Research

My research is grounded in probability and random matrix theory, and their applications to number theory.  Additionally, I am motivated by connections to combinatorics, integrable systems, and beyond.

My PhD was titled Generalized moments of characteristic polynomials of random matrices. There exists a philosophy (see Montgomery-Dyson, Keating-Snaith, Katz-Sarnak etc) that characteristic polynomials of certain types of matrices share properties with certain number theoretic functions, for example the Riemann zeta function. My work is often inspired by trying to further our understanding of this apparent connection.

Below is a list of my publications.

• Lower Bounds for the Large Deviations of Selberg's Central Limit Theorem
  Joint with L.-P. Arguin
  link

• Improved critical drift estimates for the frog model on trees
  Poly Mathews Jr. (Co-author)

link

• Critical drift estimates for the frog model on trees
  Joint with M. Junge and J. Liu
  Electronic Journal of Probability 29(52), 1--21 (2024)

link

• Large deviation estimates of Selberg's central limit theorem and applications
  Joint with L.-P. Arguin

International Mathematics Research Notices 23, 20574--20612 (2023)

link

• Maxima of log-correlated fields: some recent developments
  Joint with J. P. Keating

Journal of Physics A: Mathematical and Theoretical 55, 053001 (2022)

link

• Evidence of Random Matrix Corrections for the Large Deviations of Selberg’s Central Limit Theorem
  Joint with E. Amzallag, L.-P. Arguin, K. Hui, R. Rao

Experimental Mathematics 1--13 (2021)

link

• Moments of moments and branching random walks
  Joint with J. P. Keating
  Journal of Statistical Physics 182, 20 (2021)
  link

• On the moments of the moments of ζ(1/2+it)
  Joint with J. P. Keating
  Journal of Number Theory 223, 79--100 (2021)
  link

• On the moments of the moments of the characteristic polynomials of Haar distributed symplectic and orthogonal matrices
  Joint with T. Assiotis, J. P. Keating
  Annales de l'Institut Henri Poincaré D 9(3), 567-–604 (2022)
  link

• Mixed moments of characteristic polynomials of random unitary matrices
  Joint with S. Bettin, G. Blower, B. Conrey, A. Prokhorov, M. Rubinstein, N. Snaith
  Journal of Mathematical Physics 60.8, 083509 (2019)
  link, Editor's pick

• On the moments of the moments of the characteristic polynomials of random unitary matrices
  Joint with J. P. Keating
  Communications in Mathematical Physics 371, 689--726 (2019)
  link