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BEGIN:VEVENT
SUMMARY:Anton Mellit (University of Vienna)
DTSTART:20220221T163000Z
DTEND:20220221T180000Z
DTSTAMP:20260404T131152Z
UID:ClusterBraids/1
DESCRIPTION:Title: Cohomology of braid varieties\nby Anton Mellit (Universit
y of Vienna) as part of Clusters and braids seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ClusterBraids/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Casals (University of California\, Davis)
DTSTART:20220228T170000Z
DTEND:20220228T180000Z
DTSTAMP:20260404T131152Z
UID:ClusterBraids/2
DESCRIPTION:Title: Cluster algebras and Legendrian links\nby Roger Casals (U
niversity of California\, Davis) as part of Clusters and braids seminar\n\
nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ClusterBraids/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Honghao Gao (Michigan State University)
DTSTART:20220307T163000Z
DTEND:20220307T180000Z
DTSTAMP:20260404T131152Z
UID:ClusterBraids/3
DESCRIPTION:Title: Infinitely many Lagrangian fillings\nby Honghao Gao (Mich
igan State University) as part of Clusters and braids seminar\n\n\nAbstrac
t\nA filling is an oriented surface bounding a link. Classifications of Le
gendrian knots and their exact Lagrangian fillings are central questions i
n low-dimensional contact and symplectic topology. Lagrangian fillings can
be constructed via local moves in finite steps. In this talk\, I will sho
w that most Legendrian torus links have infinitely many exact Lagrangian f
illings. These fillings are constructed using Legendrian loops\, and prove
n to be distinct using the microlocal theory of sheaves and the theory of
cluster algebras. This is a joint work with Roger Casals.\n
LOCATION:https://stable.researchseminars.org/talk/ClusterBraids/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Etienne Ménard (Institut Fourier)
DTSTART:20220411T153000Z
DTEND:20220411T170000Z
DTSTAMP:20260404T131152Z
UID:ClusterBraids/4
DESCRIPTION:Title: Cluster structures associated to open Richardson varieties:
simply-laced types\nby Etienne Ménard (Institut Fourier) as part of C
lusters and braids seminar\n\n\nAbstract\nDuring my PhD thesis\, I worked
on an algorithm to compute explicit seeds\nfor cluster structure on a cate
gorification of the coordinate ring of an\nopen Richardson variety. I will
first explain the motivations of this\nquestion\, its context\, the categ
orification used then describe the\nalgorithm\, focusing on its formulatio
n in terms of combinatorics of\nwords representing elements of a Weyl grou
p (among the two formulations\npossible). I will then end with some result
s linked to combinatorics of\nWeyl groups in type A\,D or E and open quest
ions associated.\n
LOCATION:https://stable.researchseminars.org/talk/ClusterBraids/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lara Bossinger (Instituto de Matemáticas UNAM)
DTSTART:20220425T153000Z
DTEND:20220425T170000Z
DTSTAMP:20260404T131152Z
UID:ClusterBraids/5
DESCRIPTION:by Lara Bossinger (Instituto de Matemáticas UNAM) as part of
Clusters and braids seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ClusterBraids/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART:20220418T153000Z
DTEND:20220418T170000Z
DTSTAMP:20260404T131152Z
UID:ClusterBraids/6
DESCRIPTION:by Linhui Shen (Michigan State University) as part of Clusters
and braids seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ClusterBraids/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ralf Schiffler (University of Connecticut)
DTSTART:20220502T153000Z
DTEND:20220502T170000Z
DTSTAMP:20260404T131152Z
UID:ClusterBraids/7
DESCRIPTION:Title: Knot theory and Cluster algebras\nby Ralf Schiffler (Univ
ersity of Connecticut) as part of Clusters and braids seminar\n\n\nAbstrac
t\nTo every knot diagram (or link diagram) $K$\, we associate a quiver wit
h potential $(Q\,W)$ and\, hence\, a cluster algebra $A(Q\,W)$ as well as
a Jacobian algebra $B=\\operatorname{Jac}(Q\,W)$. The vertices of the quiv
er are in bijection with the segments of the knot diagram.\n\nFor every se
gment $i$ of $K$\, we construct an indecomposable $B$-module $T(i)$ and le
t $T$ be the direct sum of these indecomposables. Each module $T(i)$ corre
sponds to an element $F(i)$ in the cluster algebra $A(Q\,W)$\, the so-call
ed F-polynomial of the module. $F(i)$ is a polynomial in several variables
$y_1\,\\dots\, y_n$ with positive integer coefficients.\n\nWe prove that\
, for each segment $i$ of $K$\, the Alexander polynomial of $K$ is equal t
o a specific specialization of $F(i)$. Furthermore this specialization doe
s not depend on $i$. For an alternating knot\, this specialization is simp
ly $y_j= -t$ if $j$ is even\; $y_j=-t^{-1}$ if $j$ is odd\, where we label
the segments of the knot in order of appearance along the knot.\n
LOCATION:https://stable.researchseminars.org/talk/ClusterBraids/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Caitlin Leverson (Bard College)
DTSTART:20220509T153000Z
DTEND:20220509T170000Z
DTSTAMP:20260404T131152Z
UID:ClusterBraids/8
DESCRIPTION:Title: DGA Representations\, Ruling Polynomials\, and the Colored HO
MFLY-PT Polynomial\nby Caitlin Leverson (Bard College) as part of Clus
ters and braids seminar\n\n\nAbstract\nGiven a Legendrian knot $\\Lambda$
in $\\mathbb{R}^3$ with the standard contact structure\, Rutherford showed
that the ruling polynomial of $\\Lambda$ appears as a specialization of t
he HOMFLY-PT polynomial of its topological knot type. We will extend the d
efinition of the ruling polynomial to define the colored ruling polynomial
of a Legendrian knot\, analogously to how the definition of the colored H
OMFLY-PT polynomial is an extension of the HOMFLY-PT polynomial\, and show
that the colored ruling polynomial of $\\Lambda$ also appears as a specia
lization of the colored HOMFLY-PT polynomial of $\\Lambda$’s topological
knot type. We will also discuss the relationship between counts of certai
n representations of the Chekanov-Eliashberg algebra of $\\Lambda$ to the
colored ruling polynomial of $\\Lambda$ and thus the colored HOMFLY-PT pol
ynomial of $\\Lambda$’s topological knot type. Little knowledge of these
topics will be assumed. This is joint work with Dan Rutherford.\n
LOCATION:https://stable.researchseminars.org/talk/ClusterBraids/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Orsola Capovilla-Searle (UC Davis)
DTSTART:20220523T153000Z
DTEND:20220523T170000Z
DTSTAMP:20260404T131152Z
UID:ClusterBraids/10
DESCRIPTION:Title: Infinitely many planar exact Lagrangian fillings and symplec
tic Milnor fibers\nby Orsola Capovilla-Searle (UC Davis) as part of Cl
usters and braids seminar\n\n\nAbstract\nWe provide a new family of Legend
rian links with infinitely many distinct exact orientable Lagrangian filli
ngs up to Hamiltonian isotopy. This family of links includes the first exa
mples of Legendrian links with infinitely many distinct planar exact Lagra
ngian fillings\, which can be viewed as the smallest Legendrian links curr
ently known to have infinitely many distinct exact Lagrangian fillings. As
an application we find new examples of infinitely many exact Lagrangian s
pheres and tori in 4-dimensional Milnor fibers of isolated hypersurface si
ngularities with positive modality.\n
LOCATION:https://stable.researchseminars.org/talk/ClusterBraids/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfredo Nájera Chávez (Instituto de Matemáticas UNAM)
DTSTART:20220530T153000Z
DTEND:20220530T170000Z
DTSTAMP:20260404T131152Z
UID:ClusterBraids/11
DESCRIPTION:Title: Deformation theory for finite cluster complexes\nby Alfr
edo Nájera Chávez (Instituto de Matemáticas UNAM) as part of Clusters a
nd braids seminar\n\n\nAbstract\nThe purpose of this talk is to elaborate
on a geometric relationship between cluster algebras and cluster complexes
. In vague words this relationship is the following: cluster algebras of f
inite cluster type with universal coefficients may be obtained via a torus
action on a Hilbert scheme. In particular\, we will discuss the deformati
on theory of the Stanley-Reisner ring associated to a finite cluster compl
ex and present some applications related to the Gröbner theory of the ide
al of relations among cluster and frozen variables of a cluster algebra of
finite cluster type. This is based on a joint project with Nathan Ilten a
nd Hipolito Treffinger.\n
LOCATION:https://stable.researchseminars.org/talk/ClusterBraids/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Pressland (University of Glasgow)
DTSTART:20220606T153000Z
DTEND:20220606T170000Z
DTSTAMP:20260404T131152Z
UID:ClusterBraids/12
DESCRIPTION:Title: Categorification for positroid varieties\nby Matthew Pre
ssland (University of Glasgow) as part of Clusters and braids seminar\n\nA
bstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ClusterBraids/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Lam (University of Michigan)
DTSTART:20220627T153000Z
DTEND:20220627T170000Z
DTSTAMP:20260404T131152Z
UID:ClusterBraids/13
DESCRIPTION:Title: Cluster structures for braid varieties\nby Thomas Lam (U
niversity of Michigan) as part of Clusters and braids seminar\n\n\nAbstrac
t\nBraid varieties are affine varieties indexed by positive\nbraids that h
ave been studied much in this seminar series. They have\nconnections to k
not homology\, to Legendrian link geometry\, to the\ngeometry of flag vari
eties\, and also to cluster algebras.\n\nIn this talk\, I will discuss a c
luster structure on braid varieties\nbased on generalized minors\, Deodhar
geometry\, and the Louise property\nfor quivers. This is joint work with
Pavel Galashin\, Melissa\nSherman-Bennett\, and David Speyer.\n
LOCATION:https://stable.researchseminars.org/talk/ClusterBraids/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kalck (University of Freiburg)
DTSTART:20221121T170000Z
DTEND:20221121T183000Z
DTSTAMP:20260404T131152Z
UID:ClusterBraids/14
DESCRIPTION:Title: Describing Leclerc’s Frobenius categories as categories of
Gorenstein projective modules\nby Martin Kalck (University of Freibur
g) as part of Clusters and braids seminar\n\n\nAbstract\nIn 2016\, Leclerc
introduced a new class of Frobenius categories in order to obtain (partly
conjectural) cluster algebra structures on coordinate rings of open Richa
rdson varieties. \n\nVery recently\, this approach has been completed and
generalized in work of Casals\, Gorsky\, Gorsky\, Le\, Shen & Simental. Mo
re precisely\, for open Richardson varieties their construction correspond
s to the seed introduced by Ménard. An alternative approach to obtain clu
ster structures for open Richardson varieties has been announced by Galash
in\, Lam\, Sherman-Bennett & Speyer.\n\nWe explain that Leclerc's categori
es are equivalent to categories of Gorenstein projective modules (aka maxi
mal Cohen-Macaulay modules) over an Iwanaga-Gorenstein ring of virtual dim
ension at most two. This is an analogue of Buan\, Iyama\, Reiten & Scott
’s description of Geiss\, Leclerc & Schröer’s categorification for Sc
huber cells in terms of Gorenstein projective modules over quotients of pr
eprojective algebras. \n\nOur talk will be based on https://arxiv.org/pdf/
1709.04785.pdf.\n
LOCATION:https://stable.researchseminars.org/talk/ClusterBraids/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khrystyna Serhiyenko (University of Kentucky)
DTSTART:20221128T170000Z
DTEND:20221128T183000Z
DTSTAMP:20260404T131152Z
UID:ClusterBraids/15
DESCRIPTION:by Khrystyna Serhiyenko (University of Kentucky) as part of Cl
usters and braids seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ClusterBraids/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Travis Mandel (University of Oklahoma)
DTSTART:20221205T170000Z
DTEND:20221205T183000Z
DTSTAMP:20260404T131152Z
UID:ClusterBraids/16
DESCRIPTION:by Travis Mandel (University of Oklahoma) as part of Clusters
and braids seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ClusterBraids/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greg Muller (University of Oklahoma)
DTSTART:20221212T170000Z
DTEND:20221212T183000Z
DTSTAMP:20260404T131152Z
UID:ClusterBraids/17
DESCRIPTION:by Greg Muller (University of Oklahoma) as part of Clusters an
d braids seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ClusterBraids/17/
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