BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Osamu Iyama (Nagoya)
DTSTART;VALUE=DATE-TIME:20200817T130000Z
DTEND;VALUE=DATE-TIME:20200817T134500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/1
DESCRIPTION:Title: Simple-minded systems in cluster categories and generalized cl
uster complexes\nby Osamu Iyama (Nagoya) as part of Cluster algebras 2
020\n\n\nAbstract\nThe set S of simple modules over an algebra satisfies t
hree basic properties in the derived category: Schur’s Lemma\, vanishing
of negative extensions\, and generating. For a positive integer d\, Coelh
o-Simoes introduced the notion of d-simple-minded systems (d-SMS) by using
analogous 3 conditions depending on d. A typical example of d-SMS is give
n by the set of simple dg modules over a d-self-injective dg algebra in th
e singularity category [Riedtmann for d=1 (1980)\, Jin for any d\, (2019)]
.\nIn this talk\, I will discuss d-SMSs in the (−d)-cluster category C o
f the path algebra kQ of a Dynkin quiver Q. We show that there is a biject
ion between d-SMSs in C and positive maximal simplices of the generalized
cluster complex \\Delta^d(Q) of Fomin-Reading. In particular\, the number
of d-SMSs in C is given by the positive Fuss-Catalan number C_d^+(Q). To p
rove this\, we give a bijection between d-SMSs in C and silting objects in
the derived category D^b(kQ) whose cohomologies are concentrated in degre
es 0\,1\,…\,d-1. This bijection is based on the silting-t-structure corr
espondence\, and holds true also for any acyclic quiver by an independent
result of Coelho-Simoes-Pauksztello-Ploog. We also use Buan-Reiten-Thomas'
and Zhu's results on generalized cluster complexes.\nThis is a joint work
with Haibo Jin (arXiv:2002.09952).\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiuping Su (Bath)
DTSTART;VALUE=DATE-TIME:20200817T140000Z
DTEND;VALUE=DATE-TIME:20200817T144500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/2
DESCRIPTION:Title: Categorifying flow polynomials and Newton-Okounkov bodies\
nby Xiuping Su (Bath) as part of Cluster algebras 2020\n\n\nAbstract\nIn t
his talk I will define an invariant in the Grassmannian cluster category C
M(A)\, apply the invariant to study flow polynomials defined on a network
chart and explain its link to the Newton-Okounkov body constructed by Riet
sch-Williams. \n\nThis talk is based on an ongoing project joint with B T
Jensen and A King.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Goncharov (Yale)
DTSTART;VALUE=DATE-TIME:20200818T000000Z
DTEND;VALUE=DATE-TIME:20200818T004500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/4
DESCRIPTION:Title: Cluster nature of the second universal motivic Chern class
\nby Alexander Goncharov (Yale) as part of Cluster algebras 2020\n\n\nAbst
ract\nLet G be a split\, simply-connected\, semi-simple group over Q. Deno
te by BG the classifying space of the group G.\n\nThe degree 4\, weight 2\
, integral motivic cohomology group of BG is isomorphic to Z. The generato
r C_2\, known as the second universal motivic Chern class\, plays an impor
tant role in arithmetic\, algebraic geometry\, representation theory and m
athematical physics.\n\nFor the group GL(m)\, there is an explicit constru
ction of a cocycle for the generator C_2 which I found in 1993. A decade l
ater it was used in our work with V. Fock on higher Teichmuller theory. Ho
wever a similar explicit construction for any group G was not known till n
ow. \n\nI will explain that such a construction follows from\, and in fact
is essentially equivalent to\, the main result of our recent work with Li
nhui Shen on the cluster structure of the moduli space A(G\,S)\, closely r
elated to the space of G-local systems on a decorated surface S\, plus "ep
silon". \n\nApplications include the following:\n\ni) An explicit combinat
orial construction of the second Chern class of a G-bundle on a manifold.\
n\nii) An explicit construction of the determinant line bundle on the affi
ne Grassmannian\, and of the Kac-Moody group.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State)
DTSTART;VALUE=DATE-TIME:20200818T140000Z
DTEND;VALUE=DATE-TIME:20200818T144500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/5
DESCRIPTION:Title: Legendrian links with infinitely many exact Lagrangian filling
s\nby Linhui Shen (Michigan State) as part of Cluster algebras 2020\n\
n\nAbstract\nThe space $R^3$ is equipped with the standard contact structu
re from the 1-form $\\alpha = y dx -dz$. A Legendrian link in $R^3$ is a l
ink $\\Lambda$ such that the restriction of $\\alpha$ to $\\Lambda$ vanish
es. In this talk\, we focus on Legendrian links that are obtained as the r
ainbow closure of positive braids. We show that if the quiver associated t
o any positive braid is not mutation equivalent to a finite type quiver\,
then the corresponding Legendrian link has infinitely many exact Lagrangia
n fillings. The main technique of this proof includes cluster algebras and
Chekanov-Eliashberg differential graded algebras. This is joint work in p
rogress with Honghao Gao and Daping Weng.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Allegretti (U. British Columbia)
DTSTART;VALUE=DATE-TIME:20200818T150000Z
DTEND;VALUE=DATE-TIME:20200818T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/6
DESCRIPTION:Title: Exact WKB analysis and Riemann-Hilbert problems\nby Dylan
Allegretti (U. British Columbia) as part of Cluster algebras 2020\n\n\nAbs
tract\nExact WKB analysis is a tool for constructing exact solutions of Sc
hrödinger's equation. Recently\, Iwaki and Nakanishi discovered a surpris
ing link between exact WKB analysis and cluster algebras. In this talk\, I
will explain how these ideas can be used to solve a certain Riemann-Hilbe
rt problem posed by Bridgeland in the context of Donaldson-Thomas theory.\
n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Se-jin Oh (Ewha Womans U.)
DTSTART;VALUE=DATE-TIME:20200819T130000Z
DTEND;VALUE=DATE-TIME:20200819T134500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/7
DESCRIPTION:Title: Monoidal categorification and quantum affine algebras\nby
Se-jin Oh (Ewha Womans U.) as part of Cluster algebras 2020\n\n\nAbstract\
nThe notion of monoidal categorification\, introduced by Hernandez and Lec
lerc is a one of the tools for proving the (quantum) Laurent positivity an
d phenomenon of cluster algebras. In the cowork with Kashiwara\, Kim and P
ark\, we proved that lots of categories over quantum affine algebras provi
de monoidal categorification of cluster algebras by introducing new intege
r-valued invariants and using several known results. In this talk\, I will
introduce these results and show several quivers related to the result. I
f time permits\, I will show that the result can be generalized to quantum
version by using the recent result with Fujita.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sabin Cautis (U. British Columbia)
DTSTART;VALUE=DATE-TIME:20200820T000000Z
DTEND;VALUE=DATE-TIME:20200820T004500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/8
DESCRIPTION:Title: Categorical structure of Coulomb branches of 4D N=2 gauge theo
ries\nby Sabin Cautis (U. British Columbia) as part of Cluster algebra
s 2020\n\n\nAbstract\nWe will discuss the categorical structure of Coulomb
branches. For concreteness we focus on the massless case which is just th
e category of coherent sheaves on the affine Grassmannian (the coherent Sa
take category).\n\nThese categories are conjecturally governed by a cluste
r algebra structure. We describe a solution of this conjecture in the case
of general linear groups and discuss its extension to more general Coulom
b branches of 4D N=2 gauge theories. This is joint work with Harold Willia
ms.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peng Shan (YMC Tsinghua)
DTSTART;VALUE=DATE-TIME:20200820T130000Z
DTEND;VALUE=DATE-TIME:20200820T134500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/9
DESCRIPTION:Title: Coherent categorification of quantum loop sl(2)\nby Peng S
han (YMC Tsinghua) as part of Cluster algebras 2020\n\n\nAbstract\nWe expl
ain an equivalence of categories between a module category of quiver Hecke
algebras associated with the Kronecker quiver and a category of equivaria
nt perverse coherent sheaves on the nilpotent cone of type A. This provide
s a link between two different monoidal categorifications of the open quan
tum unipotent cell of affine type A_1\, one given by Kang-Kashiwara-Kim-Oh
-Park in terms of quiver Hecke algebras\, the other given by Cautis-Willia
ms in terms of equivariant perverse coherent sheaves on affine Grassmannia
ns. This is a joint work with Michela Varagnolo and Eric Vasserot.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (Toronto)
DTSTART;VALUE=DATE-TIME:20200820T140000Z
DTEND;VALUE=DATE-TIME:20200820T144500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/10
DESCRIPTION:Title: The theta basis and the Mirkovic-Vilonen basis\nby Joel K
amnitzer (Toronto) as part of Cluster algebras 2020\n\n\nAbstract\nWhen Fo
min and Zelevinsky invented cluster algebras\, one motivation was to under
stand canonical bases in representation theory. More recently\, Gross\, Ha
cking\, Keel\, and Kontsevich constructed the theta basis in a large class
of cluster algebras. On the other hand\, in representation theory\, we ha
ve the Mirkovic-Vilonen basis\, constructed using the geometric Satake cor
respondence. I will explain our attempts to relate the Mirkovic-Vilonen ba
sis to cluster algebras and to the theta basis.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gus Schrader (Columbia)
DTSTART;VALUE=DATE-TIME:20200821T010000Z
DTEND;VALUE=DATE-TIME:20200821T014500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/11
DESCRIPTION:Title: An alternative polynomial representation of spherical DAHA\nby Gus Schrader (Columbia) as part of Cluster algebras 2020\n\n\nAbstra
ct\nThe spherical subalgebra of Cherednik's double affine Hecke algebra of
type A has a polynomial representation in which the algebra acts on a spa
ce of symmetric Laurent polynomials by rational q-difference operators. Th
is representation has many useful applications e.g. to the theory of Macdo
nald polynomials. I'll present an alternative polynomial representation of
the spherical DAHA\, in which the algebra acts on a space of non-symmetri
c Laurent polynomials by Laurent polynomial q-difference operators. This l
atter representation turns out to be compatible with a natural cluster alg
ebra structure\, in such a way that the action of the modular group on DAH
A is given by cluster transformations. Based on joint work in progress wit
h Philippe di Francesco\, Rinat Kedem\, and Alexander Shapiro.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasia Volovich (Brown U.)
DTSTART;VALUE=DATE-TIME:20200821T130000Z
DTEND;VALUE=DATE-TIME:20200821T134500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/12
DESCRIPTION:Title: Cluster Algebras\, Plabic Graphs and Scattering Amplitudes\nby Anastasia Volovich (Brown U.) as part of Cluster algebras 2020\n\nAb
stract: TBA\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Song He (ITP Beijing)
DTSTART;VALUE=DATE-TIME:20200821T140000Z
DTEND;VALUE=DATE-TIME:20200821T144500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/13
DESCRIPTION:Title: Generalized associahedra and scattering of particles and stri
ngs\nby Song He (ITP Beijing) as part of Cluster algebras 2020\n\n\nAb
stract\nI will review recent works connecting generalized associahedra and
cluster algebras to scattering amplitudes of (certain generalizations) of
particles and strings. Tree amplitudes of a cubic scalar theory are given
by "canonical forms" of associahedra in kinematic space. The rule for con
structing the associahedron can be abstracted away to a certain “walk”
associated with any acyclic quiver\, remarkably yielding a finite polytop
e for the case of Dynkin quivers\, and for classical types they give scala
r amplitudes through one-loop order. Furthermore\, we introduce "cluster c
onfiguration spaces" and associated open and closed "cluster string integr
als" for any Dynkin diagram\, which for type A reduces to usual moduli spa
ces and string amplitudes. Both the geometries and integrals enjoy remarka
ble factorization properties at finite α′ (inverse of string tension)\,
obtained simply by removing nodes of the Dynkin diagram\, and as α′
→ 0 the integrals reduce to canonical forms of our generalized associahe
dra.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Hernandez (Paris)
DTSTART;VALUE=DATE-TIME:20200824T130000Z
DTEND;VALUE=DATE-TIME:20200824T134500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/14
DESCRIPTION:Title: Deformations of Grothendieck rings and toroidal cluster algeb
ras\nby David Hernandez (Paris) as part of Cluster algebras 2020\n\n\n
Abstract\nThe Grothendieck ring K(C) of a category C of finite-dimensional
representations of a quantum affine algebra admit natural quantum deforma
tions obtained from perverse sheaves on quiver varieties\, from deformed W
-algebras or from vertex operators on quantum Heisenberg algebras. We revi
ew and discuss the interplay with the cluster algebra structures introduce
d with Bernard Leclerc. We also discuss how cluster algebras with several
quantum parameters (toroidal cluster algebras) appear in this context (bas
ed in part on joint works with Laura Fedele\, Bernard Leclerc and Hironori
Oya).\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Misha Gekhtman (Notre Dame)
DTSTART;VALUE=DATE-TIME:20200824T140000Z
DTEND;VALUE=DATE-TIME:20200824T144500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/15
DESCRIPTION:Title: Generalized cluster structures related to the Drinfeld double
of GL(n)\nby Misha Gekhtman (Notre Dame) as part of Cluster algebras
2020\n\n\nAbstract\nI will present a unifying approach to a construction o
f several generalized cluster structures of geometric type. Examples inclu
de the Drinfeld double of GL(n)\, spaces of periodic difference operators
and generalized cluster structures in GL(n) compatible with a certain subc
lass of Belavin-Drinfeld Poisson-Lie brackets. Based on a joint work with
M. Shapiro and A. Vainshtein.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toshiya Yurikusa (Tohoku)
DTSTART;VALUE=DATE-TIME:20200825T010000Z
DTEND;VALUE=DATE-TIME:20200825T014500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/16
DESCRIPTION:Title: Cluster algebras with dense g-vector fans\nby Toshiya Yur
ikusa (Tohoku) as part of Cluster algebras 2020\n\n\nAbstract\nCluster var
iables (monomials) have a numerical invariant\, called g-vector. The g-vec
tors in a cluster algebra form a simplicial polyhedral fan\, called g-vect
or fan. We give a classification of cluster algebras with dense g-vector f
ans except for some types.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsukasa Ishibashi (RIMS Kyoto)
DTSTART;VALUE=DATE-TIME:20200825T130000Z
DTEND;VALUE=DATE-TIME:20200825T134500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/17
DESCRIPTION:Title: Algebraic entropy of sign-stable mutation loops\nby Tsuka
sa Ishibashi (RIMS Kyoto) as part of Cluster algebras 2020\n\n\nAbstract\n
A mutation loop is a certain equivalence class of a sequence of mutations
and permutations of indices. They form a group called the cluster modular
group\, which can be regarded as a combinatorial generalization of the map
ping class groups of marked surfaces.\nWe introduce a new property of muta
tion loops which we call the “sign stability” as a generalization of t
he pseudo-Anosov property of a mapping class.\nA sign-stable mutation loop
has a numerical invariant which we call the “cluster stretch factor”\
, in analogy with the stretch factor of a pA mapping class. We compute the
algebraic entropies of the cluster A- and X-transformations induced by a
sign-stable mutation loop\, and conclude that these two are estimated by t
he logarithm of the cluster stretch factor. This talk is based on a joint
work with Shunsuke Kano.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milen Yakimov (Louisiana State)
DTSTART;VALUE=DATE-TIME:20200825T140000Z
DTEND;VALUE=DATE-TIME:20200825T144500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/18
DESCRIPTION:Title: Green groupoids of 2-Calabi-Yau categories and derived action
s\nby Milen Yakimov (Louisiana State) as part of Cluster algebras 2020
\n\n\nAbstract\nThis is a joint work with Peter Jorgensen (Aarhus Universi
ty). Starting with work of Seidel and Thomas\, there has been a great inte
rest in the construction of faithful actions of various classes of groups
on derived categories (braid groups\, fundamental groups of hyperplane arr
angements\, mapping class groups). We will present a general construction
of this sort in the setting of algebraic 2-Calabi–Yau triangulated categ
ories. To every 2-Calabi-Yau category C (satisfying standard finiteness co
nditions) we associate a groupoid\, the green grouped of C\, defined in an
intrinsic homological way. In the case of cluster categories\, this can b
e formulated purely combinatorially using the exchange graph of the cluste
r algebra and Keller's notion of maximal green sequence. For every Frobeni
us model of the 2-Calabi-Yau category C\, we construct a categorical repre
sentation of the green groupoid of C. This action is proved to be faithful
under certain general assumptions.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peigen Cao (Paris)
DTSTART;VALUE=DATE-TIME:20200826T130000Z
DTEND;VALUE=DATE-TIME:20200826T134500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/19
DESCRIPTION:Title: The valuation pairing on an upper cluster algebra\nby Pei
gen Cao (Paris) as part of Cluster algebras 2020\n\n\nAbstract\nThis talk
is based on the joint work with B. Keller and F. Qin. It is known that man
y (upper) cluster algebras are not unique factorization domains. In order
to study the local factorization properties of upper cluster algebras\, we
introduce the valuation pairing on any upper cluster algebra $\\mathcal U
$. To each pair $(A_{k\;t}\,M)$ consisting of a cluster variable $A_{k\;t}
$ and an element $M$ in $\\mathcal U$\, it associates the largest integer
$s$ (maybe infinity) such that $M/A_{k\;t}^s$ still belongs to $\\mathcal
U$. Using the valuation pairing we prove that any full rank upper cluster
algebra has the following locally unique factorization property: For each
seed $t$ of $\\mathcal U$\, any non-zero element $M$ can be uniquely facto
rized as $M=N\\cdot L$\, where $N$ is a cluster monomial in $t$ and $L$ is
an element in $\\mathcal U$ not divisible by any cluster variable in $t$.
\n\nWe give many applications to $d$-vectors\, $F$-polynomials\, factorial
ity of upper cluster algebras and combinatorics of cluster Poisson variabl
es. To be more precisely\, firstly\, we prove that a full rank upper clust
er algebra $\\mathcal U$ with initial seed $t_0$ is factorial if and only
if each exchange binomial of $t_0$ is irreducible in the corresponding pol
ynomial ring. In particular\, full rank and primitive upper cluster algebr
as are factorial\, which include principal coefficients upper cluster alge
bras as a special case. Secondly\, we show how to express the $d$-compatib
ility degree and $d$-vectors using the valuation pairing. Thirdly\, we pro
ve that if a cluster monomial $M$ contains no initial cluster variables\,
then $M$ is uniquely determined by its $F$-polynomial $F_M$. Fourthly\, we
prove that the $F$-polynomials of non-initial cluster variables are irred
ucible.\n\nThanks to the results on $F$-polynomials\, we give several equi
valent characterizations when two cluster Poisson variables are equal. As
the first application\, we prove that the cluster Poisson variables of a c
luster Poisson algebra $\\mathcal X$ parameterize the $\\mathscr A$-exchan
ge pairs of an upper cluster algebra $\\mathcal U$ of the same type with $
\\mathcal X$. As the second application\, we prove that the $\\mathscr X$-
seeds of $\\mathcal X$ whose Poisson clusters containing particular cluste
r Poisson variables forms a connected subgraph of the exchange graph of $\
\mathcal X$.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Fraser (Minneapolis)
DTSTART;VALUE=DATE-TIME:20200826T140000Z
DTEND;VALUE=DATE-TIME:20200826T144500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/20
DESCRIPTION:Title: Cyclic symmetry loci in Grassmannians\nby Chris Fraser (M
inneapolis) as part of Cluster algebras 2020\n\n\nAbstract\nThe Grassmanni
an Gr(k\,n) admits an action by a finite cyclic group of order n via the c
yclic shift automorphism. We study cyclic symmetry loci\, i.e. the set of
points in the Grassmannian fixed by a given iterate of the cyclic shift ma
p. We give a simple geometric description of the fixed point locus\, give
a cell decomposition of its set of totally nonnegative points\, and discus
s the existence of generalized cluster charts (in the sense of Chekhov and
Shapiro).\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Sherman-Bennett (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20200826T150000Z
DTEND;VALUE=DATE-TIME:20200826T154500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/21
DESCRIPTION:Title: Many cluster structures on Schubert varieties\nby Melissa
Sherman-Bennett (UC Berkeley) as part of Cluster algebras 2020\n\n\nAbstr
act\nWe give a family of cluster structures on Schubert (and more generall
y\, positroid) varieties in the Grassmannian. Each of the cluster structur
es in this family has seeds given by face labels of relabeled plabic graph
s\, which are plabic graphs whose boundary is labeled by a permutation of
1\, ...\, n. For Schubert varieties\, all cluster structures in this famil
y quasi-coincide\, meaning they differ only by rescaling by frozen variabl
es and their cluster monomials coincide. As part of our results\, we show
the "target" and "source" cluster structures on Schubert varieties quasi-c
oincide\, confirming a conjecture of Muller and Speyer. One proof tool of
independent interest is a permuted version of the Muller-Speyer twist map\
, which we use to prove many (open) positroid varieties are isomorphic.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Yue Yu (Paris Saclay)
DTSTART;VALUE=DATE-TIME:20200827T130000Z
DTEND;VALUE=DATE-TIME:20200827T134500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/22
DESCRIPTION:Title: Cluster algebra via non-archimedean geometry\nby Tony Yue
Yu (Paris Saclay) as part of Cluster algebras 2020\n\n\nAbstract\nI will
explain the enumeration of non-archimedean analytic curves in cluster vari
eties. We can construct a canonical scattering diagram via the enumeration
of infinitesimal non-archimedean cylinders and prove the Kontsevich-Soibe
lman consistency. Moreover\, we prove a comparison theorem with the combin
atorial constructions of Gross-Hacking-Keel-Kontsevich. This has several n
ice implications\, such as the broken-line convexity conjecture\, a geomet
ric proof of the positivity in the Laurent phenomenon\, removal of the EGM
assumption in GHKK\, and the independence of the mirror algebra on the ch
oice of cluster structure\, as conjectured by GHKK. This is part of my joi
nt work with Keel\, arXiv:1908.09861.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Travis Mandel (Oklahoma)
DTSTART;VALUE=DATE-TIME:20200827T140000Z
DTEND;VALUE=DATE-TIME:20200827T144500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/23
DESCRIPTION:Title: Quantum theta bases\nby Travis Mandel (Oklahoma) as part
of Cluster algebras 2020\n\n\nAbstract\nI will discuss joint work with Ben
Davison in which we construct the quantum analog of the Gross-Hacking-Kee
l-Kontsevich theta bases. We prove that these quantum theta bases satisfy
the expected properties\, particularly universal and strong positivity an
d atomicity with respect to the quantum scattering atlas. The constructio
n uses quantum scattering diagrams\, and the positivity proof relies on de
ep ideas from the DT-theory of quiver representations. For (quantum) clus
ter algebras from surfaces\, upcoming joint work with Fan Qin will show th
at (quantum) theta bases agree with the (quantum) bracelet bases.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Man-wai Cheung (Harvard)
DTSTART;VALUE=DATE-TIME:20200828T130000Z
DTEND;VALUE=DATE-TIME:20200828T134500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/24
DESCRIPTION:Title: Polytopes\, wall crossings\, and cluster varieties\nby Ma
n-wai Cheung (Harvard) as part of Cluster algebras 2020\n\n\nAbstract\nClu
ster varieties are log Calabi-Yau varieties which are a union of algebraic
tori glued by birational "mutation" maps. Partial compactifications of th
e varieties\, studied by Gross\, Hacking\, Keel\, and Kontsevich\, general
ize the polytope construction of toric varieties. However\, it is not clea
r from the definitions how to characterize the polytopes giving compactifi
cations of cluster varieties. We will show how to describe the compactific
ations easily by broken line convexity. As an application\, we will see th
e non-integral vertex in the Newton Okounkov body of Gr(3\,6) comes from b
roken line convexity. Further\, we will also see certain positive polytope
s will give us hints about the Batyrev mirror in the cluster setting. The
mutations of the polytopes will be related to the almost toric fibration f
rom the symplectic point of view. Finally\, we can see how to extend the i
dea of gluing of tori in Floer theory which then ended up with the Family
Floer Mirror for the del Pezzo surfaces of degree 5 and 6. The talk will b
e based on a series of joint works with Bossinger\, Lin\, Magee\, Najera-C
havez\, and Vianna.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lara Bossinger (UNAM Oaxaca)
DTSTART;VALUE=DATE-TIME:20200828T140000Z
DTEND;VALUE=DATE-TIME:20200828T144500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/25
DESCRIPTION:Title: Families of Gröbner degenerations\, Grassmannians and univer
sal cluster algebras\nby Lara Bossinger (UNAM Oaxaca) as part of Clust
er algebras 2020\n\n\nAbstract\nLet V be the weighted projective variety d
efined by a weighted homogeneous ideal J and C a maximal cone in the Gröb
ner fan of J with m rays. We construct a flat family over affine m-space t
hat assembles the Gröbner degenerations of V associated with all faces of
C. This is a multi-parameter generalization of the classical one-paramete
r Gröbner degeneration associated to a weight. We show that our family ca
n be constructed from Kaveh--Manon's recent work on the classification of
toric flat families over toric varieties: it is the pullback of a toric fa
mily defined by a Rees algebra with base X_C (the toric variety associated
to C) along the universal torsor $\\mathbb A^m \\to X_C$. \nI will explai
n how to apply this construction to the Grassmannians Gr(2\,n) (with Plüc
ker embedding) and Gr(3\,6) (with "cluster embedding"). In each case there
exists a unique maximal Gröbner cone whose associated initial ideal is t
he Stanley--Reisner ideal of the cluster complex. We show that the corresp
onding cluster algebra with universal coefficients arises as the algebra d
efining the flat family associated to this cone. Further\, for Gr(2\,n) we
show how Escobar--Harada's mutation of Newton--Okounkov bodies can be rec
overed as tropicalized cluster mutation. This is joint work with Fatemeh M
ohammadi and Alfredo Nájera Chávez.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jordan (Edinburgh)
DTSTART;VALUE=DATE-TIME:20200819T140000Z
DTEND;VALUE=DATE-TIME:20200819T144500Z
DTSTAMP;VALUE=DATE-TIME:20220528T191405Z
UID:ClusterAlgebras2020/26
DESCRIPTION:Title: Cluster quantization from factorization homology\nby Davi
d Jordan (Edinburgh) as part of Cluster algebras 2020\n\n\nAbstract\nFacto
rization homology is a powerful universal invariant of (possibly\, stratif
ied) manifolds\, introduced in a series of papers by Ayala\, Francis\, Lur
ie\, and Tanaka. Many constructions in quantum topology receive new interp
retations\, stronger functoriality/TFT properties\, and much greater gener
ality when they can be recast in the framework of factorization homology.
\n\nIn this talk I'll explain some forthcoming work joint with Ian Le\, Gu
s Schrader and Sasha Shapiro\, in which we compute factorization homology
of stratified surfaces\, with coefficients taken in: quantum SL_2 for the
bulk region of the surface\; it's quantum Borel subgroup for defect lines\
, and its quantum Cartan quotient for boundary regions. The resulting ``qu
antum decorated character stacks" admit interesting systems of q-toric cha
rts which echo Fock--Goncharov's cluster quantizations of decorated charac
ter varieties. Remarkably\, these charts emerge not as a primary construct
ion/definition as in Fock--Goncharov's work -- but rather as a consequence
of the universal properties of factorization homology.\n
LOCATION:https://researchseminars.org/talk/ClusterAlgebras2020/26/
END:VEVENT
END:VCALENDAR