Representation theory, von Neumann algebras, arithmetic groups and number theory.
Publications and Preprints
1. Motzkin Algebras and the A_n Tensor Categories of Bimodules, with Vaughan F.R. Jones, International Journal of Mathematics, 32(10), 2150077.arxiv:2008.04487
2. Actions of Cusp Forms on Holomorphic Discrete Series and Von Neumann Algebras, Advances in Mathematics.457(2024), Paper No. 109912. (a revised version of my Ph.D. thesis) arxiv:2010.00759
3. A Level-Depth Correspondence between Verlinde Rings and Subfactors, Reviews in Mathematical Physics (2024) 2430008, arxiv: 2212.13214
4. Plancherel Measures of Reductive Adelic Groups and Von Neumann Dimensions, Accepted by Mathematische Zeitschrift arxiv: 2203.07974
5. Von Neumann Dimensions and Trace Formulas I: Limit Multiplicities, (submitted) arxiv:2306.02999
6. The Jacquet-Langlands correspondence of von Neumann dimensions over arithmetic groups, (submitted) (arxiv:2405.18372)
7. Von Neumann Dimensions and Trace Formulas II: the global Jacquet-Langlands correspondence for arithmetic subgroups in GL(2), arxiv:2402.18488
8. The Atiyah-Schmid formula for reductive groups, arxiv.org:2503.13929
9. A Family of Projective Representations of the Thompson Group and Lifting Problems, (in preparation) arXiv:1812.01587
Notes on the Grothendieck-Riemann-Roch Theorem
The Jacquet-Langlands correspondence of von Neumann dimensions
Some simple trace formulas