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BEGIN:VEVENT
SUMMARY:Michael Shapiro (Michigan State University)
DTSTART;VALUE=DATE-TIME:20200901T150000Z
DTEND;VALUE=DATE-TIME:20200901T160000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113801Z
UID:OCAS/1
DESCRIPTION:Title: Non-commutative Networks on a Cylinder\nby Michael Shap
iro (Michigan State University) as part of Online Cluster Algebra Seminar
(OCAS)\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li Li (Oakland University)
DTSTART;VALUE=DATE-TIME:20200908T150000Z
DTEND;VALUE=DATE-TIME:20200908T160000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113801Z
UID:OCAS/2
DESCRIPTION:Title: A proof of two conjectures on Markov Numbers\nby Li Li
(Oakland University) as part of Online Cluster Algebra Seminar (OCAS)\n\nA
bstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lara Bossinger (UNAM-Oaxaca)
DTSTART;VALUE=DATE-TIME:20200915T150000Z
DTEND;VALUE=DATE-TIME:20200915T160000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113801Z
UID:OCAS/3
DESCRIPTION:Title: Understanding universal coefficients of Grassmannians t
hrough Groebner theory\nby Lara Bossinger (UNAM-Oaxaca) as part of Online
Cluster Algebra Seminar (OCAS)\n\n\nAbstract\nIn this talk I will present
recent results of a joint work with Fatemeh Mohammadi and Alfredo Nájera
Chávez. For a polarized weighted projective variety V(J) we introduce a
flat family that combines all Groebner degenerations of V associated to a
maximal cone in the Groebner fan of J. It turns out that this family can a
lternatively be obtained as a pull-back of a toric family (in the sense of
Kaveh--Manon's classification of such).\nThe most surprising application
of this construction is its relation to cluster algebras with universal co
efficients. To demonstrate this connection we analyze the cases of the Gra
ssmannians Gr(2\,n) and Gr(3\,6) in depth.\nFor Gr(2\,n) we fix its Plueck
er embedding and for Gr(3\,6) what we call its "cluster embedding". In bot
h cases we identify a specific maximal cone C in the Groebner fan of the d
efining ideal such that the algebra defining the flat family mentioned abo
ve is canonically isomorphic to the corresponding cluster algebra with uni
versal coefficients.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Qin (Shanghai Jiao Tong University)
DTSTART;VALUE=DATE-TIME:20200922T150000Z
DTEND;VALUE=DATE-TIME:20200922T160000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113801Z
UID:OCAS/4
DESCRIPTION:Title: Dual canonical bases and triangular bases of quantum cl
uster algebras\nby Fan Qin (Shanghai Jiao Tong University) as part of Onli
ne Cluster Algebra Seminar (OCAS)\n\n\nAbstract\nOne of the main motivatio
ns for cluster algebras was to create a combinatorial framework to study t
he dual canonical bases. Correspondingly\, it has been long expected that
the quantum cluster monomials (certain monomials of generators) belong to
the dual canonical bases (of quantum unipotent subgroups) up to scalar mul
tiples. We discuss how to use the triangular bases to show this conjecture
in full generality. Moreover\, we show that the (double) triangular bases
verify an analog of Leclerc’s conjecture for dual canonical bases.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Esther Banaian (University of Minnesota)
DTSTART;VALUE=DATE-TIME:20200929T150000Z
DTEND;VALUE=DATE-TIME:20200929T160000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113801Z
UID:OCAS/5
DESCRIPTION:Title: Frieze Patterns from Dissections\nby Esther Banaian (Un
iversity of Minnesota) as part of Online Cluster Algebra Seminar (OCAS)\n\
n\nAbstract\nFinite frieze patterns of positive integers were shown by Co
nway and Coxeter to be in bijection with triangulated polygons. Baur\, Par
sons\, and Tschabold generalized this result\, showing that infinite\nfrie
ze patterns of positive integers are in bijection with triangulated annul
i and once-punctured discs. More recently\, Holm and Jørgensen investigat
ed frieze patterns arising from dissected polygons.\nThe frieze patterns o
f Holm and Jørgensen involve algebraic integers of the form 2cos(pi/p)
for an integer p. We combine these generalizations and present results on
frieze patterns from dissected\nannuli\, using these same algebraic integ
ers. We also discuss how some of these frieze patterns from dissections ca
n be connected to generalized cluster algebras\, in the sense of Chekhov
and Shapiro.\nThis is based on joint work with Jiuqi (Lena) Chen and with
Elizabeth Kelley.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Sherman-Bennett (UC Berkely and Harvard University)
DTSTART;VALUE=DATE-TIME:20201006T150000Z
DTEND;VALUE=DATE-TIME:20201006T160000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113801Z
UID:OCAS/6
DESCRIPTION:Title: Many cluster structures on positroid varieties\nby Meli
ssa Sherman-Bennett (UC Berkely and Harvard University) as part of Online
Cluster Algebra Seminar (OCAS)\n\n\nAbstract\nEarly in the history of clus
ter algebras\, Scott showed that the homogeneous coordinate ring of the Gr
assmannian is a cluster algebra\, with seeds given by Postnikov's plabic
graphs for the\nGrassmannian. Recently the analogous statement has been pr
oved for open Schubert varieties (Leclerc\, Serhiyenko-SB-Williams) and mo
re generally\, for open positroid varieties (Galashin-Lam). I'll\ndiscuss
joint work with Chris Fraser\, in which we give a family of cluster struct
ures on open Schubert (and more generally\, positroid) varieties. Each of
the cluster structures in this family has seeds given by face labels of re
labeled plabic graphs\, which are plabic graphs whose boundary is labeled
by a permutation of 1\, ...\, n. For Schubert varieties\, all cluster stru
ctures in this family\nquasi-coincide\, meaning they differ only by rescal
ing by frozen variables and their cluster monomials coincide. In particula
r\, all relabeled plabic graphs for a Schubert variety give rise to seeds
in the "usual" cluster algebra structure on the coordinate ring. As part o
f our results\, we show the "target" and "source" cluster structures on Sc
hubert varieties quasi-coincide\, confirming a conjecture of Muller and Sp
eyer. One proof tool of independent interest is a permuted version of the
Muller-Speyer twist map\, which we use to prove many (open) positroid vari
eties are isomorphic.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Jørgensen (Aarhus University)
DTSTART;VALUE=DATE-TIME:20201013T150000Z
DTEND;VALUE=DATE-TIME:20201013T160000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113801Z
UID:OCAS/7
DESCRIPTION:Title: The green groupoid and its action on derived categories
(joint work with Milen Yakimov)\nby Peter Jørgensen (Aarhus University)
as part of Online Cluster Algebra Seminar (OCAS)\n\n\nAbstract\nWe introdu
ce the green groupoid $\\mathcal{G}$ of a $2$-Calabi-Yau triangulated cate
gory $\\mathcal{C}$. It is an augmentation of the mutation graph of $\\ma
thcal{C}$\, which is defined by means of silting theory.\n\nThe green grou
poid $\\mathcal{G}$ has certain key properties:\n\n1. If $\\mathcal{C}$ is
the stable category of a Frobenius category $\\mathcal{E}$\, then $\\math
cal{G}$ acs on the derived categories of the endomorphism rings $\\mathcal
{E}(m\,m)$ where $m$ is a maximal rigid object.\n\n2. $\\mathcal{G}$ can b
e obtained geometrically from the $g$-vector fan of $\\mathcal{C}$.\n\n3.
If the $g$-vector fan of $\\mathcal{C}$ is a hyperplane arrangement $\\mat
hcal{H}$\, then $\\mathcal{G}$ specialises to the Deligne groupoid of $\\m
athcal{H}$\, and $\\mathcal{G}$ acts faithfully on the derived categories
of the endomorphism rings $\\mathcal{E}(m\,m)$.\n\nThe situation in (3) oc
curs if $\\Sigma_{\\mathcal{C}}^2$\, the square of the suspension functor\
, is the identity. It recovers results by Donovan\, Hirano\, and Wemyss w
here $\\mathcal{E}$ is the category of maximal Cohen-Macaulay modules over
a suitable singularity.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Lam (University of Michigan)
DTSTART;VALUE=DATE-TIME:20201020T150000Z
DTEND;VALUE=DATE-TIME:20201020T160000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113801Z
UID:OCAS/8
DESCRIPTION:Title: Cluster configuration spaces of finite type\nby Thomas
Lam (University of Michigan) as part of Online Cluster Algebra Seminar (OC
AS)\n\n\nAbstract\nI will talk about a "cluster configuration space" $M_D$
\,\ndepending on a finite Dynkin diagram $D$. The space $M_D$ is an affin
e\nalgebraic variety that is defined using only the compatibility degree\n
of the corresponding finite-type cluster algebra. In the case that $D$\ni
s of type $A$\, we recover the configuration space $M_{0\,n}$ of $n$\n(dis
tinct) points in $P^1$. There are many relations to finite-type\ncluster
theory\, but an especially close connection to the finite-type\ncluster al
gebra with universal coefficients.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregg Musiker (University of Minnesota)
DTSTART;VALUE=DATE-TIME:20201117T160000Z
DTEND;VALUE=DATE-TIME:20201117T170000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113801Z
UID:OCAS/9
DESCRIPTION:Title: Double-dimer configurations and quivers of dP3 (del Pez
zo) type\nby Gregg Musiker (University of Minnesota) as part of Online Clu
ster Algebra Seminar (OCAS)\n\n\nAbstract\nIn this talk\, I will describe
our work extending combinatorial interpretations for so called toric clust
er variables as was previously studied by myself and Tri Lai. In [LM 2017]
and [LM 2020]\, most toric cluster variables were shown to have Laurent e
xpansions agreeing with partition functions of dimers on subgraphs cut out
by six-sided contours. However\, the case of cluster variables\nparameter
ized by six-sided contours with a self-intersection eluded our techniques.
In this talk we discuss our research rectifying this issue by using Helen
Jenne’s condensation results for the\ndouble-dimer model [J 2019]. Whil
e we focus on quivers of dP3 type of Model 1 and Model 4\, we anticipate o
ur techniques will extend to certain additional cluster algebras related t
o brane tilings. \nThis is joint work with Helen Jenne and Tri Lai.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karin Baur (University of Leeds)
DTSTART;VALUE=DATE-TIME:20201103T160000Z
DTEND;VALUE=DATE-TIME:20201103T170000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113801Z
UID:OCAS/10
DESCRIPTION:Title: Flips in triangulations and matchings\nby Karin Baur (U
niversity of Leeds) as part of Online Cluster Algebra Seminar (OCAS)\n\n\n
Abstract\nPlane perfect matchings of $2n$ points in convex position are kn
own to be in\nbijection with triangulations of convex polygons of size $n
+ 2$\; they are\nboth counted by the Catalan numbers.\nWe explain how to g
ive a direct bijection and how it can be extended to a\nbijection between
monochromatic matchings on $k$ colours and tilings by\n$(k+2)$-gons. Edge
flips are a classic operation to perform local changes in\nboth sets. We u
se the above bijection to determine the two types of edge\nflips are relat
ed. We use this to give an algebraic interpretation of the\nflip graph of
triangulations in terms of elements of the corresponding\nTemperley-Lieb a
lgebra.\nThis is joint work with\nO. Aichholzer\, L. Donner (Andritsch)\,
B. Vogtenhuber.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Allegretti (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20201110T160000Z
DTEND;VALUE=DATE-TIME:20201110T170000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113801Z
UID:OCAS/11
DESCRIPTION:Title: Stability conditions and cluster varieties\nby Dylan Al
legretti (University of British Columbia) as part of Online Cluster Algebr
a Seminar (OCAS)\n\n\nAbstract\nIn the first part of the talk\, I will des
cribe a construction in low-dimensional topology that takes a holomorphic
quadratic differential on a surface and produces a $PGL(2)$-local system.
This\nconstruction provides a local homeomorphism from the moduli space of
quadratic differentials to the moduli space of local systems. In the seco
nd part of the talk\, I will propose a categorical\ngeneralization of this
construction. In this generalization\, the space of quadratic differentia
ls is replaced by a complex manifold parametrizing Bridgeland stability co
nditions on a certain\n3-Calabi-Yau triangulated category\, while the spac
e of local systems is replaced by a cluster variety. I will describe a loc
al homeomorphism from the space of stability conditions to the cluster\nva
riety in a large class of examples and explain how it preserves the struct
ures of these two spaces.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christof Geiss
DTSTART;VALUE=DATE-TIME:20201208T160000Z
DTEND;VALUE=DATE-TIME:20201208T170000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113801Z
UID:OCAS/12
DESCRIPTION:by Christof Geiss as part of Online Cluster Algebra Seminar (O
CAS)\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Reading (North Carolina State University)
DTSTART;VALUE=DATE-TIME:20210119T160000Z
DTEND;VALUE=DATE-TIME:20210119T170000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113801Z
UID:OCAS/13
DESCRIPTION:by Nathan Reading (North Carolina State University) as part of
Online Cluster Algebra Seminar (OCAS)\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruce Sagan (Michigan State University)
DTSTART;VALUE=DATE-TIME:20201124T160000Z
DTEND;VALUE=DATE-TIME:20201124T170000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113801Z
UID:OCAS/14
DESCRIPTION:Title: On a rank-unimodality conjecture of Morier-Genoud and O
vsienko\nby Bruce Sagan (Michigan State University) as part of Online Clus
ter Algebra Seminar (OCAS)\n\n\nAbstract\nLet $\\alpha=(a\,b\,\\ldots)$ be
a composition\, that is\, a finite sequence of positive integers. Consid
er the associated partially ordered set $F(\\alpha)$\, called a fence\, wh
ose covering relations are\n$$
\nx_1\\lhd x_2 \\lhd \\ldots\\lhd x_{a+1}\\rhd x_{a+2}\\rhd \\l
dots\\rhd x_{a+b+1}\\lhd x_{a+b+2}\\lhd \\ldots\\ .
\n$$\nWe study the associated distributive lattice $L(\\alpha)$ co
nsisting of all lower order ideals of $F(\\alpha)$.\nThese lattices are im
portant in the theory of cluster algebras and their rank generating functi
ons can be used to define $q$-analogues of rational numbers.\nWe make prog
ress on a recent conjecture of Morier-Genoud and Ovsienko that $L(\\alpha)
$ is rank unimodal.\nAll terms from the theory of partially ordered sets w
ill be carefully defined. This is joint work with Thomas McConville and C
lifford Smyth.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elizabeth Kelley (University of Minnesota)
DTSTART;VALUE=DATE-TIME:20201201T160000Z
DTEND;VALUE=DATE-TIME:20201201T170000Z
DTSTAMP;VALUE=DATE-TIME:20201029T113801Z
UID:OCAS/15
DESCRIPTION:by Elizabeth Kelley (University of Minnesota) as part of Onlin
e Cluster Algebra Seminar (OCAS)\n\nAbstract: TBA\n
END:VEVENT
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