A(achen)-B(ochum)-C(ologne)-D(arstellungstheorie) Seminar
Wintersemester 2019/20
Organizer: Peter Littelmann, Xin Fang
Speakers
Fabian Korthauer (Bochum), Sara Lamboglia (Frankfurt), Verity Mackscheidt (Aachen), Elizabeth Milićević (Haverford), Elizaveta Vishnyakova (Cologne)Schedule
The seminar will be held on 4, February, 2020 in the Hoersaal (Main Lecture Hall, 2.03) inDepartment of Mathematics
University of Cologne
Weyertal 86-90
50931, Cologne
Schedule of talks:
11h-12h Elizaveta Vishnyakova, Simple Harish-Chandra modules over invariant subalgebras in a skew-group ring
12h-14h Lunch break
14h-14h15 Fabian Korthauer, Arithmetic representation growth of groups
14h30-15h30 Elizabeth Milićević, The Peterson Isomorphism: Moduli of Curves and Alcove Walks
15h30-16h Coffee break
16h-17h Sara Lamboglia, Tropical convex hulls of infinite sets
17h-17h15 Verity Mackscheidt, PBW deformations arising from algebraic groups
Abstract
Elizaveta Vishnyakova
Simple Harish-Chandra modules over invariant subalgebras in a skew-group ringAbstract of the talk
Fabian Korthauer
Arithmetic representation growth of groupsIn 2014 Mozgovoy-Reineke proved that completely reducible representations of finitely generated free groups over the finite field F_q can be counted by evaluating polynomials with integer coefficients at q. This and some related results and ongoing generalizations of these will be presented in this talk.
Elizabeth Milićević
The Peterson Isomorphism: Moduli of Curves and Alcove WalksIn this talk, I will explain the combinatorial tool of folded alcove walks, in addition to surveying a wide range of applications in combinatorics, representation theory, and algebraic geometry. As a concrete example, I will describe a labeling of the points of the moduli space of genus zero curves in the complete complex flag variety using the combinatorial machinery of alcove walks. Following Peterson, this geometric labeling partially explains the "quantum equals affine" phenomenon which relates the quantum cohomology of this flag variety to the homology of the affine Grassmannian. This is joint work with Arun Ram.
Sara Lamboglia
Tropical convex hulls of infinite setsIn this talk I will present some recent results on the interplay between tropical and classical convexity. In particular, I will focus on the tropical convex hull of convex sets and polyhedral complexes and their explicit computation. This will lead to a lower bound on the degree of tropical curves. This is joint work with Cvetelina Hill and Faye Pasley Simon.
Verity Mackscheidt
PBW deformations arising from algebraic groupsStarting from a graded algebra given by generators and relations, one can deform the algebra by deforming the relations. In this talk, a special class of deformations, namely PBW deformations, will be presented. They are well known in some cases, e.g. for Lie algebras, but the theory contains interesting open questions in general. This talk presents some known results and generalises the context to PBW deformations arising from algebraic groups, which is ongoing work.
Practical information
There is no registration needed.For further questions, please contact xfang@math.uni-koeln.de
Arbeitsgruppe Algebra und Zahlentheorie, Mathematisches Institut, Universität zu Köln