## Department Colloquium

### Friday, November 1st, 2019

**Time:** 2:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Atabey Kaygun (Istanbul Technical University)

**Title:** Noncommutative Geometry for Fun and Profit.

**Abstract: ** There are whole fields of mathematics devoted to transferring problems of geometry and topology to commutative algebra (and vice versa) and solving them. This practice produced different "dictionaries'" of terms that tell us which type of objects in the realm of geometry or topology correspond to which other types of objects in the realm of algebra. In this talk, I am going to describe such a dictionary from the perspective of a homological algebraist who forgoes commutativity "for fun and profit" going through K-theory, cyclic and Hochschild homology, Hopf algebras, and quantum groups.

**Prof. Atabey Kaygun** works on homological and homotopical algebra in the context of noncommutative geometry. He obtained his Ph.D. from The Ohio State University in 2005. He was a postdoctoral fellow at the University of Western Ontario, KMMF-Warsaw University, Max-Plank-Institut fur Mathematik and University of Buenos Aires before joining the faculty of Bahcesehir University in 2009. He has been an associate professor at the Istanbul Technical University since 2016. Prof. Kaygun is currently on sabbatical and visiting Queen's University.