My research revolves around representation theory, categorification and related combinatorics.

Algebraic structures and their representations can be difficult to operate with, hence one profits from unraveling their underlying combinatorics.  Another possible approach is to consider families of algebraic structures, such as the collection of all symmetric groups or their representations. The language of category theory suits well this line of thought.  Resulting categories admit interesting structures on their own, for example one can recover the ring of symmetric functions from the representation category of symmetric groups.

I have experience working with categories and diagrammatic 2-categories, mostly in the context of Heisenberg categories. My work has revealed some algebraic and combinatorial structures arising from these categories. 

Publications

Trace of the twisted Heisenberg Category - Can Ozan Oğuz, Micheal Reeks  - Communications in Mathematical Physics, DOI:10.1007/s00220-017-2992-9

The center of the twisted Heisenberg category, factorial Schur functions, and transition functions on the Schur graph- Henry Kvinge, Can Ozan Oğuz, Micheal Reeks - Journal of Algebraic Combinatorics, DOI: 10.1007/s10801-019-00910-w

Natural transformations between induction and restriction on iterated wreath product of symmetric group of order 2 - Mee Seong Im, Can Ozan Oğuz - Mathematics 2022, 10, 3761. https://doi.org/10.3390/math10203761