BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alex Weekes (University of British Columbia) DTSTART:20201003T183000Z DTEND:20201003T193000Z DTSTAMP:20260423T024741Z 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