## 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, Robbie Buckingham, Elizabeth Collins-Wildman, Ivan Corwin, Percy Deift, Jeff DiFranco, Patrik Ferrari,
Alexander Its, Bob Jenkins, Kurt Johansson, Thomas Kriecherbauer, Pierre Le Doussal,
Ji Oon Lee, Karl Liechty,
Zhipeng Liu, Ken T.-R. McLaughlin, Peter Miller, Raj Rao Nadakuditi, Sandrine Péché,
Eric Rains, Grégory Schehr, Guilherme Silva, Jack Silverstein, Eugene Strahov, Toufic Suidan,
Dong Wang, Hao Wu, Xin Zhou