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BEGIN:VEVENT
SUMMARY:Peigen Cao (University of Paris)
DTSTART:20200703T074500Z
DTEND:20200703T084500Z
DTSTAMP:20260404T095036Z
UID:charms-inaugural-meeting/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/charm
 s-inaugural-meeting/1/">The valuation pairing on an upper cluster algebra<
 /a>\nby Peigen Cao (University of Paris) as part of CHARMS inaugural meeti
 ng\n\nLecture held in on Zoom.\n\nAbstract\nIt is known that many (upper) 
 cluster algebras are not unique factorization\ndomains. In order to study 
 their local factorization properties\, we introduce the\nvaluation pairing
  on any upper cluster algebra $U$. To each pair $(a\,u)$ consisting\nof a 
 cluster variable $a$ and a non zero element $u$ of $U$\, it associates the
  largest\ninteger $v$ such that that $u/a^v$ still belongs to $U$. Using t
 he valuation pairing\nwe prove that any full rank geometric upper cluster 
 algebra has the following local unique \nfactorization property: For each 
 seed $t$ of $U$\, any non-zero element $u \\in U$ can be uniquely factored
  as $u = ml$\, where m is a cluster monomial in the seed $t$ and $l$ is an
  element in $U$ not divisible by any cluster variable in $t$. We have many
  applications to $d$-vectors\, $F$-polynomials\, factoriality of upper clu
 ster algebras and combinatorics of cluster Poisson variables. In this talk
 \, we focus on the application to $d$-vectors. We will show how to express
  $d$-vectors using the valuation pairing. This is a report on joint work w
 ith Bernhard Keller and Fan Qin.\n
LOCATION:https://stable.researchseminars.org/talk/charms-inaugural-meeting
 /1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Guy Plamondon (Université Paris-Sud)
DTSTART:20200703T090000Z
DTEND:20200703T100000Z
DTSTAMP:20260404T095036Z
UID:charms-inaugural-meeting/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/charm
 s-inaugural-meeting/2/">The g-vector fan of a tame algebra</a>\nby Pierre-
 Guy Plamondon (Université Paris-Sud) as part of CHARMS inaugural meeting\
 n\n\nAbstract\nTwo-term complexes of projective modules have been much stu
 died recently\, in particular with respect to their links with tau-tilting
  theory and additive categorification of cluster algebras. The $g$-vector 
 of such a complex is its class in the Grothendieck group of the category o
 f complexes of projective modules. These 2-term complexes form an extriang
 ulated category in the sense of Nakaoka and Palu. Moreover\, the $g$-vecto
 rs of those complexes that are rigid form a simplicial fan.\nIn this talk\
 , I will present a result obtained in a recent joint work with Toshiya Yur
 ikusa (Tohoku University): for a tame algebra\, the fan of $g$-vectors of 
 rigid 2-term complexes of projectives is dense. Algebras with this propert
 ies are said to be "$g$-tame". I will introduce the main tools in the proo
 f of this result\, including a variation on the theme of twist functors of
  Seidel and Thomas.\n
LOCATION:https://stable.researchseminars.org/talk/charms-inaugural-meeting
 /2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Wagner (University of Paris)
DTSTART:20200703T120000Z
DTEND:20200703T130000Z
DTSTAMP:20260404T095036Z
UID:charms-inaugural-meeting/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/charm
 s-inaugural-meeting/3/">Categorical action of the braid group of the annul
 us</a>\nby Emmanuel Wagner (University of Paris) as part of CHARMS inaugur
 al meeting\n\nLecture held in on Zoom.\n\nAbstract\nThe usual braid group 
 is an ubiquitous object in mathematics due to its various possible definit
 ions: diagrammatic presentation\, mapping class group\, fundamental group 
 of configuration space... Using all these points of view Khovanov and Seid
 el constucted a faithful categorical action of the braid group. The usual 
 braid group is also called the Artin group of type A. Among all other Arti
 n groups of finite type the one that shares very similar various possible 
 definitions is the Artin group of type B. Using a similar approach to Khov
 anov-Seidel\, we construct a categorical action of the Artin group of type
  B which is a categorification of a natural homological representation. Th
 is a joint work with A. Gadbled and A-L. Thiel.\n
LOCATION:https://stable.researchseminars.org/talk/charms-inaugural-meeting
 /3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Pilaud (Ecole Polytechnique)
DTSTART:20200703T131500Z
DTEND:20200703T141500Z
DTSTAMP:20260404T095036Z
UID:charms-inaugural-meeting/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/charm
 s-inaugural-meeting/4/">Shard polytopes</a>\nby Vincent Pilaud (Ecole Poly
 technique) as part of CHARMS inaugural meeting\n\nLecture held in on Zoom.
 \n\nAbstract\nFor any lattice congruence of the weak order on permutations
 \, N. Reading proved that glueing together the cones of the braid fan that
  belong to the same congruence class defines a complete fan\, called quoti
 ent fan\, and F. Santos and I showed that it is the normal fan of a polyto
 pe\, called quotientope. In this talk\, I will present an alternative simp
 ler approach to realize this quotient fan based on Minkowski sums of eleme
 ntary polytopes\, called shard polytopes\, which have remarkable combinato
 rial and geometric properties. In contrast to the original construction of
  quotientopes\, this Minkowski sum approach extends to type B. Joint work 
 with Arnau Padrol and Julian Ritter.\n
LOCATION:https://stable.researchseminars.org/talk/charms-inaugural-meeting
 /4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Yue Yu (Université Paris-Sud)
DTSTART:20200703T143000Z
DTEND:20200703T153000Z
DTSTAMP:20260404T095036Z
UID:charms-inaugural-meeting/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/charm
 s-inaugural-meeting/5/">Cluster algebra via non-archimedean geometry</a>\n
 by Tony Yue Yu (Université Paris-Sud) as part of CHARMS inaugural meeting
 \n\nLecture held in on Zoom.\n\nAbstract\nI will explain the enumeration o
 f non-archimedean curves in cluster varieties. We can construct a scatteri
 ng diagram via the enumeration of infinitesimal non-archimedean cylinders 
 and prove its consistency. Then we prove a comparison theorem with the com
 binatorial constructions of Gross-Hacking-Keel-Kontsevich. This has severa
 l very nice implications\, such as the broken-line convexity conjecture\, 
 a geometric proof of the positivity in the Laurent phenomenon\, and the in
 dependence of the mirror algebra on the choice of cluster structure\, as c
 onjectured by GHKK. This is joint work with Keel\, arXiv:1908.09861.\n
LOCATION:https://stable.researchseminars.org/talk/charms-inaugural-meeting
 /5/
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