Koç University, Mathematics Seminar

Date & Time: Thursday, April 21, 16:00-17:00

Place: SCI 129

Speaker: Ergün Yalçın (Bilkent University)

Title: Representation Rings for Fusion Systems and Dimension Functions

Abstract: I will talk about a problem we recently came across to when we were studying finite group actions on homotopy spheres. To construct an action of a finite group G on a homotopy sphere, one often needs to start with representations of Sylow subgroups of G satisfying certain properties. These properties can be expressed best by considering these representations as representations of the corresponding fusion system. Fusion system is a category defined to emulate the p-structure of a finite group. We define representation rings for fusion systems and express this problem as a realization problem for super class functions for fusion systems. We give a partial answer to this problem (joint work with Sune Precht Reeh) but the problem is still open in full generality. The talk will be a gentle introduction to fusion systems, representations rings of finite groups (and fusion systems), and will mention some interesting problems and new results on constructing finite group actions on homotopy spheres.

Speaker's Brief Biography: Ergün Yalçın studied Electrical Engineering at Bilkent University as an undergraduate. He received his PhD in Mathematics at University of Wisconsin in 1998. After the PhD, he held positions at Indiana University in Bloomington, U.S.A. and at McMaster University in Hamilton, Canada. Since August 2000, he is a faculty member at Bilkent University and since 2012, a Professor of Mathematics. During 2007-2008 and 2014-2015 academic years he was a visitor at McMaster University. He received TÜBA-Distinguished young researcher award (2005-2008), TÜBİTAK Encouragement award (2007), H. Lyman Hooker Distinguished visitor award from McMaster University (2007 and 2014), and Masatoshi Gündüz Ikeda award (2009). He served in the editor board of Turkish Journal of Mathematics (2009-2014). He is a member of Bilimler Akademisi (Science Academy) since 2013.