My research interests manily lie within the circle of ideas related to the Atiyah-Singer index theorem, the equivariant geometry of loop spaces, and noncommutative local index theory as innitated by Connes-Moscovici. These subjects give a rich interplay between micro-local analysis, Chern-Weil theory, algebraic topology, and operator theory and have found applications outside of pure mathematics, particularly within mathematical physics. More recently I have been interested in a various topics in gauge theory ranging from the Fueter operators describing the compactifications of moduli spaces in gauge theory to the dualities which govern the interrelationships between various field theories.
Below is a list of my publications and preprints.
"Connes-Moscovici Residue Cocycle For Some Dirac-Type Operators” (2021) (with A.R.H.S. Sadegh, Y. Loizides) Muenster Math Journal
"On Perrot’s Index Cocycles" (2022) (with J. Block, N. Higson) AMS Contemporary book Cyclic Cohomology at 40: Achievements and Future Prospects
"The Geometry of Mehler’s Kernel" (2023) preprint arxiv 2312.02076
"A fixed point formula for Dirac operators on Lie groupoids" (2024) (with S. Liu, Y. Loizides, A.R.H.S. Sadegh) Journal of Functional Analysis
"Explicit Families of Spinor Representations" (2025) preprint arxiv 2505.16203
"Hypoellipticity of the Asymptotic Bismut Superconnection on Contact Manifolds" (2026) Journal of Topology and Analysis
"A Fueter Operator for 3/2 Spinors" (2026) (with A.R.H.S. Sadegh, M. L. Nguyen) (To Appear)
"Fermionic Constraints and Filtered Manifolds" (2026) (To Appear)