# 2010 Bowen Lectures

*The Thirtieth Annual Bowen Lectures will be delivered by Michael Hopkins, Harvard University, on October 26, 27 and 28.*

Department of Mathematics, University of California, Berkeley, presents

The 2009 Bowen Lectures

Michael Hopkins

Harvard University

**Lecture I:** The Kervaire invariant problem

October 26, 50 Birge Hall, 4:10-5:00 pm

** Abstract:** The Kervaire invariant problem is one of the oldest
questions in algebraic and differential topology. It impacts both the
classification of manifolds and the homotopy groups of spheres. This
lecture will be devoted to the long history of the Kervaire invariant
problem, and the different places it arises in algebraic and
differential topology.

**Lecture II:**Solution of the Kervaire invariant problem.

October 27, 50 Birge Hall, 4:10-5:00 pm

**This talk will describe the recent solution of the Kervaire invariant problem. It involves innovations in equivariant stable homotopy which are inspired by the homotopy theory of schemes. This is joint work with Mike Hill and Doug Ravenel.**

*Abstract:***Lecture III:**Elementary examples and and possible constructions.

October 28, 50 Birge Hall, 4:10-5:00 pm

**There are some very elementary examples of "Kervaire invariants" in the theory of immersions. This talk will present some of these classical examples, and describe approaches to constructing smooth manifolds with Kervaire invariant one.**

*Abstract:*