I study topological or geometric invariants that allow classifications of manifolds in topological or smooth categories.  These invariants are obtained from various methods, such as index theory and gauge theory, as they pertain to my research. 

Published Papers:

1.  The three-dimensional Seiberg-Witten equations for 3/2-spinors: a compactness theorem, with M. L. Nguyen. (Mathematische Nachtrichten)(2025)

2. On Deformation spaces, tangent groupoids and generalized filtrations of Banach and Fredholm manifolds, with Jody Trout. (2025)

3. A fixed-point formula for Dirac operators on Lie groupoids, with S. Liu, Y. Loizides, and J. Sanchez. (J. Functional Analysis )(2024)

4. On the Z_2-valued index of elliptic odd symmetric operators on non-compact manifolds, with Maxim Braverman. (Annales Math du Quebec)(2024) 

5. Deformation spaces, rescaled bundles, and the Kirillov character formula, with Maxim Braverman. (J. Noncommutative Geometry)(2024)  

6. Connes-Moscovici residue cocycle for some Dirac-type operators, with J. Sanchez and Y. Loizides. ( Muenster Journal of Mathematics) (2023)

7. A coarse relative-partitioned index theorem with M. Karami and M.E. Zadeh. (Bulletin des Sciences Mathematiques)(2019)

8. Euler-like vector fields and manifolds with filtered structure, with N. Higson. (Documenta Mathematica)(2018)

Preprints:

1. A glueing formula for the Z_2-valued index of odd symmetric operators (arXiv)(2025)

2. The Z_2-valued spectral flow of a symmetric family of Toeplitz operators, with Maxim Braverman (arXiv)(2024)

3. A Fueter operator for 3/2-spinors, with M. L. Nguyen. (arXiv)(2024)