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.