I am broadly interested probability, analysis, combinatorics and highdimensional geometry. Most of my research falls within Random Matrix Theory, which intersects all of these fields. Random matrices also have important applications in mathematical physics, dynamical systems (neural networks and ecological food webs), number theory, and to the study of random graphs.
Papers and preprints:

Preprint.

Maximum for the characteristic polynomial of a random permutation matrix (with Ofer Zeitouni). arXivPreprint.

Circular law for the sum of random permutation matrices (with Anirban Basak and Ofer Zeitouni). arXivElectronic Journal of Probability, 23:1–51, 2018. doi:10.1214/18EJP162

The circular law for random regular digraphs. arXivAnnales de l'Institute Henri Poincaré, Probabilités et Statistiques, to appear.

NonHermitian random matrices with a variance profile (I): Deterministic equivalents and ESDs (with Walid Hachem, Jamal Najim and David Renfrew). arXivElectronic Journal of Probability, to appear.

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

Spectral properties of nonHermitian random matrices. urlPhD Thesis, UCLA.

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

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

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

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

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, November 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, November 2015