BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Peigen Cao (University of Paris) DTSTART:20200703T074500Z DTEND:20200703T084500Z DTSTAMP:20260422T213046Z UID:charms-inaugural-meeting/1 DESCRIPTION:Title: The valuation pairing on an upper cluster algebra\nby Peigen Cao (University of Paris) as part of CHARMS inaugural meeting\n\nL ecture held in on Zoom.\n\nAbstract\nIt is known that many (upper) cluster algebras are not unique factorization\ndomains. In order to study their l ocal 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 larges t\ninteger $v$ such that that $u/a^v$ still belongs to $U$. Using the valu ation 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 elemen t in $U$ not divisible by any cluster variable in $t$. We have many applic ations to $d$-vectors\, $F$-polynomials\, factoriality of upper cluster al gebras and combinatorics of cluster Poisson variables. In this talk\, we f ocus on the application to $d$-vectors. We will show how to express $d$-ve ctors using the valuation pairing. This is a report on joint work with Ber nhard Keller and Fan Qin.\n LOCATION:https://researchseminars.org/talk/charms-inaugural-meeting/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre-Guy Plamondon (Université Paris-Sud) DTSTART:20200703T090000Z DTEND:20200703T100000Z DTSTAMP:20260422T213046Z UID:charms-inaugural-meeting/2 DESCRIPTION:Title: The g-vector fan of a tame algebra\nby Pierre-Guy Pla mondon (Université Paris-Sud) as part of CHARMS inaugural meeting\n\n\nAb stract\nTwo-term complexes of projective modules have been much studied re cently\, 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 of compl exes of projective modules. These 2-term complexes form an extriangulated category in the sense of Nakaoka and Palu. Moreover\, the $g$-vectors of t hose complexes that are rigid form a simplicial fan.\nIn this talk\, I wil l present a result obtained in a recent joint work with Toshiya Yurikusa ( Tohoku University): for a tame algebra\, the fan of $g$-vectors of rigid 2 -term complexes of projectives is dense. Algebras with this properties are said to be "$g$-tame". I will introduce the main tools in the proof of th is result\, including a variation on the theme of twist functors of Seidel and Thomas.\n LOCATION:https://researchseminars.org/talk/charms-inaugural-meeting/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Emmanuel Wagner (University of Paris) DTSTART:20200703T120000Z DTEND:20200703T130000Z DTSTAMP:20260422T213046Z UID:charms-inaugural-meeting/3 DESCRIPTION:Title: Categorical action of the braid group of the annulus\ nby Emmanuel Wagner (University of Paris) as part of CHARMS inaugural meet ing\n\nLecture held in on Zoom.\n\nAbstract\nThe usual braid group is an u biquitous object in mathematics due to its various possible definitions: d iagrammatic presentation\, mapping class group\, fundamental group of conf iguration space... Using all these points of view Khovanov and Seidel cons tucted a faithful categorical action of the braid group. The usual braid g roup is also called the Artin group of type A. Among all other Artin group s of finite type the one that shares very similar various possible definit ions is the Artin group of type B. Using a similar approach to Khovanov-Se idel\, we construct a categorical action of the Artin group of type B whic h is a categorification of a natural homological representation. This a jo int work with A. Gadbled and A-L. Thiel.\n LOCATION:https://researchseminars.org/talk/charms-inaugural-meeting/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Pilaud (Ecole Polytechnique) DTSTART:20200703T131500Z DTEND:20200703T141500Z DTSTAMP:20260422T213046Z UID:charms-inaugural-meeting/4 DESCRIPTION:Title: Shard polytopes\nby Vincent Pilaud (Ecole Polytechniq ue) as part of CHARMS inaugural meeting\n\nLecture held in on Zoom.\n\nAbs tract\nFor any lattice congruence of the weak order on permutations\, N. R eading proved that glueing together the cones of the braid fan that belong to the same congruence class defines a complete fan\, called quotient fan \, and F. Santos and I showed that it is the normal fan of a polytope\, ca lled quotientope. In this talk\, I will present an alternative simpler app roach to realize this quotient fan based on Minkowski sums of elementary p olytopes\, called shard polytopes\, which have remarkable combinatorial an d geometric properties. In contrast to the original construction of quotie ntopes\, this Minkowski sum approach extends to type B. Joint work with Ar nau Padrol and Julian Ritter.\n LOCATION:https://researchseminars.org/talk/charms-inaugural-meeting/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Tony Yue Yu (Université Paris-Sud) DTSTART:20200703T143000Z DTEND:20200703T153000Z DTSTAMP:20260422T213046Z UID:charms-inaugural-meeting/5 DESCRIPTION:Title: Cluster algebra via non-archimedean geometry\nby Tony Yue Yu (Université Paris-Sud) as part of CHARMS inaugural meeting\n\nLec ture held in on Zoom.\n\nAbstract\nI will explain the enumeration of non-a rchimedean curves in cluster varieties. We can construct a scattering diag ram via the enumeration of infinitesimal non-archimedean cylinders and pro ve its consistency. Then we prove a comparison theorem with the combinator ial constructions of Gross-Hacking-Keel-Kontsevich. This has several very nice implications\, such as the broken-line convexity conjecture\, a geome tric proof of the positivity in the Laurent phenomenon\, and the independe nce of the mirror algebra on the choice of cluster structure\, as conjectu red by GHKK. This is joint work with Keel\, arXiv:1908.09861.\n LOCATION:https://researchseminars.org/talk/charms-inaugural-meeting/5/ END:VEVENT END:VCALENDAR