CSE 599: Polynomial Paradigm in Algorithms Algorithms

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

Assignments

Related Courses

Lecture Topic Notes Bonus Materials
Lecture 1 (01/06/20) Real Rooted Polynomials pdf
Lecture 2 (01/10/20) Real Stable Polynomials, Closure Properties pdf
(01/13/20) No Class: ITCS 2020
Lecture 3 (01/17/20 ) Gurvtis Machinery, Log-Concavity pdf Approximating Mixed Volume
A 2^n Approx for Permanent
(01/20/20) No Class: Martin Luther King's Day
Lecture 4 (01/24/20) Applications: DPPs, TSP
Lecture 5 (01/27/20) Convex Programming and Real Stable Polynomials
Lecture 6 (01/31/20) Hyperbolic Programming
Lecture 7 (02/03/20) Introduction to Hodge Theory
Lecture 8 (02/10/20) Combinatorial Geometries, Bergman Fan
Lecture 9 (02/14/20) Hodge theory and log concavity
(02/17/20) No Class: President's Day
Lecture 10 (02/21/20) CLC Polynomials I
Lecture 11 (02/24/20) CLC Polynomials II: Mason's Conjecture
Lecture 12 (02/28/20) Expander Graphs, HDX
Lecture 13 (03/02/20) Local to Global Theorems
Lecture 14 (03/06/20) HDX, CLC and Matrids
Lecture 15 (03/09/20) Beyond Log-Concavity
Lecture 16 (03/13/20) Barvinok's Interpolation Method