I am an assistant professor in the Department of Mathematics at Middle East Technical University (METU).
A brief history: I got my PhD from METU in 2021 under the supervision of Ali Ulaş Özgür Kişisel (Dept. of Math, METU) and Bayram Tekin (Dept. of Phys., METU). My thesis concerns stacky constructions and higher structures in gravity theories. Subsequently, I became a postdoctoral researcher at METU, the University of Zurich, and Istanbul Technical University. From 2023 to 2025, I served as a visiting assistant professor in the Department of Mathematics at Bilkent University. Since Fall 2025, I have been holding my current position at METU.
My research focuses on higher structures in geometry and physics, using derived algebraic geometry and higher category theory. Currently, I am working on derived symplectic geometry and neighboring subjects. More specifically, I have been investigating the theory of derived contact geometry.
Assistant Professor, Department of Mathematics, Middle East Technical University, Fall 2025 - present
Visiting Assistant Professor, Department of Mathematics, Bilkent University, Fall 2023 - Fall 2025
Postdoctoral Researcher, Department of Mathematics Engineering, Istanbul Technical University, Spring 2023 - Fall 2023
Postdoctoral Researcher, Institute of Mathematics, University of Zurich, Spring 2022- Spring 2023
Postdoctoral Researcher, Institute of Applied Mathematics, METU, Fall 2021
Instructor, Department of Mathematics, METU, Summer 2021
Research Assistant, Department of Mathematics, METU, 2014-2021
Algebraic/differential geometry, derived geometry;
category theory, higher categorical structures in geometry and physics;
mathematical physics (low-dimensional topology and gauge theory; TQFTs and more general functorial field theories; gravity theories and quantization).
Currently: Derived algebraic/symplectic geometry and neighboring subjects.
For more details, see Research page.
K. İ. Berktav, Introduction to derived contact geometry (2025), submitted contribution to the Springer-INdAM volume "Poisson Geometry and Mathematical Physics."
K. İ. Berktav, Legendrian structures in derived geometry (2025), doi: 10.13140/RG.2.2.31642.04808; arXiv:2406.17416.
K. İ. Berktav, On shifted contact derived Artin stacks (2025), Higher Structures 9 (2): 103-135, 2025.
K. İ. Berktav, Stacks in Einstein Gravity, Turk J. of Math. (2024) Vol. 48: No. 4, Article 5.
K. İ. Berktav, Shifted contact structures and their local theory (2024), arXiv:2209.09686, Ann. Fac. Sci. Toulouse, Math., Serie 6, Vol. 33, No. 4 (2024), pp. 1019-1057.
K.İ. Berktav, Notes on Derived Geometric Formulations in Physics (2022), Int. J. Geom. Methods in Mod. Phys. Vol. 19, No. 10 (2022), arXiv:1904.13331.
K. İ. Berktav, F. Özbudak, Euclidean Polynomials for Certain Arithmetic Progressions and the Multiplicative Group of F_p^2 (2022), Quaest. Math. 46 (7), 1283-1292, 2023.
K. İ. Berktav, Moduli theory, stacks, and 2-Yoneda’s Lemma (2020), arXiv:2202.06628.
K. İ. Berktav, An Introduction to Geometric Quantization and Witten’s Quantum Invariant (2019). arXiv:1902.10813 (in Proceedings of the Workshop on Mathematical Topics in Quantization, Galatasaray University, 2018).
Ph.D. in Mathematics (June 2021), Middle East Technical University (METU).
B.S. in Mathematics (High Honor, 2013) with Minor in Physics, METU.
International Postdoctoral Research Fellowship, The Scientific and Technological Research Council of Turkey, Fall 2021
Graduate Performance Awards, METU Graduate School of Natural and Applied Sciences, 2014 - 2015
Selected to be placed on the High Honor Roll of METU
The Merit Scholarship from the Dept. of Mathematics, METU, 2011-2012