# 2015-2016 Bowen Lectures

**The Fall 2015 Bowen Lectures** were given by Jacob Lurie of Harvard University, on November 2nd, 3rd and 4th, 2015. Each lecture begins at 4:10pm and ends at 5:00pm.

Series Title: **Between Characteristic Zero and Characteristic $p$**

Monday November 2nd

Lecture 1: *Cohomology Theories, Rings, and Fields*

2060 Valley Life Sciences Building

Reception following Monday’s lecture

5:15 pm, 1015 Evans Hall

Tuesday November 3rd

Lecture 2: *Representation Theory in Intermediate Characteristic*

141 McCone Hall

Wednesday November 4th

Lecture 3: *Roots of Unity in Intermediate Characteristic*

3108 Etcheverry Hall

Series Abstract:

In algebra and 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 this series talks, I'll introduce the subject of $K(n)$-local homotopy theory, which in some sense interpolates between characteristic zero and characteristic $p$, and describe the curious behavior of roots of unity in this intermediate regime.