Recent Developments on Universal Forms
Prof. Myung-Hwan Kim
Seoul National University, visiting Wesleyan University, CT

Abstract:

In the talk, a brief history and recent developments on universal forms are introduced. For a set $S$ of quadratic forms, an $S$-universal form is a quadratic form that represents all forms in $S$. Recent developments include so called the Fifteen Theorem of Conway and Schneeberger on $\mathbb Z^+$-universal forms, Bhargava's Finiteness Theorem on representability of certain infinite subsets of $\mathbb Z^+$, and their generalizations to higher rank representations. Some applications and related topics will be discussed if time allows.