BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Evgeny Feigin (National Research University Higher School of Econo mics) DTSTART:20201002T150000Z DTEND:20201002T160000Z DTSTAMP:20260422T212926Z UID:LieTheory/1 DESCRIPTION:Title: Veronese embeddings\, arc schemes and global Demazure modules\nby Ev geny Feigin (National Research University Higher School of Economics) as p art of CRM-Regional Conference in Lie Theory\n\nLecture held in Virtual.\n \nAbstract\nVeronese curve of degree d (also known as rational normal curv e) can be realized as an embedding of the complex projective line into a d -dimensional projective space. The equations cutting out the image of thi s embedding can be written down explicitly and the homogeneous coordinate ring has an explicit description in terms of representations of the comple x Lie algebra sl(2). To pass to the corresponding arc scheme\, one replace s the field of complex numbers with the ring of formal Taylor series in on e variable. We describe the reduced ideal of the arc scheme and the homoge neous coordinate ring in terms of representation theory of the current alg ebra of sl(2).\nThe whole picture generalizes to the case of an arbitrary simple Lie algebra. The analogues of the rational normal curves are the V eronese embeddings of the flag varieties for the corresponding Lie group. We identify the homogeneous coordinate ring of the reduced arc scheme of t he Veronese embedding with the direct sum of the global Demazure modules o f the current algebra (the higher level analogues of the global Weyl modu les). Joint work with Ilya Dumanski. Geometric flows of $G_2$ and Spin(7 )-structures\n LOCATION:https://researchseminars.org/talk/LieTheory/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Yvan Saint-Aubin (Université de Montréal) DTSTART:20201002T170000Z DTEND:20201002T180000Z DTSTAMP:20260422T212926Z UID:LieTheory/2 DESCRIPTION:Title: The strucutre of the periodic spin chain XXZ seen as a module over the a ffine Temperley-Lieb algebra\nby Yvan Saint-Aubin (Université de Mont réal) as part of CRM-Regional Conference in Lie Theory\n\nLecture held in Virtual.\n\nAbstract\nhttp://www.crm.umontreal.ca/2020/LieAutomne20/pdf/S aint-Aubin.pdf\n LOCATION:https://researchseminars.org/talk/LieTheory/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Creutzig (University of Alberta) DTSTART:20201002T183000Z DTEND:20201002T193000Z DTSTAMP:20260422T212926Z UID:LieTheory/3 DESCRIPTION:Title: VOAs: From representation theory to physics\nby Thomas Creutzig (Uni versity of Alberta) as part of CRM-Regional Conference in Lie Theory\n\nLe cture held in Virtual.\n\nAbstract\nVertex operator algebras (VOAs) often serve as a bridge connecting interesting problems. I aim to explain such a n exciting connection to non-experts. The problem are representations of affine Lie superalgebras and related W-superalgebras and their connection to geometry and physics.\nI will introduce VOA-analogues of the space of functions on a compact Lie group. Then I will explain what these VOAs tell us about equivalences of representation categories of different VOAs and how they are motivated from dualities in four-dimensional gauge theories.\ n LOCATION:https://researchseminars.org/talk/LieTheory/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Martina Lanini (Università degli Studi di Roma “Tor Vergata”) DTSTART:20201003T150000Z DTEND:20201003T160000Z DTSTAMP:20260422T212926Z UID:LieTheory/4 DESCRIPTION:Title: Torus actions on cyclic quiver Grassmannians\nby Martina Lanini (Uni versità degli Studi di Roma “Tor Vergata”) as part of CRM-Regional Co nference in Lie Theory\n\nLecture held in Virtual.\n\nAbstract\nI will rep ort on recent joint work with Alexander Puetz\, where we define and invest igate algebraic torus actions on quiver Grassmannians for nilpotent repres entations of the equioriented cycle.\nThese quiver Grassmannians\, equippe d with such torus actions\, are equivariantly formal spaces\, and the corr esponding moment graphs can be combinatorially described and exploited to compute equivariant cohomology. Our construction generalises the very much investigated (maximal) torus actions on type A flag varieties.\n LOCATION:https://researchseminars.org/talk/LieTheory/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Georgia Benkart (University of Wisconsin-Madison) DTSTART:20201003T170000Z DTEND:20201003T180000Z DTSTAMP:20260422T212926Z UID:LieTheory/5 DESCRIPTION:Title: Fusion Rules\nby Georgia Benkart (University of Wisconsin-Madison) a s part of CRM-Regional Conference in Lie Theory\n\nLecture held in Virtual .\n\nAbstract\nFusion rules encode information about tensoring different t ypes of modules \n(simple\, projective) with a finite-dimensional module V\, and this information\ncan be recorded in a matrix that depends on V. When the objects are complex \nsimple modules for a finite group\, the re sulting matrix (often called the McKay \nmatrix due to inspiration from th e McKay correspondence)\, has as its right \neigenvectors the columns of t he character table of the group\, and the eigenvalues\nare the character o f V evaluated on conjugacy class representatives. So in that\nparticular case\, the eigenvectors are independent of V. We consider extensions of \nsuch results to other settings where tensor products are defined such a s finite-dimensional\nHopf algebras (e.g. quantum groups at roots of unity \, restricted enveloping algebras\nof Lie algebras in prime characteristic \, and Drinfeld doubles). The eigenvectors and \neigenvalues have connecti ons with the characters of the Hopf algebra\, and in some \nexamples\, man y connections with Chebyshev polynomials of various kinds. Fusion rule \nm atrices have applications to chip-firing dynamics and to Markov chains.\n\ nIn this talk I will explain a joint work with Javier Aramayona\, Julio Ar oca\, Rachel Skipper and Xiaolei Wu. We define a new family of groups that are subgroups of the mapping class group $Map(\\Sigma_g)$ of a surface $\ \Sigma_g$ of genus $g$ with a Cantor set removed and we will call these gr oups Block Mapping Class Groups $B(H)$\, where $H$ is a subgroup of $\\Sig ma_g$ . More visually\, this family will be constructed by making a tree-l ike surface gluing pair of pants and taking homeomorphisms that depend on $H$ with certain preservation properties (it will preserve what we will ca ll a block decomposition of this surface\, hence the name of our groups). We will see that this family is closely related to Thompson’s groups and that it has the property of being of type $F_n$ if and only if $H$ is. As a consequence\, for every $g\\in \\mathbb N \\cup \\{0\, \\infty\\}$ and every $n\\ge 1$\, we construct a subgroup $G <\\Map(\\Sigma_g)$ that is of type $F_n$ but not of type $F_{n+1}$\, and which contains the mapping cla ss group of every compact surface of genus less or equal to $\\g$ and with non-empty boundary. As expected in this workshop\, the techniques involve manipulating cube complexes\, as the Stein-Farley cube complex.\n LOCATION:https://researchseminars.org/talk/LieTheory/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Weekes (University of British Columbia) DTSTART:20201003T183000Z DTEND:20201003T193000Z DTSTAMP:20260422T212926Z UID:LieTheory/6 DESCRIPTION:Title: Coulomb branches and Yangians\nby Alex Weekes (University of British Columbia) as part of CRM-Regional Conference in Lie Theory\n\nLecture hel d in Virtual.\n\nAbstract\nA classical result of Jørgensen and Thurston s hows that the set of volumes of finite volume complete hyperbolic 3-manifo lds is a \nwell-ordered subset of the real numbers of order type w^w\; mor eover\, they showed that each volume can only be attained by finitely many isometry types of hyperbolic 3-manifolds.\nWe will discuss a group-theore tic analogue of this result: If $\\Gamma$\nis a non-elementary hyperbolic group\, then the set of exponential growth rates of $\\Gamma$ is well-ord ered\, the order type is at least w^w\, and each growth rate can only be a ttained\n by finitely many finite generating sets (up to automorphisms)\, and further generalizations of these results.\nThe talk is intended to be for a wider audience. All the notions that are mentioned in the abstract w ill be explained. It is based on a joint work with K. Fujiwara.\n\n\n\n\n\ nBraverman\, Finkelberg and Nakajima have recently given a mathematical de finition of the Coulomb branches associated to certain 3-dimensional quant um field theories. They define Coulomb branches as affine algebraic variet ies\, and showed that many interesting varieties\narise in this way.\n\nTh e BFN construction also produces quantized Coulomb branches\, which are no n-commutative algebra. It is interesting to try to relate these non-commut ative algebras with more familiar ones\; one nice example \nthat arises is the enveloping algebra of gl(n).\n\nI'll discuss how certain quantized Co ulomb branches can be described using Yangians. This means that there are explicit generators for the quantized Coulomb branch (which is otherwise r ather abstractly defined)\, a fact which has found application in describi ng connections between Coulomb branches and cluster algebras. But going th e other way\, we may also learn more about Yangians and their modules by l everaging results from the Coulomb branch theory. In my talk\, I will over view recent progress on these topics.\n\n\nThe classical umkehr map of Hop f assigns to a map of oriented manifolds\, $f:M \\to N\,$ `wrong-way' homo morphisms in homology $f_!: H_*(N) \\to H_*(M)$ and in cohomology $f^!:H^* (M) \\to H^*(N)\,$ the latter a version of `integration over the fibers'. Similar wrong-way maps\, sometimes known as transfer maps or Gysin maps\, are defined for other generalized (co)homology theories as long as the ma nifolds are suitably oriented and have had many applications. While these maps are defined only for manifolds there has long been interest in extend ing them to singular spaces. I'll discuss joint work with Markus Banagl an d Paolo Piazza in which we capitalize on recent work on the index theory o f signature operators to give analytic definitions of transfer maps in K-h omology for stratified spaces and relate them to topological orientations. \n LOCATION:https://researchseminars.org/talk/LieTheory/6/ END:VEVENT END:VCALENDAR