Invited Address

Margaret Robinson, Adams Professor of Mathematics
Mount Holyoke College

Two Ways to Count Solutions to Polynomial Equations

Abstract:
In this talk we will focus on two ways to count solutions to polynomial equations: solutions in finite fields and solutions modulo powers of a prime. For several polynomials, we will consider these cardinalities and show how for each counting method they fit together to form very similar-looking generating functions. The talk will finish with the tantalizing, sometimes frustrating, questions about how these generating functions are related to one another and to the very different-looking zeta functions of Weil and Igusa.

About our speaker:
Margaret Robinson is Julia and Sarah Ann Adams Professor of Mathematics at Mount Holyoke College. Her undergraduate degree is from Bowdoin College and her PhD is from Johns Hopkins University where her thesis advisor was Jun-ichi Igusa. In January of 2013, she was very honored to be awarded the Mathematical Association of America's Haimo Award for Distinguished Teaching.

She knew that she had to learn more about number theory when her calculus teacher connected the infinite sum of 1/n2 to the chance that two numbers chosen at random might be relatively prime. Since then, she and her students at Mount Holyoke and in Mount Holyoke's Summer Research Experiences for Undergraduates Program have been looking for more unlikely connections.