In this course we discuss the fruitful paradigm of encoding discrete phenomena in complex multivariate polynomials, and understanding them via the interplay of the coefficients, zeros, and function values of these polynomials. For example, the states of a statistical physics model and the corresponding phase transition, the clusters in a graph, and the convex cones of linear and semidefinite programming can all be viewed in these terms. Over the last fifteen years, this perspective has led to several breakthroughs in computer science, and an unexpected bridge between distant scientific areas including combinatorics, probability, statistical physics, convex and algebraic geometry, and computer science has been built.
In this course I plan to cover part of these developments with an emphasis on more recent developments specially connections to matroids, Hodge theory, high dimensional expanders and mixing time of random walks.
Administrative Information
 Instructor: Shayan Oveis Gharan
 Office Hours: By appointment, email me at shayan at cs dot washington dot edu.
 Lectures: Monday  Friday 1:30  2:50 at CSE II Room 271 (note change of room)
 TA: Nathan Klein, OH: Tue 2:303:30 at CSE2 Room 223.
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