Y. Yılmaz: Supergeometry, Differential Operators and Bracket Structures; Ph.D. Dissertation, University of Toledo, 2025.
Y. Yılmaz, E. Shemyakova: A Quantum Anchor for Higher Koszul Brackets; Preprint, 2024. arXiv:2410.15664
A Quantum Anchor for Higher Koszul Brackets
This work develops a quantized framework for higher Koszul brackets, which generalize the classical Koszul bracket on multivector fields. Together with E. Shemyakova, I construct a quantum anchor that maps higher Koszul brackets to Schouten brackets via quantized pullbacks. The approach relies on the formalism of thick morphisms and ℏ-differential operators, bridging homotopy Poisson geometry with quantization methods. The result provides new tools for studying L∞-algebroids and related homotopy structures in mathematical physics.
Y. Yılmaz, H. Varlı, M. Pamuk: Homological Properties of Persistent Homology; Journal of Algebra and Its Applications, 2024.
doi.org/10.1142/S0219498826500374
Homological Properties of Persistent Homology
This paper investigates the mathematical structure of persistent homology within the framework of algebraic topology. By extending classical tools such as long exact sequences and the Mayer–Vietoris sequence to persistence, it establishes structural results that clarify how persistent homology behaves.