Work in mathematics, scientific computing, and machine learning.
Coprime Actions and Characters Nonvanishing on the Fixed-Point Subgroup. Answered a question of G. Navarro (Problem 21.100 in the Kourovka Notebook) in the negative by constructing a coprime action of a cyclic group of order 21 on a 2-group for which the number of invariant irreducible characters that are nonzero on the fixed-point subgroup is strictly smaller than the number of linear characters of that subgroup. The same example settles Problems 6.3 and 6.7 of Navarro's problem list and two questions of Isaacs on head characters, and the construction is shown to be minimal over all operator groups of odd order. PDF · Code
Cofinite Zeros of High Derivatives. A bounded-coefficient construction of a transcendental entire function whose sufficiently high derivatives have a zero in every prescribed nonempty open subset of the complex plane. The manuscript acknowledges earlier Gaussian proposed solutions and develops a different hole-probability argument together with a deterministic growth consequence for a 1973 theorem of Boas and Reddy. PDF · Repository
Approximation-Free Diffusion Posterior Sampling. Stanford University, 2026-present. Working with a Stanford professor and Ph.D. student on approximation-free diffusion posterior sampling for scientific inverse problems. Applied the method to InverseBench tasks including linear inverse scattering, the Navier-Stokes equations, and full-waveform inversion.