**Professor Percy A. Deift** from Courant Institute of Mathematical Sciences, NYU, presented the Myhill Lecture Series 2013-14. This 3-part lecture series was held in the Fall, and included a reception in honor of Professor Deift after the first lecture.

Deift is a fellow of the American Mathematical Society, and a member of the National Academy of Sciences, one of the highest levels of scientific recognition. Co-winner of the Pólya Prize, and a Guggenheim Fellow, he is called "the grand-master of a school of classical and spectral analysis who has successfully used this expertise in various domains ranging from Integrable Systems to Random Matrices Theory and to Combinatorics. With Jinho Baik and Kurt Johansson, Deift solved one of the deepest conjectures of the field, the Ulam conjecture on the fluctuations of the longest increasing subsequence of a random permutation, and thus opened a rich new vein of results. [Courant]

**Lecture 1: Toeplitz matrices and determinants under the impetus of the Ising model I.**

The first talk will describe the development of Toeplitz theory over the years in response to questions that arose in the analysis of the Ising model in statistical physics.

**Lecture 2: Toeplitz matrices and determinants under the impetus of the Ising model II.**

The second talk will follow on from the first, and will describe more technical aspects, together with applications, of the modern theory of Toeplitz matrices.

**Lecture 3: Computing the eigenvalues of a random symmetric matrix: Universality properties.**

Deift will describe some recent numerical experiments on the computation of the eigenvalues of a random symmetric matrix. Fix an eigenvalue algorithm and choose an ensemble for the matrices: it turns out that the statistics of eigenvalue computation, for a given algorithm, display universality properties, independent of the choice of ensemble.