BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mikhail Gorsky (St-Etienne) DTSTART:20261005T120000Z DTEND:20261005T130000Z DTSTAMP:20261114T075119Z UID:paris-algebra-seminar/235 DESCRIPTION:Title: Torus actions on compactified braid varieties and polytopa lity of subword complexes\nby Mikhail Gorsky (St-Etienne) as part of P aris algebra seminar\n\n\nAbstract\nEvery cluster variety admits a faithfu l regular group action scaling all cluster variables. Given a partial comp actification of a cluster variety\, a natural question is whether this act ion extends to a regular action on the compactification. I will explain th at\, in the case of braid varieties for simple Lie groups\, the answer is affirmative for brick compactifications. If the braid variety is an open R ichardson variety in the flag variety\, the same result holds for the corr esponding closed Richardson variety. In the latter case\, the faithfully a cting group is a torus of rank the Kazhdan-Lusztig d-invariant. The same r esult holds for projected Richardson varieties. I will also explain that\, in general\, a braid variety is a torus if and only if each of its brick compactifications is a toric variety with respect to this extended action\ , if and only if the polar dual of the moment polytope for this action rea lizes the corresponding subword complex. The braid words satisfying this p roperty turn out to be precisely the double root free words of V. Pilaud a nd C. Stump. This provides a novel approach to the longstanding open quest ion of the polytopality of spherical subword complexes asked by A. Knutson and E. Miller in 2004\, and in particular gives infinite families of subw ord complexes admitting polytopal realizations in dimension higher than th e rank of the corresponding Coxeter group. The talk is based on joint work with Lara Bossinger and José Simental\, arXiv:2609.12414.\n\nThis talk w ill take place in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/235/ END:VEVENT END:VCALENDAR