All of my work thus far is connected in some way with random matrices. Much of my work going back to my PhD centers on using tools from highdimensional probability and graph theory to understand the spectrum and condition number of various nonHermitian random matrix models. Recently I've branched in some new directions (see below).
Current interests:
 Large deviations for nonlinear functionals of random graphs and random matrices, and connections with the naive mean field approximation in statistical physics;
 Extreme values of logarithmically correlated fields, with connections to random matrices, number theory, branching processes and PDE (the Fisher–KPP equation and related reactiondiffusion equations);
 Brown's spectral measure for nonnormal operators and related topics in random matrix theory and free probability.
See also my arXiv page and Google Scholar citations.
Papers and preprints:

Convergence to Brown's spectral measure for quadratic polynomials in Ginibre matrices, slideswith Alice Guionnet and Jonathan Husson.In preparation.

NonHermitian random matrices with a variance profile (II): Properties and examples,with Walid Hachem, Jamal Najim and David Renfrew.In preparation.

10.with Amir Dembo.Preprint.

9.with Ofer Zeitouni.Commun. Pure Appl. Math, to appear.

8.with Anirban Basak and Ofer Zeitouni.Electronic Journal of Probability, 23:paper no. 33, 51 pp., 2018. doi:10.1214/18EJP162

7.Ann. Inst. H. Poincaré, Probab. Statist., 55(4):2111–2167, 2019. doi:10.1214/18AIHP943

6.NonHermitian random matrices with a variance profile (I): Deterministic equivalents and ESDs, arXivwith Walid Hachem, Jamal Najim and David Renfrew.
slidesElectronic Journal of Probability, 23:paper no. 110, 61 pp., 2018. doi:10.1214/18EJP230 
Spectral properties of nonHermitian random matrices. urlPhD Thesis, UCLA.

5.Lower bounds for the smallest singular value of structured random matrices. arXivAnnals of Probability, 46(6):3442–3500, 2018. doi:10.1214/17AOP1251

4.Size biased couplings and the spectral gap for random regular graphs, arXivwith Larry Goldstein and Toby Johnson.Annals of Probability, 46(1):72–125, 2018. doi:10.1214/17AOP1180

3.The circular law for random regular digraphs with random edge weights. arXivRandom Matrices: Theory Appl., 06, 1750012, 2017. doi:10.1142/S2010326317500125.

2.Discrepancy properties for random regular digraphs. arXivRandom Struct. Algor., 50:23–58, 2016. doi:10.1002/rsa.20643.

1.On the singularity of adjacency matrices for random regular digraphs. arXivProbab. Theory Relat. Fields, 167(1):143200, Feb 2017. doi:10.1007/s0044001506798.
Slides:

Pseudospectra of structured random matrices. pdfRandom matrices workshop, Oberwolfach, Dec 2019

Large deviations for sparse random graphs. pdfRandom matrices and random graphs workshop, CIRM, Luminy, Apr 2019

Large deviations of subgraph counts for sparse random graphs. pdfAmir Dembo’s 60th birthday conference, Stanford, Dec 2018

Pseudospectrum and spectral anticoncentration: Beyond mean field models. pdfIPAM QLA Culminating Workshop, Lake Arrowhead, CA, June 2018

The maximum of the characteristic polynomial for a random permutation matrix. pdfRandom matrices and free probability workshop, IPAM, UCLA, May 2018

Circular laws for random regular digraphs. pdfAMS Fall Western Sectional Meeting, UC Riverside, Nov 2017

Inhomogeneous circular laws for random matrices with nonidentically distributed entries. pdfProbability and Mathematical Physics Seminar, UC Davis, April 2017

Random regular digraphs: singularity and spectrum. pdfProbability Seminar, Stanford, Nov 2015