Factors of sparse polynomials: structural results and some algorithms

Combinatorics Seminar
Event time: 
Thursday, April 25, 2019 - 4:00pm
DL 431
Shubhangi Saraf
Speaker affiliation: 
Rutgers University
Event description: 
Are factors of sparse polynomials sparse? This is a really basic question and we are still quite far from understanding it in general. 
In this talk, I will discuss a recent result showing 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.
Research Area(s):