Nicolas Banks, Department of Pure Mathematics, University of Waterloo
"ABC Conjecture and Fermat's Last Theorem for Polynomials"
The ABC conjecture, posed in the 1980s, asserts (roughly) that if integers A and B are divisible by large powers of small primes, then their sum C=A+B is usually divisible by small powers of large primes. It has a number of important consequences, both known and unknown, such as Roth's theorem on approximations of rational numbers, Faltings' theorem on rational points on projective curves, and the Fermat-Catalan conjecture, which generalizes Fermat's Last Theorem. Despite a claimed proof by Mochizuki in the last decade, the conjecture is still considered unproved by the general mathematical community.
There is an analogous result for polynomials called the Mason-Stothers theorem. Oddly, this theorem is far easier to prove. In fact, an elegant elementary proof was discovered by a high school student in 2000. We present this proof, then use it to prove an analogue of Fermat's Last Theorem for polynomials.
Zoom meeting: https://uwaterloo.zoom.us/j/95669082908?pwd=L0NhbVZBakFGQXUycUZka01CL2lsQT09