I am Jun Yang, a postdoc at Harvard University working with Arthur Jaffe. I received my Ph.D. degree in Mathematics under the supervision of Vaughan Jones and Dietmar Bisch at Vanderbilt University in 2021. Before this, I studied Mathematics and Computer Science at Nankai University, China. 

Research Interest

representation theory, von Neumann algebras, especially arithmetic groups and automorphic representations.  

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, (Accepted by Reviews in Mathematical Physics) arxiv: 2212.13214 

4. Plancherel Measures of Reductive Adelic Groups and Von Neumann Dimensions, (submitted) 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. A Family of Projective Representations of the Thompson Group and Lifting Problems, (in preparation) arXiv:1812.01587

Notes

1. Notes on the Grothendieck-Riemann-Roch Theorem