EVENT DETAILS AND ABSTRACT

Title: Between characteristic zero and characteristic p
Speaker: Jacob Lurie
Speaker Info: Harvard University
Brief Description:
Special Note:
Abstract:

In classical algebraic geometry, there is often a stark difference between the behavior of fields of characteristic zero (such as the complex numbers) and fields of characteristic p (such as finite fields). For example, the equation x^p = 1 has p distinct solutions over the field of complex numbers, but only one solution over any field of characteristic p. In these talks, I will give an informal introduction to the theory of ring spectra. In this setting, one has "fields" (called Morava K-theories) which in some sense lie between characteristic zero and characteristic p. I'll then discuss some curious features of representation theory and algebraic geometry in these intermediate regimes.