A self-contained exposition of TQFT from first principles: the categorical formalism of symmetric monoidal categories and Atiyah’s axioms, the classification of 2-dimensional TQFTs via commutative Frobenius algebras, and connections to cobordism theory and quantum invariants of manifolds.
Research
I am drawn to topological quantum field theories — functors from the category of cobordisms to the category of vector spaces — and the remarkable way they encode geometric information through algebraic invariants. A second thread of my work concerns hyperbolic geometry: discrete subgroups of PSL(2,ℂ) acting on hyperbolic 3-space and the manifolds they produce.
Thesis
Topological Quantum Field Theory: From Mathematical Foundations to Physical Implications
Research projects
The equality case in an extension of Jørgensen’s inequality for purely loxodromic 2-generator free Kleinian groups
Constructing hyperbolic 3-manifolds and computing their volumes by identifying Kleinian groups that are free and consist entirely of loxodromic isometries.
Category theory: from abstract patterns to topological quantum field theory
A systematic development of category theory as a foundational framework: from elementary categorical constructions through functors and natural transformations, culminating in monoidal categories and their application to TQFT.
TÜBİTAK electromagnetism laboratory
Assisted in the calibration of electromagnetic devices and contributed to theoretical studies on the spectrum of the rubidium atom, using Python to process and analyze experimental data.
Writing in preparation
Notes on hyperbolic 3-manifolds and Kleinian groups
Covering the geometry of limit sets, fundamental domains, and the topology of quotient manifolds.
Talks
An introduction to topological quantum field theory
Category theory: from abstract patterns to TQFT
Mathematics Community seminars
Regular presentations on category theory, manifolds, Lie theory, and the interplay of physics with pure mathematics.