SEMINAR:Racks from the viewpoint of finite group theory

Speaker:Selçuk Kayacan, Bahçeşehir University

Title: Racks from the viewpoint of finite group theory

Date/Time: Nov 22,  2023, 13:40-14:30

Place: FENS L062

Abstract: A rack is a (possibly empty) set with a binary operation such that left multiplications are the automorphisms of the set and a quandle is a rack satisfying a certain condition. One of the motivating themes of those algebraic objects is that they axiomatize group conjugation operator. Although racks and quandles have appeared in literature from time to time under various names, they are not treated comprehensively from the viewpoint of finite group theory. In this talk, after reviewing the basic algebraic structure of racks we present a group theoretical approach that shares common elements with an already established area in literature known as "subgroup complexes". If time permits we discuss some of the results that are obtained in this direction.

Bio:Selçuk Kayacan graduated from Mimar Sinan Fine Arts University with a degree in Mathematics in 2006. He completed his M.Sc. and Ph.D. degrees in Mathematics Engineering Programme at İstanbul Technical University in 2010 and 2016, respectively. He also worked as a research assistant at the same university from 2009 to 2016 and he was a visiting scholar at Graz Technical University for a duration of one year in 2015 with TÜBİTAK 2214/A fellowship. Selçuk Kayacan worked at TÜBİTAK BİLGEM from 2016 to 2019 as a senior researcher. He was a post-doctoral research fellow at METU NCC for the next two years. From 2021 onwards he works at Bahçeşehir University as an assistant professor. His main research interests include Group Theory, Combinatorics and Cryptography.