Research

KPZ universality: totally asymmetric simple exclusion process, last passage percolation

Spin glass: spherical Sherrington-Kirkpatrik model

Tracy-Widom distribution, Painlevé, and integrable PDE: properties of TW distributions, total integrals of Painleve II, Riemann-Hilbert problem, KP equestion for multi-point distributions

Limit theorems in combinatorics: longest increasing subsequence of random permutation, Plancherel measure on partitions, symmetrized random permutaitons, maximal crossing and nesting of random matching

Random matrix theory: discrete orthogonal polynomial ensembles, spiked sample covariance matrices, Hermitian matrix model with external source, universality of random matrix theory

Applications to Statistics: transitional behavior of spiked sample covariance matrices, tandem queues

Universality: discrete orthogonal polynomial ensemble, non-intersecting walks, Hermitian matrix model with spiked external source

Last passage percolation, random growth, interacting particle systems: PNG model, TASEP, phase transition, limit theorems, limit process

Non-intersecting processes: random vicious walks, random tiling of hexagon, bus system in Cuernevaca

Coauthors: Guillaume Barraquand, Gérard Ben Arous, Alexei Borodin, Thomas Bothner, Robert Buckingham, Elizabeth Collins-Wildman, Dylan Cordaro, Ivan Corwin, Percy Deift, Jeffery DiFranco, Patrik Ferrari, Alexander Its, Robert Jenkins, Kurt Johansson, Thomas Kriecherbauer, Pierre Le Doussal, Ji Oon Lee, Yuchen Liao, Karl Liechty, Zhipeng Liu, Ken T.-R. McLaughlin, Peter Miller, Raj Rao Nadakuditi, Sandrine Péché, Andrei Prokhorov, Eric Rains, Grégory Schehr, Guilherme Silva, Jack Silverstein, Eugene Strahov, Toufic Suidan, Tejaswi Tripaphi, Dong Wang, Hao Wu, Xin Zhou