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