Geometry of Polynomials
Nikhil Srivastava
(UC Berkeley).
Course Summary 
About the lecturer 
Location and schedule 
Materials 
Videos 
Assignment
We will 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. 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 talk we will introduce and discuss several classes of these polynomials and their surprising applications, focusing on expander graphs, mixing of markov chains, and linear algebra problems.
About the lecturer:Nikhil Srivastava is an assistant professor in the Mathematics Department at UC Berkeley. He received his PhD in Computer Science from Yale in 2010, advised by Daniel Spielman, and his BS from Union College in 2005. After postdocs at the IAS, Princeton, and MSRI, he spent two and a half years as a researcher at Microsoft Research India, before coming to Berkeley. He is currently interested in algorithms, spectral graph theory, random matrices, and the geometry of polynomials.
In 2014, he was named a recipient of the PÃ³lya Prize with Adam Marcus and Daniel Spielman for their solution to the Kadisonâ€“Singer problem in functional analysis, which employed random polynomials. He gave an invited lecture at the International Congress of Mathematicians in 2014. In 2016, he
has been selected as a 2016 Sloan Research Fellow.
MIMUW, room 5440.



Materials
 some lecture notes corresponding to the first day of the lectures: part 1, part 2 and part 3.
 Videos: The video recordings of the lectures are now available here.
Assignment: problem set. Please submit the solutions to nikhil at math berkeley edu by 29 March.