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BEGIN:VEVENT
SUMMARY:Anton Mellit (University of Vienna)
DTSTART;VALUE=DATE-TIME:20220221T163000Z
DTEND;VALUE=DATE-TIME:20220221T180000Z
DTSTAMP;VALUE=DATE-TIME:20221209T222508Z
UID:ClusterBraids/1
DESCRIPTION:Title: Cohomology of braid varieties\nby Anton Mellit (University of Vi
enna) as part of Clusters and braids seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ClusterBraids/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Casals (University of California\, Davis)
DTSTART;VALUE=DATE-TIME:20220228T170000Z
DTEND;VALUE=DATE-TIME:20220228T180000Z
DTSTAMP;VALUE=DATE-TIME:20221209T222508Z
UID:ClusterBraids/2
DESCRIPTION:Title: Cluster algebras and Legendrian links\nby Roger Casals (Universi
ty of California\, Davis) as part of Clusters and braids seminar\n\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/ClusterBraids/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Honghao Gao (Michigan State University)
DTSTART;VALUE=DATE-TIME:20220307T163000Z
DTEND;VALUE=DATE-TIME:20220307T180000Z
DTSTAMP;VALUE=DATE-TIME:20221209T222508Z
UID:ClusterBraids/3
DESCRIPTION:Title: Infinitely many Lagrangian fillings\nby Honghao Gao (Michigan St
ate University) as part of Clusters and braids seminar\n\n\nAbstract\nA fi
lling is an oriented surface bounding a link. Classifications of Legendria
n knots and their exact Lagrangian fillings are central questions in low-d
imensional contact and symplectic topology. Lagrangian fillings can be con
structed via local moves in finite steps. In this talk\, I will show that
most Legendrian torus links have infinitely many exact Lagrangian fillings
. These fillings are constructed using Legendrian loops\, and proven 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://researchseminars.org/talk/ClusterBraids/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Etienne Ménard (Institut Fourier)
DTSTART;VALUE=DATE-TIME:20220411T153000Z
DTEND;VALUE=DATE-TIME:20220411T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T222508Z
UID:ClusterBraids/4
DESCRIPTION:Title: Cluster structures associated to open Richardson varieties: simply-
laced types\nby Etienne Ménard (Institut Fourier) as part of Clusters
and braids seminar\n\n\nAbstract\nDuring my PhD thesis\, I worked on an a
lgorithm to compute explicit seeds\nfor cluster structure on a categorific
ation of the coordinate ring of an\nopen Richardson variety. I will first
explain the motivations of this\nquestion\, its context\, the categorifica
tion used then describe the\nalgorithm\, focusing on its formulation in te
rms of combinatorics of\nwords representing elements of a Weyl group (amon
g the two formulations\npossible). I will then end with some results linke
d to combinatorics of\nWeyl groups in type A\,D or E and open questions as
sociated.\n
LOCATION:https://researchseminars.org/talk/ClusterBraids/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lara Bossinger (Instituto de Matemáticas UNAM)
DTSTART;VALUE=DATE-TIME:20220425T153000Z
DTEND;VALUE=DATE-TIME:20220425T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T222508Z
UID:ClusterBraids/5
DESCRIPTION:by Lara Bossinger (Instituto de Matemáticas UNAM) as part of
Clusters and braids seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ClusterBraids/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART;VALUE=DATE-TIME:20220418T153000Z
DTEND;VALUE=DATE-TIME:20220418T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T222508Z
UID:ClusterBraids/6
DESCRIPTION:by Linhui Shen (Michigan State University) as part of Clusters
and braids seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ClusterBraids/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ralf Schiffler (University of Connecticut)
DTSTART;VALUE=DATE-TIME:20220502T153000Z
DTEND;VALUE=DATE-TIME:20220502T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T222508Z
UID:ClusterBraids/7
DESCRIPTION:Title: Knot theory and Cluster algebras\nby Ralf Schiffler (University
of Connecticut) as part of Clusters and braids seminar\n\n\nAbstract\nTo e
very knot diagram (or link diagram) $K$\, we associate a quiver with poten
tial $(Q\,W)$ and\, hence\, a cluster algebra $A(Q\,W)$ as well as a Jacob
ian algebra $B=\\operatorname{Jac}(Q\,W)$. The vertices of the quiver are
in bijection with the segments of the knot diagram.\n\nFor every segment $
i$ of $K$\, we construct an indecomposable $B$-module $T(i)$ and let $T$ b
e the direct sum of these indecomposables. Each module $T(i)$ corresponds
to an element $F(i)$ in the cluster algebra $A(Q\,W)$\, the so-called F-po
lynomial 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 e
ach segment $i$ of $K$\, the Alexander polynomial of $K$ is equal to a spe
cific specialization of $F(i)$. Furthermore this specialization does not d
epend on $i$. For an alternating knot\, this specialization is simply $y_j
= -t$ if $j$ is even\; $y_j=-t^{-1}$ if $j$ is odd\, where we label the se
gments of the knot in order of appearance along the knot.\n
LOCATION:https://researchseminars.org/talk/ClusterBraids/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Caitlin Leverson (Bard College)
DTSTART;VALUE=DATE-TIME:20220509T153000Z
DTEND;VALUE=DATE-TIME:20220509T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T222508Z
UID:ClusterBraids/8
DESCRIPTION:Title: DGA Representations\, Ruling Polynomials\, and the Colored HOMFLY-PT
Polynomial\nby Caitlin Leverson (Bard College) as part of Clusters an
d braids seminar\n\n\nAbstract\nGiven a Legendrian knot $\\Lambda$ in $\\m
athbb{R}^3$ with the standard contact structure\, Rutherford showed that t
he ruling polynomial of $\\Lambda$ appears as a specialization of the HOMF
LY-PT polynomial of its topological knot type. We will extend the definiti
on of the ruling polynomial to define the colored ruling polynomial of a L
egendrian knot\, analogously to how the definition of the colored HOMFLY-P
T polynomial is an extension of the HOMFLY-PT polynomial\, and show that t
he colored ruling polynomial of $\\Lambda$ also appears as a specializatio
n of the colored HOMFLY-PT polynomial of $\\Lambda$’s topological knot t
ype. We will also discuss the relationship between counts of certain repre
sentations of the Chekanov-Eliashberg algebra of $\\Lambda$ to the colored
ruling polynomial of $\\Lambda$ and thus the colored HOMFLY-PT polynomial
of $\\Lambda$’s topological knot type. Little knowledge of these topics
will be assumed. This is joint work with Dan Rutherford.\n
LOCATION:https://researchseminars.org/talk/ClusterBraids/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Orsola Capovilla-Searle (UC Davis)
DTSTART;VALUE=DATE-TIME:20220523T153000Z
DTEND;VALUE=DATE-TIME:20220523T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T222508Z
UID:ClusterBraids/10
DESCRIPTION:Title: Infinitely many planar exact Lagrangian fillings and symplectic Mil
nor fibers\nby Orsola Capovilla-Searle (UC Davis) as part of Clusters
and braids seminar\n\n\nAbstract\nWe provide a new family of Legendrian li
nks with infinitely many distinct exact orientable Lagrangian fillings up
to Hamiltonian isotopy. This family of links includes the first examples o
f Legendrian links with infinitely many distinct planar exact Lagrangian f
illings\, which can be viewed as the smallest Legendrian links currently k
nown to have infinitely many distinct exact Lagrangian fillings. As an app
lication we find new examples of infinitely many exact Lagrangian spheres
and tori in 4-dimensional Milnor fibers of isolated hypersurface singulari
ties with positive modality.\n
LOCATION:https://researchseminars.org/talk/ClusterBraids/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfredo Nájera Chávez (Instituto de Matemáticas UNAM)
DTSTART;VALUE=DATE-TIME:20220530T153000Z
DTEND;VALUE=DATE-TIME:20220530T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T222508Z
UID:ClusterBraids/11
DESCRIPTION:Title: Deformation theory for finite cluster complexes\nby Alfredo Ná
jera Chávez (Instituto de Matemáticas UNAM) as part of Clusters and brai
ds seminar\n\n\nAbstract\nThe purpose of this talk is to elaborate on a ge
ometric relationship between cluster algebras and cluster complexes. In va
gue words this relationship is the following: cluster algebras of finite c
luster type with universal coefficients may be obtained via a torus action
on a Hilbert scheme. In particular\, we will discuss the deformation theo
ry of the Stanley-Reisner ring associated to a finite cluster complex and
present some applications related to the Gröbner theory of the ideal of r
elations among cluster and frozen variables of a cluster algebra of finite
cluster type. This is based on a joint project with Nathan Ilten and Hipo
lito Treffinger.\n
LOCATION:https://researchseminars.org/talk/ClusterBraids/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Pressland (University of Glasgow)
DTSTART;VALUE=DATE-TIME:20220606T153000Z
DTEND;VALUE=DATE-TIME:20220606T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T222508Z
UID:ClusterBraids/12
DESCRIPTION:Title: Categorification for positroid varieties\nby Matthew Pressland
(University of Glasgow) as part of Clusters and braids seminar\n\nAbstract
: TBA\n
LOCATION:https://researchseminars.org/talk/ClusterBraids/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Lam (University of Michigan)
DTSTART;VALUE=DATE-TIME:20220627T153000Z
DTEND;VALUE=DATE-TIME:20220627T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T222508Z
UID:ClusterBraids/13
DESCRIPTION:Title: Cluster structures for braid varieties\nby Thomas Lam (Universi
ty of Michigan) as part of Clusters and braids seminar\n\n\nAbstract\nBrai
d varieties are affine varieties indexed by positive\nbraids that have bee
n studied much in this seminar series. They have\nconnections to knot hom
ology\, to Legendrian link geometry\, to the\ngeometry of flag varieties\,
and also to cluster algebras.\n\nIn this talk\, I will discuss a cluster
structure on braid varieties\nbased on generalized minors\, Deodhar geomet
ry\, and the Louise property\nfor quivers. This is joint work with Pavel
Galashin\, Melissa\nSherman-Bennett\, and David Speyer.\n
LOCATION:https://researchseminars.org/talk/ClusterBraids/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kalck (University of Freiburg)
DTSTART;VALUE=DATE-TIME:20221121T170000Z
DTEND;VALUE=DATE-TIME:20221121T183000Z
DTSTAMP;VALUE=DATE-TIME:20221209T222508Z
UID:ClusterBraids/14
DESCRIPTION:Title: Describing Leclerc’s Frobenius categories as categories of Gorens
tein projective modules\nby Martin Kalck (University of Freiburg) as p
art of Clusters and braids seminar\n\n\nAbstract\nIn 2016\, Leclerc introd
uced a new class of Frobenius categories in order to obtain (partly conjec
tural) cluster algebra structures on coordinate rings of open Richardson v
arieties. \n\nVery recently\, this approach has been completed and general
ized in work of Casals\, Gorsky\, Gorsky\, Le\, Shen & Simental. More prec
isely\, for open Richardson varieties their construction corresponds to th
e seed introduced by Ménard. An alternative approach to obtain cluster st
ructures for open Richardson varieties has been announced by Galashin\, La
m\, Sherman-Bennett & Speyer.\n\nWe explain that Leclerc's categories are
equivalent to categories of Gorenstein projective modules (aka maximal Coh
en-Macaulay modules) over an Iwanaga-Gorenstein ring of virtual dimension
at most two. This is an analogue of Buan\, Iyama\, Reiten & Scott’s desc
ription of Geiss\, Leclerc & Schröer’s categorification for Schuber cel
ls in terms of Gorenstein projective modules over quotients of preprojecti
ve algebras. \n\nOur talk will be based on https://arxiv.org/pdf/1709.0478
5.pdf.\n
LOCATION:https://researchseminars.org/talk/ClusterBraids/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khrystyna Serhiyenko (University of Kentucky)
DTSTART;VALUE=DATE-TIME:20221128T170000Z
DTEND;VALUE=DATE-TIME:20221128T183000Z
DTSTAMP;VALUE=DATE-TIME:20221209T222508Z
UID:ClusterBraids/15
DESCRIPTION:by Khrystyna Serhiyenko (University of Kentucky) as part of Cl
usters and braids seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ClusterBraids/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Travis Mandel (University of Oklahoma)
DTSTART;VALUE=DATE-TIME:20221205T170000Z
DTEND;VALUE=DATE-TIME:20221205T183000Z
DTSTAMP;VALUE=DATE-TIME:20221209T222508Z
UID:ClusterBraids/16
DESCRIPTION:by Travis Mandel (University of Oklahoma) as part of Clusters
and braids seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ClusterBraids/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greg Muller (University of Oklahoma)
DTSTART;VALUE=DATE-TIME:20221212T170000Z
DTEND;VALUE=DATE-TIME:20221212T183000Z
DTSTAMP;VALUE=DATE-TIME:20221209T222508Z
UID:ClusterBraids/17
DESCRIPTION:by Greg Muller (University of Oklahoma) as part of Clusters an
d braids seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ClusterBraids/17/
END:VEVENT
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