# Mathematics Colloquium

## Professor Katherine Stevenson

speaks on

### Analytic Geometry in Characteristic p

Abstract. Many concepts from real and complex geometry carry over to geometry over fields of characteristic $p>0$. The field $K = {\bf Z}/p((x))$, like R or C, is metrically complete, and this allows us to do analytic geometry over K. While analysis over $K$ is in many ways similar to real and complex analysis, there are also many differences, and some concepts which are easy in one setting are harder in the other. For example, a series in $K$ converges if and only if the terms go to zero. On the other hand, analytic continuation does not carry over easily to $K$ because the topology is totally disconnected. In this talk, after surveying $K$-analytic spaces, we will consider the problem of finding the fundamental group of compact Riemann Surfaces'' without boundary in characteristic $p>0$.

Tea. High tea will be served at 3:30pm in the Lounge.
Emmy's. Certain refreshments will be available at the Emmy's after the talk.
Host. Megan Kerr will be the host. Anybody who is interested in having dinner with the speaker should contact Megan at 646-1614.