharov a
nd Kenyon on surface bipartite graphs\, we prove that this holomorphic pre
symplectic structure becomes symplectic after we reduce the number of mark
ed points to a single marked per link component.\n
LOCATION:https://researchseminars.org/talk/LCM2021/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Lam (University of Michigan)
DTSTART:20210113T000000Z
DTEND:20210113T005000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/31
DESCRIPTION:Title: Positroid varieties and $q\,t$ -Catalan numbers\nby Thomas Lam (Univ
ersity of Michigan) as part of Legendrians\, Cluster algebras\, and Mirror
symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbst
ract\nPositroid varieties are subvarieties of the Grassmannian defined as
intersections of rotations of Schubert varieties in my work with Knutson a
nd Speyer. They also appear in the work of Shende-Treumann-Williams-Zaslow
as moduli spaces of constructible sheaves with microsupport in a Legendri
an link. $\\newline$\nWe show that the "top open positroid variety" has mi
xed Hodge polynomial given by the $q\,t$-rational Catalan numbers (up to
a simple factor). The $q\,t$-rational Catalan numbers satisfy remarkable s
ymmetry and unimodality properties\, and we show that these follow from th
e curious Lefschetz phenomenon for cluster varieties. The cohomologies of
open positroid varieties are shown to be related to Khovanov-Rosanzky knot
homology.$\\newline$\nThis talk is based on joint work with Pavel Galashi
n.\n
LOCATION:https://researchseminars.org/talk/LCM2021/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naoki Fujita (The University of Tokyo)
DTSTART:20210113T010000Z
DTEND:20210113T015000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/32
DESCRIPTION:Title: Newton-Okounkov bodies arising from cluster structures and mutations on p
olytopes\nby Naoki Fujita (The University of Tokyo) as part of Legendr
ians\, Cluster algebras\, and Mirror symmetry\n\nLecture held in POSTECH\,
Pohang\, Republic of Korea.\n\nAbstract\nA toric degeneration is a flat d
egeneration from a projective variety to a toric variety\, which can be us
ed to apply the theory of toric varieties to other projective varieties. I
n this talk\, we discuss relations among the following three constructions
of toric degenerations: representation theory\, Newton-Okounkov bodies\,
and cluster algebras. More precisely\, we construct Newton-Okounkov bodies
using cluster structures\, and realize representation-theoretic and clust
er-theoretic toric degenerations using this framework. We also discuss 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 by combi
natorial mutations. This talk is based on joint works with Hironori Oya an
d Akihiro Higashitani.\n
LOCATION:https://researchseminars.org/talk/LCM2021/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyun Kyu Kim (Ewha Womans University)
DTSTART:20210113T020000Z
DTEND:20210113T025000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/33
DESCRIPTION:Title: $SL_3$-laminations as bases for $PGL_3$ cluster varieties for surfaces\nby Hyun Kyu Kim (Ewha Womans University) as part of Legendrians\, Clust
er algebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Re
public of Korea.\n\nAbstract\nI will recall Fock-Goncharov's duality conje
cture for cluster $A$- and $X$-varieties\, and Fock-Goncharov's solution f
or the case of certain enhanced moduli spaces of $G$-local systems on a pu
nctured surface when $G$ is $SL_2$ and $PGL_2$. Then I will explain how Ku
perberg's web can be used to extend this result to the case when $G$ is $S
L_3$ and $PGL_3$.\n
LOCATION:https://researchseminars.org/talk/LCM2021/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Gammage (Harvard)
DTSTART:20210114T000000Z
DTEND:20210114T005000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/34
DESCRIPTION:Title: Mirror symmetry through perverse schobers\nby Benjamin Gammage (Harva
rd) as part of Legendrians\, Cluster algebras\, and Mirror symmetry\n\nLec
ture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nWe explain
how the language of perverse schobers gives a natural tool for describing
a generalization of the Seidel-Sheridan strategy for computing Fukaya cat
egories to the non-Lefschetz situation. We apply this technique to calcula
te the Fukaya category of the Milnor fiber of a Berglund-Hübsch singulari
ty\, building on some earlier computations of David Nadler. This calculati
on proves a conjecture of Lekili-Ueda.\n
LOCATION:https://researchseminars.org/talk/LCM2021/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yat-Hin Suen (IBS-CGP)
DTSTART:20210114T010000Z
DTEND:20210114T015000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/35
DESCRIPTION:Title: Tropical Lagrangian multi-sections and smoothing of locally free sheaves
on log Calabi-Yau surfaces\nby Yat-Hin Suen (IBS-CGP) as part of Legen
drians\, Cluster algebras\, and Mirror symmetry\n\nLecture held in POSTECH
\, Pohang\, Republic of Korea.\n\nAbstract\nHomological mirror symmetry su
ggests that Lagrangian multi-sections over an integral affine manifold wit
h singularities $B$ should mirror to holomorphic vector bundles. In this t
alk\, I will introduce the tropical version of Lagrangian multi-sections\,
called tropical Lagrangian multi-sections. I will mainly focus on dimensi
on 2. To certain tropical Lagrangian multi-sections over $B$\, I will con
struct a locally free sheaf $E_0$ on the log Calabi-Yau surface $X_0(B)$ a
ssociated 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://researchseminars.org/talk/LCM2021/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sangwook Lee (Soongsil University)
DTSTART:20210114T020000Z
DTEND:20210114T025000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/36
DESCRIPTION:Title: Orbifold Jacobian algebras and generalized Kodaira-Spencer maps\nby S
angwook Lee (Soongsil University) as part of Legendrians\, Cluster algebra
s\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of
Korea.\n\nAbstract\nGiven an algebraic function\, its Jacobian algebra enc
odes the information of the singularity. There is also a notion of orbifol
d Jacobian algebras for functions which admit finite (abelian) group actio
ns. We give a construction of an orbifold Jacobian algebra as Floer cohomo
logy of a Lagrangian submanifold which represents homological mirror funct
or. We also discuss generalized Kodaira-Spencer maps whose image is not ne
cessarily an ordinary Jacobian algebra. This talk is based on the joint wo
rk with C.-H. Cho.\n
LOCATION:https://researchseminars.org/talk/LCM2021/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (Osaka University)
DTSTART:20210115T000000Z
DTEND:20210115T005000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/37
DESCRIPTION:Title: Cluster coordinates from sheaf quantization of spectral curve\nby Tat
suki Kuwagaki (Osaka University) as part of Legendrians\, Cluster algebras
\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of K
orea.\n\nAbstract\nA sheaf quantization is a sheaf associated to a Lagrang
ian brane. In this talk\, I will explain my construction of sheaf quantiza
tion of the spectral curves of Schrodinger equations\, which is a part of
conjectural $\\hbar$-Riemann—Hilbert correspondence. The construction is
based on exact WKB analysis. I will also explain an application to cluste
r theory. Iwaki—Nakanishi have found cluster variables in exact WKB anal
ysis. The construction of sheaf quantization gives a geometric explanation
of Iwaki—Nakanishi’s cluster variables and their variants. A part of
this talk is based on my joint work in progress with T. Ishibashi.\n
LOCATION:https://researchseminars.org/talk/LCM2021/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Zaslow (Northwestern University)
DTSTART:20210115T010000Z
DTEND:20210115T015000Z
DTSTAMP:20260422T212727Z
UID:LCM2021/38
DESCRIPTION:Title: Dimers and Mirror Moduli\nby Eric Zaslow (Northwestern University) as
part of Legendrians\, Cluster algebras\, and Mirror symmetry\n\nLecture h
eld in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nI will try to de
scribe a counting problem that arises from considering mirror approaches t
o dimer integrable systems. Some of this talk is based on joint work with
David Treumann and Harold Williams\, and some is an ongoing project with H
elge Ruddatand others.\n
LOCATION:https://researchseminars.org/talk/LCM2021/38/
END:VEVENT
END:VCALENDAR