Roger Van Peski



I am a mathematician interested in a variety of topics around probability, mathematical physics, random matrices, algebraic combinatorics, and representation theory, currently working as a Ritt Assistant Professor (postdoc) at Columbia. I obtained my PhD in 2023 at MIT, advised by Alexei Borodin, and before that I was an undergraduate at Princeton.

Office: Columbia Mathematics Department, Room 621

email:
firstname lastname (no spaces/periods) at gmail dot com (general), or
rv2549 at columbia dot edu (columbia/teaching-related)

CV (pdf)

Papers

Reverse chronological order of arxiv submission; links go to arxiv versions, which are updated with changes once accepted for publication (i.e. you shouldn't worry about having to go to the journal for the most current version). See also arxiv and Google Scholar.
  1. (with J. Shen) Non-Archimedean GUE corners and Hecke modules Preprint, (2024).
  2. (with H. H. Nguyen) Rank fluctuations of matrix products and a moment method for growing groups Preprint, (2024). slides
  3. The rank of a random triangular matrix over \( \mathbb{F}_q \) Preprint, (2024).
  4. Symmetric functions and the explicit moment problem for abelian groups Preprint, (2024).
  5. Reflecting Poisson walks and dynamical universality in p-adic random matrix theory Preprint, (2023). slides
  6. Local limits in p-adic random matrix theory Proceedings of the London Mathematical Society 129(3):e12626, (2023). slides
  7. What is a p-adic Dyson Brownian motion? Preprint, (2023). To appear in Annales de l'Institut Henri Poincare (B) Probabilites et statistiques.
  8. (with H. H. Nguyen) Universality for cokernels of random matrix products Advances in Mathematics, 438:109451, (2024). slides
  9. (with P. Cohen, J. Dell, O. E. Gonzalez, G. Iyer, S. Khunger, C. H. Kwan, S. J. Miller, A. Shashkov, A. Smith Reina, C. Sprunger, N. Triantafillou, N. Truong, S. Willis, and Y. Yang) Extending support for the centered moments of the low lying zeroes of cuspidal newforms Preprint, (2022).
  10. q-TASEP with position-dependent slowing Electronic Journal of Probability (27): 1-35 (2022). slides (though about half cover other things)
  11. Hall-Littlewood polynomials, boundaries, and p-adic random matrices International Math Research Notices, 2023 (13): 11217-11275. slides
  12. (with A. Ahn) Lyapunov exponents for truncated unitary and Ginibre matrices Annales de l'Institut Henri Poincare (B) Probabilites et statistiques, 59 (2): 1029-1039 (2023).
  13. (with A. Ahn and M. Russkikh) Lozenge tilings and the Gaussian free field on a cylinder Communications in Mathematical Physics, 396 (3): 1221-1275 (2022). slides
  14. Limits and fluctuations of p-adic random matrix products Selecta Mathematica, 27 (05):1-71 (2021).
  15. Spectral distributions of periodic random matrix ensembles Random Matrices: Theory and Applications, 10(01) 2021.
  16. (with S. DeHority, X. Gonzalez, and N. Vafa) Moonshine for all finite groups Res. Math. Sci, 5 (2018).
  17. (with O. E. Gonzalez, C. H. Kwan, S. J. Miller, and T. A. Wong) On smoothing singularities of elliptic orbital integrals on GL(n) and Beyond Endoscopy Journal of Number Theory 183 (Supplement C) (2018) 407-437.
  18. (with P. Burkhardt, P. Cohen, J. Dewitt, M. Hlavacek, S.J. Miller, C. Sprunger, Y.N. Truong Vu, and K. Yang) Random matrix ensembles with split limiting behavior Random Matrices: Theory and Applications 5 (2018) no. 3, 1850006. slides
  19. (with S. J. Miller, C. Peterson, and C. Sprunger) The bidirectional ballot polytope Integers: The Electronic Journal of Combinatorial Number Theory 18 (2018).
  20. (with V. Gupta and U. Roy) A generalization of Tokuyama's formula to the Hall-Littlewood polynomials Electronic J. Combin. 22 (2015), no. 2.
Other writings: PhD thesis and undergraduate thesis.
Many of the above papers have linked slides next to them, which might be helpful to flip through. Some miscellaneous other notes/slides:

Seminars

Teaching

As instructor of record at Columbia:
  • Spring 2025: Math UN1101, Calculus I (2 sections)
  • Fall 2024: Math UN2500, Analysis and Optimization
For TA jobs before this, see full CV.

Mentoring

Some mentoring/outreach efforts I've been involved with and would recommend are the MIT Directed Reading Program, SPUR, UROP, GUMMI, PROMYS, Princeton Splash (but there are versions at lots of other schools as well!), Mentoring Möbius; to decode what these actually are see either CV or the links.

Miscellaneous

In high school I spent several summers at the PROMYS program, a 6-week math summer camp, and also worked there once I got older. I highly recommend it for any high school age students who like math, or undergraduates looking for a stimulating summer job.