AMS short couse 2013:  Universality for random non-Hermitian matrices.

Roles of random noise in data analysis. (Dec 2012).

Universality for Wigner matrices (July 2012, Medallion lecture, Bernoulli World Congress, Istanbul 2012).

Law of the determinant (the log determinant of a random matrix satisfies CLT)

Random Discrete Matrices (This is a survey I gave at IPAM in 2009, some updated version will appear soon. It contains a fair amount of topics and open questions)