A Tale of Three Co’s: Coalgebras, Cohomology and Computations


Atabey Kaygun, Istanbul Technical University

Associative and unital algebras are well-known objects.  In this talk, we are going to investigate their categorical duals called“coalgebras.”  To motivate their use, we will introduce them purely computationally with several examples.  After a brief introduction to simplicial and cyclic objects, and the two-sided bar complex of algebras and coalgebras, we will demonstrate a few cohomological computations.  We will finish the talk by introducing algebra/coalgebra duality pairing on the level of simplicial/cyclic objects and bar complexes, and then investigate the use of such pairings in calculations of cohomology. (Parts of this talk are from our joint work with Serkan Sütlü from Işık University.)

Speaker’s Brief Biography : Atabey Kaygun received his Bachelor and Masters degrees at Boğaziçi University, and his PhD from the Ohio State University.  After his PhD, he did his post-doctorate studies in the US, Canada, Poland, Germany and Argentina before returning to Türkiye. He worked at Bahçeşehir University several years before moving to Istanbul Technical University.  His work splits into two main areas: On the theoretical side, he does homological and homotopical algebra in the context of noncommutative geometry.  On the applied side, he does data analysis, natural language processing, and applied statistics.