# 2008 Chern Lectures

*The 2008 Chern Lectures will be delivered by Dennis Sullivan on April 8, 9 and 10, 2008.*

Department of Mathematics, University of California, Berkeley, presents

The 2008 Chern Lectures

Dennis Sullivan

Department of Mathematics

SUNY, Stony Brook, New York

**Strings in a Manifold**

**Talk 1: **

*April 8, Sibley Auditorium, 4:00-5:00pm*

**Talk 2: **

*April 9, Sibley Auditorium, 5:00-6:00pm*

**Talk 3: **

*April 10, Sibley Auditorium, 4:00-5:00pm*

** Abstract:** In the first lecture, strings on a surface will be
discussed in an elementary manner. An interesting algebraic structure
emerges discovered in the 80's by Goldman and Turaev. Certain problems
and conjectures about curves on surfaces that were expressed in this
algebraic structure have recently been treated successfully. If time
permits we will survey briefly what will be discussed in the second and
third lectures:

To discuss strings in general manifolds heuristically physicists use action functionals and path integrals. We will discuss a rigorous string theory that instead makes use of algebraic topology. Families of strings are made to interact using the classical intersection of chains due to Lefschetz. Again interesting algebra emerges. This algebra includes a derived version of the algebra that appears for surfaces. This piece fits with symplectic or contact topology invariants of the cotangent bundle of the manifold. If time permits we will speculate on a more precise version of this string theory using differential forms on a Riemannian manifold. This version of our string theory should link up with other state of the art discussions out there.

**Reception in 1015 Evans Hall following the April 8 lecture.**