Geometry of Polynomials in Algorithm Design

Over the years, many powerful algorithms have been built via tools such as linear programming relaxations, spectral properties of graphs, and others, that all bridge the discrete and continuous worlds. This course will cover another such tool recently gaining popularity: polynomials, their roots, and their analytic properties, collectively known as geometry of polynomials. The course will cover fundamental properties of polynomials that are useful in designing algorithms, and then will showcase applications in several areas of algorithm design: combinatorial optimization, graph sparsification, high-dimensional expanders, analysis of random walks on combinatorial objects, and counting algorithms. Prerequisites: CS161 or equivalent. Basic knowledge of probability, linear algebra, and calculus.