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BEGIN:VEVENT
SUMMARY:Honghao Gao (Michigan State University)
DTSTART;VALUE=DATE-TIME:20210104T000000Z
DTEND;VALUE=DATE-TIME:20210104T010000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/1
DESCRIPTION:Title: Sheaves in contact topology I\nby Honghao Gao (Michigan
State University) as part of Legendrians\, Cluster algebras\, and Mirror
symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstr
act\nMicrolocal sheaf theory was introduced by Kashiwara-Schapira around 8
0s. With the notion of micro-support\, one can use sheaves on smooth manif
olds to access the geometry of their cotangent bundles. In recent years\,
microlocal sheaf theory entered contact and symplectic topology\, and has
been used to solve open problems. In this lecture series\, we will introdu
ce microlocal sheaf theory in the context of low-dimensional contact topol
ogy\, and supply the audience with background for its applications such as
producing non-classical invariants for Legendrian knots and distinguishin
g exact Lagrangian fillings.\n\nLecture 1: Legendrian knots and sheaves $\
\newline$\nBasics of Legendrain knots\, sheaves and microsupport\, local c
onditions at arcs\, cusps\, crossings.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Honghao Gao (Michigan State University)
DTSTART;VALUE=DATE-TIME:20210104T010000Z
DTEND;VALUE=DATE-TIME:20210104T020000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/2
DESCRIPTION:Title: Sheaves in contact topology II\nby Honghao Gao (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\nMicrolocal sheaf theory was introduced by Kashiwara-Schapira around
80s. With the notion of micro-support\, one can use sheaves on smooth mani
folds to access the geometry of their cotangent bundles. In recent years\,
microlocal sheaf theory entered contact and symplectic topology\, and has
been used to solve open problems. In this lecture series\, we will introd
uce microlocal sheaf theory in the context of low-dimensional contact topo
logy\, and supply the audience with background for its applications such a
s producing non-classical invariants for Legendrian knots and distinguishi
ng exact Lagrangian fillings.\n\nLecture 2: invariance $\\newline$\nCatego
ry of sheaves\, non-classical invariants for Legendrian submanifolds (theo
rem by Guillermou-Kashiwara-Schapira)\, combinatorial verification under R
eidemeister moves.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheol-Hyun Cho (Seoul National University)
DTSTART;VALUE=DATE-TIME:20210104T040000Z
DTEND;VALUE=DATE-TIME:20210104T050000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/3
DESCRIPTION:Title: Homological mirror symmetry via Lagrangian Floer theory
I\nby Cheol-Hyun Cho (Seoul National University) as part of Legendrians\,
Cluster algebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohan
g\, Republic of Korea.\n\nAbstract\nA version of homological mirror symmet
ry(HMS) conjecture relates the Fukaya category of a symplectic manifold an
d matrix factorization category of a mirror Landau-Ginzburg model. In this
introductory lecture series\, we illustrate geometric ideas behind such c
orrespondences from a biased point of view of the theory of localized mirr
or functor in Lagrangian Floer theory.\n\nLecture 1 : A-infinity category\
, HMS and localized mirror functor\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheol-Hyun Cho (Seoul National University)
DTSTART;VALUE=DATE-TIME:20210104T050000Z
DTEND;VALUE=DATE-TIME:20210104T060000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/4
DESCRIPTION:Title: Homological mirror symmetry via Lagrangian Floer theory
II\nby Cheol-Hyun Cho (Seoul National University) as part of Legendrians\
, Cluster algebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Poha
ng\, Republic of Korea.\n\nAbstract\nA version of homological mirror symme
try(HMS) conjecture relates the Fukaya category of a symplectic manifold a
nd matrix factorization category of a mirror Landau-Ginzburg model. In thi
s introductory lecture series\, we illustrate geometric ideas behind such
correspondences from a biased point of view of the theory of localized mir
ror functor in Lagrangian Floer theory.\n\nLecture 2 : Monotone Floer theo
ry and its HMS\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhyung Cho (Sungkyunkwan University)
DTSTART;VALUE=DATE-TIME:20210104T063000Z
DTEND;VALUE=DATE-TIME:20210104T073000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/5
DESCRIPTION:Title: Mutations and toric degenerations I\nby Yunhyung Cho (S
ungkyunkwan University) as part of Legendrians\, Cluster algebras\, and Mi
rror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\n
Abstract\nThe aim of this lecture is to understand a relation between the
wall crossing phenomenon of Lagrangians and the mutations in cluster theor
y via toric degenerations.\n\nLecture 1: Fano toric varieties and potentia
ls $\\newline$\n- A brief introduction to toric varieties $\\newline$\n- P
otential functions of smooth Fano toric varieties\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhyung Cho (Sungkyunkwan University)
DTSTART;VALUE=DATE-TIME:20210104T073000Z
DTEND;VALUE=DATE-TIME:20210104T083000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/6
DESCRIPTION:Title: Mutations and toric degenerations II\nby Yunhyung Cho (
Sungkyunkwan University) as part of Legendrians\, Cluster algebras\, and M
irror 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 theo
ry via toric degenerations.\n\nLecture 2: Toric degenerations\, examples a
nd construction $\\newline$\n- Toric degenerations\; definitions and examp
les $\\newline$\n- Construction of toric degenerations $\\newline$\n- Pote
ntial functions via toric degenerations $\\newline$\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Honghao Gao (Michigan State University)
DTSTART;VALUE=DATE-TIME:20210105T000000Z
DTEND;VALUE=DATE-TIME:20210105T010000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/7
DESCRIPTION:Title: Sheaves in contact topology III\nby Honghao Gao (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\nMicrolocal sheaf theory was introduced by Kashiwara-Schapira around
80s. With the notion of micro-support\, one can use sheaves on smooth man
ifolds to access the geometry of their cotangent bundles. In recent years\
, microlocal sheaf theory entered contact and symplectic topology\, and ha
s been used to solve open problems. In this lecture series\, we will intro
duce microlocal sheaf theory in the context of low-dimensional contact top
ology\, and supply the audience with background for its applications such
as producing non-classical invariants for Legendrian knots and distinguish
ing exact Lagrangian fillings.\n\nLecture 3: moduli space of sheaves $\\ne
wline$\nmoduli space of sheaves for elementary tangles\, microlocal rank 1
sheaves\, positive braid Legendrian knots\, flags and Bott-Samelson cells
.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Honghao Gao (Michigan State University)
DTSTART;VALUE=DATE-TIME:20210105T010000Z
DTEND;VALUE=DATE-TIME:20210105T020000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/8
DESCRIPTION:Title: Sheaves in contact topology IV\nby Honghao Gao (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\nMicrolocal sheaf theory was introduced by Kashiwara-Schapira around
80s. With the notion of micro-support\, one can use sheaves on smooth mani
folds to access the geometry of their cotangent bundles. In recent years\,
microlocal sheaf theory entered contact and symplectic topology\, and has
been used to solve open problems. In this lecture series\, we will introd
uce microlocal sheaf theory in the context of low-dimensional contact topo
logy\, and supply the audience with background for its applications such a
s producing non-classical invariants for Legendrian knots and distinguishi
ng exact Lagrangian fillings.\n\nLecture 4: Lagrangian fillings $\\newline
$\nSingularities of Legendrian fronts\, exact Lagrangian fillings and Lege
ndrian weaves\, sheaf quantization of Lagrangian fillings.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheol-Hyun Cho (Seoul National University)
DTSTART;VALUE=DATE-TIME:20210105T040000Z
DTEND;VALUE=DATE-TIME:20210105T050000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
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 algebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Poh
ang\, Republic of Korea.\n\nAbstract\nA version of homological mirror symm
etry(HMS) conjecture relates the Fukaya category of a symplectic manifold
and matrix factorization category of a mirror Landau-Ginzburg model. In th
is introductory lecture series\, we illustrate geometric ideas behind such
correspondences from a biased point of view of the theory of localized mi
rror functor in Lagrangian Floer theory.\n\nLecture 3 : Fukaya category of
surfaces and its HMS\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheol-Hyun Cho (Seoul National University)
DTSTART;VALUE=DATE-TIME:20210105T050000Z
DTEND;VALUE=DATE-TIME:20210105T060000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
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 algebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Poha
ng\, Republic of Korea.\n\nAbstract\nA version of homological mirror symme
try(HMS) conjecture relates the Fukaya category of a symplectic manifold a
nd matrix factorization category of a mirror Landau-Ginzburg model. In thi
s introductory lecture series\, we illustrate geometric ideas behind such
correspondences from a biased point of view of the theory of localized mir
ror functor in Lagrangian Floer theory.\n\nLecture 4 : Singularities and i
ts HMS\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhyung Cho (Sungkyunkwan University)
DTSTART;VALUE=DATE-TIME:20210105T063000Z
DTEND;VALUE=DATE-TIME:20210105T073000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/11
DESCRIPTION:Title: Mutations and toric degenerations III\nby Yunhyung Cho
(Sungkyunkwan University) 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 th
e wall crossing phenomenon of Lagrangians and the mutations in cluster the
ory via toric degenerations.\n\nLecture 3: Mutations of potentials $\\newl
ine$\n- Mutations of Laurent polynomials\, polytopes\, and Lagrangian tori
\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhyung Cho (Sungkyunkwan University)
DTSTART;VALUE=DATE-TIME:20210105T073000Z
DTEND;VALUE=DATE-TIME:20210105T083000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/12
DESCRIPTION:Title: Mutations and toric degenerations IV\nby Yunhyung Cho (
Sungkyunkwan University) as part of Legendrians\, Cluster algebras\, and M
irror 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 theo
ry via toric degenerations.\n\nLecture 4: Examples: flag variety $\\newlin
e$\n- Toric degenerations of flag varieties $\\newline$\n- Cluster structu
res of G/B and potential functions\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART;VALUE=DATE-TIME:20210106T000000Z
DTEND;VALUE=DATE-TIME:20210106T010000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
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 symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\
n\nAbstract\nCluster algebras are commutative algebras equipped with remar
kable combinatorial structures. Since its inception in 2000\, the theory o
f cluster algebras has found numerous exciting applications in mathematics
and physics. This series of lectures aim to provide an accessible introdu
ction to cluster algebras for a general mathematical audience. In particul
ar\, we will investigate the following topics.\n\nLecture 1: Cluster algeb
ras of rank 2: positive Laurent Phenomenon and greedy bases $\\newline$\nT
his lecture will focus on cluster algebras of rank 2. Using elementary com
binatorial tools\, we will prove the positive Laurent Phenomenon and const
ruct greedy bases for cluster algebras of rank 2.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART;VALUE=DATE-TIME:20210106T010000Z
DTEND;VALUE=DATE-TIME:20210106T020000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/14
DESCRIPTION:Title: An introduction to cluster algebras II\nby Linhui Shen
(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 algebras are commutative algebras equipped with rema
rkable combinatorial structures. Since its inception in 2000\, the theory
of cluster algebras has found numerous exciting applications in mathematic
s and physics. This series of lectures aim to provide an accessible introd
uction to cluster algebras for a general mathematical audience. In particu
lar\, we will investigate the following topics.\n\nLecture 2: Cluster alge
bras and Finite 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 expl
ain their connections to generalized associahedra.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART;VALUE=DATE-TIME:20210107T000000Z
DTEND;VALUE=DATE-TIME:20210107T010000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/15
DESCRIPTION:Title: An introduction to cluster algebras III\nby Linhui Shen
(Michigan State University) as part of Legendrians\, Cluster algebras\, a
nd Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea
.\n\nAbstract\nCluster algebras are commutative algebras equipped with rem
arkable combinatorial structures. Since its inception in 2000\, the theory
of cluster algebras has found numerous exciting applications in mathemati
cs and physics. This series of lectures aim to provide an accessible intro
duction to cluster algebras for a general mathematical audience. In partic
ular\, we will investigate the following topics.\n\nLecture 3: Poisson geo
metry and quantization$\\newline$\nCluster varieties carry intrinsic Poiss
on structures. We present a quantization of cluster varieties and explore
their connections with the theory of quantum groups.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART;VALUE=DATE-TIME:20210108T000000Z
DTEND;VALUE=DATE-TIME:20210108T010000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/16
DESCRIPTION:Title: An introduction to cluster algebras IV\nby Linhui Shen
(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 algebras are commutative algebras equipped with rema
rkable combinatorial structures. Since its inception in 2000\, the theory
of cluster algebras has found numerous exciting applications in mathematic
s and physics. This series of lectures aim to provide an accessible introd
uction to cluster algebras for a general mathematical audience. In particu
lar\, we will investigate the following topics.\n\nLecture 4: Categorifica
tion and Donaldson-Thomas theory$\\newline$\nEvery cluster variety can be
categorized and gives rise to a 3d Calabi-Yau category with a generic stab
ility condition. In this lecture\, we will investigate their connections
to the motivic Donaldson-Thomas theory.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (Michigan State University)
DTSTART;VALUE=DATE-TIME:20210107T010000Z
DTEND;VALUE=DATE-TIME:20210107T020000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/17
DESCRIPTION:Title: Examples of cluster varieties from plabic graphs I\nby
Daping Weng (Michigan State University) as part of Legendrians\, Cluster a
lgebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republ
ic of Korea.\n\nAbstract\nCluster varieties were introduced by Fock and Go
ncharov as geometric counterparts of Fomin and Zelevinsky’s cluster alge
bras. Simply speaking\, cluster varieties are algebraic varieties with an
atlas of torus charts\, whose transition maps are captured by certain comb
inatorial process called cluster mutations. Many interesting geometric obj
ects turn out to be examples of cluster varieties\, and one can then use c
luster theoretical techniques to study these geometric objects. In this le
cture series\, we will discuss various examples of cluster varieties whose
combinatorics can be captured by plabic graphs\, including Grassmannians
and double Bruhat/Bott-Samelson cells of $SL_n$. This lecture series will
be complementary to Linhui Shen’s lecture series on cluster theory.\n\nL
ecture 1: $Gr(2\,n)$ and $M(0\,n)$ $\\newline$\nWe discuss the cluster str
uctures on Grassmannian $Gr(2\,n)$ and on the moduli space of $n$ points i
n $\\mathbb{P}^1$. 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:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (Osaka University)
DTSTART;VALUE=DATE-TIME:20210107T050000Z
DTEND;VALUE=DATE-TIME:20210107T060000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/18
DESCRIPTION:Title: Symplectic geometry in algebraic analysis I\nby Tatsuki
Kuwagaki (Osaka University) as part of Legendrians\, Cluster algebras\, a
nd Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea
.\n\nAbstract\nIn these lectures\, I will explain two ideas in algebraic a
nalysis: sheaf quantization and exact WKB analysis\, with emphasis on rela
tions to symplectic geometry. The ideas presented in the lectures will be
used in my talk in the workshop.\n\nLecture 1: Sheaf quantization: basic i
deas and examples\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (Osaka University)
DTSTART;VALUE=DATE-TIME:20210107T060000Z
DTEND;VALUE=DATE-TIME:20210107T070000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/19
DESCRIPTION:Title: Symplectic geometry in algebraic analysis II\nby Tatsuk
i Kuwagaki (Osaka University) as part of Legendrians\, Cluster algebras\,
and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Kore
a.\n\nAbstract\nIn these lectures\, I will explain two ideas in algebraic
analysis: sheaf quantization and exact WKB analysis\, with emphasis on rel
ations to symplectic geometry. The ideas presented in the lectures will be
used in my talk in the workshop.\n\nLecture 2: Sheaf quantization: contin
ued\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (Michigan State University)
DTSTART;VALUE=DATE-TIME:20210107T020000Z
DTEND;VALUE=DATE-TIME:20210107T030000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
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\, Repub
lic of Korea.\n\nAbstract\nCluster varieties were introduced by Fock and G
oncharov as geometric counterparts of Fomin and Zelevinsky’s cluster alg
ebras. Simply speaking\, cluster varieties are algebraic varieties with an
atlas of torus charts\, whose transition maps are captured by certain com
binatorial process called cluster mutations. Many interesting geometric ob
jects turn out to be examples of cluster varieties\, and one can then use
cluster theoretical techniques to study these geometric objects. In this l
ecture series\, we will discuss various examples of cluster varieties whos
e combinatorics can be captured by plabic graphs\, including Grassmannians
and double Bruhat/Bott-Samelson cells of $SL_n$. This lecture series will
be complementary to Linhui Shen’s lecture series on cluster theory.\n\n
Lecture 2: plabic 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:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (Michigan State University)
DTSTART;VALUE=DATE-TIME:20210108T010000Z
DTEND;VALUE=DATE-TIME:20210108T020000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/21
DESCRIPTION:Title: Examples of cluster varieties from plabic graphs III\nb
y Daping Weng (Michigan State University) as part of Legendrians\, Cluster
algebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Repu
blic of Korea.\n\nAbstract\nCluster varieties were introduced by Fock and
Goncharov as geometric counterparts of Fomin and Zelevinsky’s cluster al
gebras. Simply speaking\, cluster varieties are algebraic varieties with a
n atlas of torus charts\, whose transition maps are captured by certain co
mbinatorial process called cluster mutations. Many interesting geometric o
bjects turn 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 who
se combinatorics can be captured by plabic graphs\, including Grassmannian
s and double Bruhat/Bott-Samelson cells of $SL_n$. This lecture series wil
l be complementary to Linhui Shen’s lecture series on cluster theory.\n\
nLecture 3: double Bruhat cells of $SL_n$ $\\newline$\nWe introduce double
Bruhat cells of a semisimple Lie group and discuss the cluster structures
on double Bruhat cells of $SL_n$ in terms of plabic graphs.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (Michigan State University)
DTSTART;VALUE=DATE-TIME:20210108T020000Z
DTEND;VALUE=DATE-TIME:20210108T030000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
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\, Repub
lic of Korea.\n\nAbstract\nCluster varieties were introduced by Fock and G
oncharov as geometric counterparts of Fomin and Zelevinsky’s cluster alg
ebras. Simply speaking\, cluster varieties are algebraic varieties with an
atlas of torus charts\, whose transition maps are captured by certain com
binatorial process called cluster mutations. Many interesting geometric ob
jects turn out to be examples of cluster varieties\, and one can then use
cluster theoretical techniques to study these geometric objects. In this l
ecture series\, we will discuss various examples of cluster varieties whos
e combinatorics can be captured by plabic graphs\, including Grassmannians
and double Bruhat/Bott-Samelson cells of $SL_n$. This lecture series will
be complementary to Linhui Shen’s lecture series on cluster theory.\n\n
Lecture 4: double Bott-Samelson cells of $SL_n$ and positive braid closure
s $\\newline$\nWe introduce double Bott-Samelson cells of $SL_n$ as a gene
ralization of double Bruhat cells. We will describe their cluster structur
es and the connection to positive braid closures.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (Osaka University)
DTSTART;VALUE=DATE-TIME:20210108T050000Z
DTEND;VALUE=DATE-TIME:20210108T060000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/23
DESCRIPTION:Title: Symplectic geometry in algebraic analysis III\nby Tatsu
ki Kuwagaki (Osaka University) as part of Legendrians\, Cluster algebras\,
and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Kor
ea.\n\nAbstract\nIn these lectures\, I will explain two ideas in algebraic
analysis: sheaf quantization and exact WKB analysis\, with emphasis on re
lations to symplectic geometry. The ideas presented in the lectures will b
e used in my talk in the workshop.\n\nLecture 3: Exact WKB analysis: basic
s\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (Osaka University)
DTSTART;VALUE=DATE-TIME:20210108T060000Z
DTEND;VALUE=DATE-TIME:20210108T070000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/24
DESCRIPTION:Title: Symplectic geometry in algebraic analysis IV\nby Tatsuk
i Kuwagaki (Osaka University) as part of Legendrians\, Cluster algebras\,
and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Kore
a.\n\nAbstract\nIn these lectures\, I will explain two ideas in algebraic
analysis: sheaf quantization and exact WKB analysis\, with emphasis on rel
ations to symplectic geometry. The ideas presented in the lectures will be
used in my talk in the workshop.\n\nLecture 4: Exact WKB analysis: cluste
r algebra and local systems\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lenhard L. Ng (Duke University)
DTSTART;VALUE=DATE-TIME:20210111T010000Z
DTEND;VALUE=DATE-TIME:20210111T015000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/25
DESCRIPTION:Title: Infinitely many fillings through augmentations\nby Lenh
ard L. Ng (Duke University) as part of Legendrians\, Cluster algebras\, an
d Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.
\n\nAbstract\nIn 2020\, a few groups of people proved that certain Legendr
ian links in R^3 have infinitely many exact Lagrangian fillings that are d
istinct under Hamiltonian isotopy. These groups (Casals-Gao\, Gao-Shen-Wan
g\, Casals-Zaslow) used a variety of approaches involving microlocal sheaf
theory and cluster structures. I'll describe a different\, Floer-theoreti
c 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 the Floerapproach but not (yet?) the other approaches. This is
joint work with Roger Casals.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Casals (University of California\, Davis)
DTSTART;VALUE=DATE-TIME:20210111T000000Z
DTEND;VALUE=DATE-TIME:20210111T005000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/26
DESCRIPTION:Title: Legendrian knots and their Lagrangian fillings: A consp
ectus on recent developments\nby Roger Casals (University of California\,
Davis) as part of Legendrians\, Cluster algebras\, and Mirror symmetry\n\n
Lecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nIn this
talk I will survey some of the recent developments in the study of Lagran
gian fillings of Legendrian knots. First\, I will introduce and motivate t
he leading questions. Then\, we will discuss the current methods and techn
iques available to tackle them. Finally\, I will suggest some open problem
s that now seem at reach\, along with some strategies to approach them.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Honghao Gao (Michigan State University)
DTSTART;VALUE=DATE-TIME:20210111T020000Z
DTEND;VALUE=DATE-TIME:20210111T025000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/27
DESCRIPTION:Title: Infinitely many fillings through sheaves\nby Honghao Ga
o (Michigan State University) as part of Legendrians\, Cluster algebras\,
and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Kore
a.\n\nAbstract\nThis talk will complement other talks in the day and prese
nt concrete examples. Specifically\, I will construct infinitely many Lagr
angian fillings for the Legendrian torus link (3\,6)\, and explain how to
distinguish them using sheaves and cluster algebras. Time permitting\, I w
ill discuss other torus links (joint work with R. Casals) and positive bra
id links (joint work with L. Shen and D. Weng).\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byung Hee An (Kyungpook National University)
DTSTART;VALUE=DATE-TIME:20210112T000000Z
DTEND;VALUE=DATE-TIME:20210112T005000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
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 algebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang
\, Republic of Korea.\n\nAbstract\nIn this talk\, we will focus on Legendr
ian links admitting cluster structures of finite type (via N-graph ways) a
nd prove that those Legendrian links of type ADE have embedded exact Lagra
ngian fillings as many as the number of seeds in their cluster structures.
$\\newline$\nFurthermore\, we will describe the cluster structures of BCF
G-type among Lagrangian fillings of ADE-type Legendrian links\, which have
certain partial symmetries. $\\newline$\nThis is joint work with Youngjin
Bae (Incheon National University) and Eunjeong Lee (IBS-CGP).\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART;VALUE=DATE-TIME:20210112T010000Z
DTEND;VALUE=DATE-TIME:20210112T015000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/29
DESCRIPTION:Title: Quantum geometry of moduli spaces of local systems\nby
Linhui Shen (Michigan State University) as part of Legendrians\, Cluster a
lgebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republ
ic of Korea.\n\nAbstract\nLet $G$ be a split semi-simple algebraic group o
ver $\\mathbb{Q}$. We introduce a natural cluster structure on moduli spac
es 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 repres
entations of such quantum spaces. It will recover many classical topics\,
such as the $q$-deformed Toda systems\, quantum groups\, and the modular f
unctor conjecture for such representations. This talk will mainly be based
on joint work with A.B. Goncharov.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (Michigan State University)
DTSTART;VALUE=DATE-TIME:20210112T020000Z
DTEND;VALUE=DATE-TIME:20210112T025000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/30
DESCRIPTION:Title: Symplectic Structure on Augmentation Varieties\nby Dapi
ng Weng (Michigan State University) as part of Legendrians\, Cluster algeb
ras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic o
f Korea.\n\nAbstract\nIn a recent joint project with H. Gao and L. Shen\,
we introduce a cluster K2 structure on the augmentation variety of the Che
kanov-Eliashberg dga for the rainbow closure of any positive braid with ma
rked point decorations. This cluster K2 structure defines a holomorphic pr
esymplectic structure on the complex augmentation variety. Using a result
of Goncharov and Kenyon on surface bipartite graphs\, we prove that this h
olomorphic presymplectic structure becomes symplectic after we reduce the
number of marked points to a single marked per link component.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Lam (University of Michigan)
DTSTART;VALUE=DATE-TIME:20210113T000000Z
DTEND;VALUE=DATE-TIME:20210113T005000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/31
DESCRIPTION:Title: Positroid varieties and $q\,t$ -Catalan numbers\nby Th
omas Lam (University of Michigan) as part of Legendrians\, Cluster algebra
s\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of
Korea.\n\nAbstract\nPositroid varieties are subvarieties of the Grassmanni
an defined as intersections of rotations of Schubert varieties in my work
with Knutson and Speyer. They also appear in the work of Shende-Treumann-W
illiams-Zaslow as moduli spaces of constructible sheaves with microsupport
in a Legendrian link. $\\newline$\nWe show that the "top open positroid v
ariety" has mixed Hodge polynomial given by the $q\,t$-rational Catalan n
umbers (up to a simple factor). The $q\,t$-rational Catalan numbers satisf
y remarkable symmetry and unimodality properties\, and we show that these
follow from the curious Lefschetz phenomenon for cluster varieties. The co
homologies of open positroid varieties are shown to be related to Khovanov
-Rosanzky knot homology.$\\newline$\nThis talk is based on joint work with
Pavel Galashin.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naoki Fujita (The University of Tokyo)
DTSTART;VALUE=DATE-TIME:20210113T010000Z
DTEND;VALUE=DATE-TIME:20210113T015000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/32
DESCRIPTION:Title: Newton-Okounkov bodies arising from cluster structures
and mutations on polytopes\nby Naoki Fujita (The University of Tokyo) as p
art of Legendrians\, Cluster algebras\, and Mirror symmetry\n\nLecture hel
d in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nA toric degenerati
on is a flat degeneration from a projective variety to a toric variety\, w
hich can be used to apply the theory of toric varieties to other projectiv
e varieties. In this talk\, we discuss relations among the following three
constructions of toric degenerations: representation theory\, Newton-Okou
nkov bodies\, and cluster algebras. More precisely\, we construct Newton-O
kounkov bodies using cluster structures\, and realize representation-theor
etic and cluster-theoretic toric degenerations using this framework. We al
so 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 struc
tures by combinatorial mutations. This talk is based on joint works with H
ironori Oya and Akihiro Higashitani.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyun Kyu Kim (Ewha Womans University)
DTSTART;VALUE=DATE-TIME:20210113T020000Z
DTEND;VALUE=DATE-TIME:20210113T025000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/33
DESCRIPTION:Title: $SL_3$-laminations as bases for $PGL_3$ cluster varieti
es for surfaces\nby Hyun Kyu Kim (Ewha Womans University) as part of Legen
drians\, Cluster algebras\, and Mirror symmetry\n\nLecture held in POSTECH
\, Pohang\, Republic of Korea.\n\nAbstract\nI will recall Fock-Goncharov's
duality conjecture for cluster $A$- and $X$-varieties\, and Fock-Goncharo
v's solution for the case of certain enhanced moduli spaces of $G$-local s
ystems 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:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Gammage (Harvard)
DTSTART;VALUE=DATE-TIME:20210114T000000Z
DTEND;VALUE=DATE-TIME:20210114T005000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/34
DESCRIPTION:Title: Mirror symmetry through perverse schobers\nby Benjamin
Gammage (Harvard) as part of Legendrians\, Cluster algebras\, and Mirror s
ymmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstra
ct\nWe explain how the language of perverse schobers gives a natural tool
for describing a generalization of the Seidel-Sheridan strategy for comput
ing Fukaya categories to the non-Lefschetz situation. We apply this techni
que to calculate the Fukaya category of the Milnor fiber of a Berglund-Hü
bsch singularity\, building on some earlier computations of David Nadler.
This calculation proves a conjecture of Lekili-Ueda.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yat-Hin Suen (IBS-CGP)
DTSTART;VALUE=DATE-TIME:20210114T010000Z
DTEND;VALUE=DATE-TIME:20210114T015000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/35
DESCRIPTION:Title: Tropical Lagrangian multi-sections and smoothing of loc
ally free sheaves on log Calabi-Yau surfaces\nby Yat-Hin Suen (IBS-CGP) as
part of Legendrians\, Cluster algebras\, and Mirror symmetry\n\nLecture h
eld in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nHomological mirr
or symmetry suggests that Lagrangian multi-sections over an integral affin
e manifold with singularities $B$ should mirror to holomorphic vector bund
les. In this talk\, I will introduce the tropical version of Lagrangian mu
lti-sections\, called tropical Lagrangian multi-sections. I will mainly fo
cus on dimension 2. To certain tropical Lagrangian multi-sections over $B
$\, I will construct a locally free sheaf $E_0$ on the log Calabi-Yau surf
ace $X_0(B)$ 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:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sangwook Lee (Soongsil University)
DTSTART;VALUE=DATE-TIME:20210114T020000Z
DTEND;VALUE=DATE-TIME:20210114T025000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/36
DESCRIPTION:Title: Orbifold Jacobian algebras and generalized Kodaira-Spen
cer maps\nby Sangwook Lee (Soongsil University) as part of Legendrians\, C
luster algebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\
, Republic of Korea.\n\nAbstract\nGiven an algebraic function\, its Jacobi
an algebra encodes the information of the singularity. There is also a not
ion of orbifold Jacobian algebras for functions which admit finite (abelia
n) group actions. We give a construction of an orbifold Jacobian algebra a
s Floer cohomology of a Lagrangian submanifold which represents homologica
l mirror functor. We also discuss generalized Kodaira-Spencer maps whose i
mage is not necessarily an ordinary Jacobian algebra. This talk is based o
n the joint work with C.-H. Cho.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (Osaka University)
DTSTART;VALUE=DATE-TIME:20210115T000000Z
DTEND;VALUE=DATE-TIME:20210115T005000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/37
DESCRIPTION:Title: Cluster coordinates from sheaf quantization of spectral
curve\nby Tatsuki Kuwagaki (Osaka University) as part of Legendrians\, Cl
uster algebras\, and Mirror symmetry\n\nLecture held in POSTECH\, Pohang\,
Republic of Korea.\n\nAbstract\nA sheaf quantization is a sheaf associate
d to a Lagrangian brane. In this talk\, I will explain my construction of
sheaf quantization of the spectral curves of Schrodinger equations\, which
is a part of conjectural $\\hbar$-Riemann—Hilbert correspondence. The c
onstruction is based on exact WKB analysis. I will also explain an applica
tion to cluster theory. Iwaki—Nakanishi have found cluster variables in
exact WKB analysis. The construction of sheaf quantization gives a geometr
ic explanation of Iwaki—Nakanishi’s cluster variables and their varian
ts. A part of this talk is based on my joint work in progress with T. Ishi
bashi.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Zaslow (Northwestern University)
DTSTART;VALUE=DATE-TIME:20210115T010000Z
DTEND;VALUE=DATE-TIME:20210115T015000Z
DTSTAMP;VALUE=DATE-TIME:20210124T153828Z
UID:LCM2021/38
DESCRIPTION:Title: Dimers and Mirror Moduli\nby Eric Zaslow (Northwestern
University) as part of Legendrians\, Cluster algebras\, and Mirror symmetr
y\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbstract\nI
will try to describe a counting problem that arises from considering mirro
r approaches to dimer integrable systems. Some of this talk is based on jo
int work with David Treumann and Harold Williams\, and some is an ongoing
project with Helge Ruddatand others.\n
LOCATION:Lecture held in POSTECH\, Pohang\, Republic of Korea
END:VEVENT
END:VCALENDAR