Curriculum Vitae
Academic Positions
Visiting Assistant Professor, Department of Mathematics, Bilkent University, Fall 2023 - present
Postdoctoral Researcher, Department of Mathematics, 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, Middle East Technical University (METU), Fall 2021
Instructor, Department of Mathematics, METU, Summer 2021
Research Assistant, Department of Mathematics, METU, 2014-2021
Research Interests
Algebraic/differential geometry; derived algebraic/symplectic geometry; category theory, higher categorical structures/spaces in geometry and physics; stacks and moduli problems; mathematical physics (low dimensional topology and gauge theory; TQFTs and more general functorial field theories; gravity theories and quantization). For more details, see Research page.
Currently: Derived algebraic/symplectic geometry and neighboring subjects.
Publications and Preprints
K. İ. Berktav, Legendrian structures in derived geometry, doi: 10.13140/RG.2.2.31642.04808; arXiv:2406.17416
K. İ. Berktav, Stacks in Einstein Gravity, Turk J. of Math. (2024) Vol. 48: No. 4, Article 5.
K. İ. Berktav, On shifted contact derived Artin stacks, doi: 10.13140/RG.2.2.21012.88969; arXiv:2401.03334 (submitted & under revision)
K. İ. Berktav, Shifted contact structures and their local theory, arXiv:2209.09686. (To appear in the Ann. Fac. Sci. Toulouse, Math.)
K.İ. Berktav, Notes on Derived Geometric Formulations in Physics, 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, Quaest. Math. (2022) 1-10.
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 (to appear in Proceedings of the Workshop on Mathematical Topics in Quantization, Galatasaray University, 2018).
Education
Ph.D. in Mathematics (June 2021), Dept. of Mathematics, Middle East Technical University (METU).
B.S. in Mathematics with High Honor (2013), Dept. of Mathematics, METU.
Minor in Physics (2013), Dept. of Physics, METU.
Honors and Scholarships
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