# Combinatorics Seminar - Shubhangi Saraf

16:15-18:00

Speaker: Shubhangi Saraf

Title: Factors of sparse polynomials: structural results and some algorithms

Abstract: Are factors of sparse polynomials sparse? This is basic question, and we are still quite far from understanding it in general. In this talk, I will show that this is in some sense true for multivariate polynomials when the polynomial has each variable appearing only with bounded degree. Our sparsity bound uses techniques from convex geometry, such as the theory of Newton polytopes and an approximate version of the classical Caratheodory's Theorem.

Using our sparsity bound, we then show how to devise efficient deterministic factoring algorithms for sparse polynomials of bounded individual degree.
The talk is based on joint work with Vishwas Bhargav and Ilya Volkovich.