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Work Experience

• Visiting Assistant Professor University of Notre Dame 2021 - 2022
• Zorn Postdoctoral Fellow Indiana University Bloomington 2018 - 2021

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Research Descriptions

My research interests are in random matrix theory, probability theory and free probability theory. I look at the limiting eigenvalue distribution of random matrices. Recently, I study the phenomenon that the limiting eigenvalue distributions of certain random matrices can be canonically deformed into the limiting eigenvalue distribution of another random matrix. I also work on some basic questions of free probability.

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Selected Publications

1. (with Brian Hall, Jonas Jalowy, Zakhar Kabluchko) "The heat flow, GAF, and SL(2;R)" , arXiv: 2304.06665 , 2023.
2. (with Brian C. Hall) "The Brown measure of the sum of a self-adjoint element and an imaginary multiple of a semicircular element" , Letters in mathematical physics , 2022.
3. "The Brown measure of the sum of a self-adjoint element and an elliptic element" , Electronic journal of probability , 27, 1-32, 2022.
4. "The Brown measure of unbounded variables with free semicircular imaginary part" , Journal of operator theory , 2022.
5. (with Hari Bercovici, Jiun-Chau Wang, and Ping Zhong) "Superconvergence in free probability limit theorems for arbitrary triangular arrays" , Proceedings of the American mathematical society , 150 (12), 5253-5265, 2022.
6. (with Serban Belinschi, Hari Bercovici) "On the convergence of Denjoy-Wolff point." , arXiv:2203.16728 , 2022.
7. (with Serban Belinschi and Hari Bercovici) "Regularity for free multiplicative convolution on the unit circle" , Pacific Journal of Mathematics (To appear) , 2022.
8. (with Ping Zhong) "Deformed single ring theorems" , arXiv:2210.11147 , 2022.
9. (with Brian C. Hall) "The heat flow conjecture for random matrices" , arXiv:2202.09660 , 2022.
10. (with Brian C. Hall) "The Brown measure of a family of free multiplicative Brownian motions" , Probability theory and related fields (To appear) , 2022.
11. (with Ping Zhong) "Brown measures of free circular and multiplicative Brownian motions with self-adjoint and unitary initial conditions" , Journal of European mathematical society (JEMS) (To appear) , 2022.
12. "A local limit theorem and delocalization of eigenvectors for polynomials in two matrices" , International mathematics research notices (IMRN) (3), 1734-1769, 2022.
13. (with Guillaume Cebron) "Segal-Bargmann transform: the q-deformation" , Letters in mathematical physics , 2018.
14. "The two-parameter free unitary Segal-Bargmann transform and its Biane-Gross-Malliavin identification" , Journal of functional analysis , 271 (12), 3765-3817, 2016.
15. (with Renee Bell, Robert S. Strichartz) "Energy measures of harmonic functions on the Sierpinski gasket" , Indiana university mathematics journal , 2014.