My research lies in probability, where my main focus is on random marices. I also have a secondary focus on stochastic analysis and another secondary focus on sampling algorithms.
1) Random matrices and random operators
Non-Hermitian spectral laws, invertibility and singular-value gaps, outliers, finite-rank perturbations, heavy-tailed matrices, and random Schrödinger operators.
2) Stochastic analysis and stochastic partial differential equations
Uniqueness and ergodicity for equations with irregular diffusion coefficients, stochastic wave equations, and entropy methods for McKean–Vlasov dynamics.
3) Sampling in disordered systems, including Glauber dynamics and rapid mixing for random-field Ising models.