https://mechmath.bdu.info.az/xeberler/professor-olcay-coskun-meruze-etdi

Abstract

On September 24, 2024, at 10:15 AM, a scientific seminar was held in room 506 of the Faculty of Mechanics and Mathematics. In the seminar, Professor Olcay Coşkun (Baku State University, Digital Research ETL) presented a lecture titled "Representation Theory through the Lens of Category Theory."

The seminar began with an overview of group theory and category theory. It was noted that the theory of representations of finite groups was introduced at the end of the 19th century by Frobenius and Schur, and further developed through the efforts of Brauer, Burnside, Green, and others. Due to its wide applications, it has become one of the main branches of algebra.

In addition, starting from the mid-20th century, category theory emerged as a new framework for explaining the foundations of mathematics and studying abstract structures within a unified framework. In a short period of time, category theory found applications not only across all areas of mathematics but also in related fields like physics and computer science.

With the development of category theory, a new branch of representation theory emerged, utilizing methods from category theory. Over the past 60 years, it has been refined through the collaborative work of many prominent mathematicians, becoming a foundational part of representation theory.

This lecture begins with the basics of representation theory and presents certain categorical methods frequently used to solve problems in representation theory. The lecture will be delivered in Turkish and is aimed at a broad audience.