Research

Summary

I study higher structures in geometry and physics. My research mainly involves ideas from (derived) algebraic geometry and (higher) category theory.  More precisely, I focus on the following subjects:

1. Stacky constructions.  I am interested in how stacks appear in geometry and physics (e.g., moduli spaces, gauge and functorial field theories). In particular, my Ph.D. thesis presents stacky constructions for specific gravity theories. 

2. Derived geometry. I focus mainly on derived algebraic/symplectic geometry and neighboring subjects. In particular, my postdoc project (at the Uni. of Zurich) introduces shifted contact structures on derived stacks. It examines their possible consequences (e.g., Darboux-type local presentations, the notion of symplectification, the construction of examples and further structures), leading to the development of derived contact geometry. Currently, I work on different aspects of these structures. The results obtained so far can be categorized as:

   • We refer to the first three corresponding papers as the Foundational Trilogy (2022-2025).  

   • Building upon that trilogy, we have established various new results and applications. I prefer to call this work the EI&KiB-Trilogy (2026). Huge thanks to Efe İzbudak for the enormous impact and dedication.

   • Further developments are in progress. One project extends symplectic/contact fibrations into the derived setting. This is a joint work with M. F. Arıkan and E. İzbudak. We call this program ABİ's Derived Fibrations Trilogy (2026-2027).
     >> A joke: "ABİ" forms a Turkish word and is translated as "Bro", so you may also call us "Derived Fibrations Bros."
     >> A follow-up joke: Our catchphrase might then be like: "We don't just lift weights, bro. We lift fibrations. We are the Derived Fibrations Bros."

   • Other companion papers and projects are in progress.
     Stay tuned for more trilogies (fingers crossed) and jokes !!!

3. Mathematical physics. I am also curious about the constructions and classifications of (un)extended functorial field theories (Topological, Homotopical, Geometrical). 

Some keywords: Algebraic/differential geometry, category theory, derived algebraic/symplectic/contact geometry, higher categorical structures, stacks, and mathematical physics (low-dimensional topology and gauge theory;  TQFTs and more general functorial field theories; gravity theories and quantization).

Live long and prosper _V/