Title: How to prove Fermat’s last theorem
Abstract: If you’ve heard of Fermat’s last theorem, you may have heard that its proof involves some sophisticated geometric objects that seemingly have nothing to do with whether a^n + b^n = c^n for n > 2. These objects, called “elliptic curves” and “modular forms”, each admit their own rich and beautiful theories and are interesting in their own right. I will attempt to explain what they are, and how despite their apparent unrelatedness (both from each other and from Fermat’s “theorem”) they are bound together in intricate and unexpected ways. I will assume basic familiarity with matrices, infinite series, and polynomial equations, but in general the talk should be widely accessible.