Friday Frebrary 13 Bear Hall 201D 2:00pm

Title: The Multi-Faceted Area of Additive Combinatorics

Speaker: Dr. Michael Freeze

Abstract:

Consider the following elementary assertions:

1. Take any 5 integers. There is some subset of those integers whose sum is divisible by 5.

2. Take any 9 integers. There is some subset of exactly 5 of those integers whose sum is divisible by 5.

3. Take any two polynomials with coefficients from a finite field, each in 9 variables, whose combined degree is less than 9. There is a nontrivial simultaneous solution.

We consider the relationships among these assertions, describe their connection to problems of interest in non-unique factorization theory, and highlight the intersection of these problems with multiple active research areas at the interface of disciplines within and beyond mathematics.