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Summary: UNIVERSITY OF CALIFORNIA, SANTA BARBARA
BERKELEY · DAVIS · IRVINE · LOS ANGELES · MERCED · RIVERSIDE · SAN DIEGO · SAN FRANCISCO
CSANTA BARBARA · SANTA CRUZ
Geometry, Topology, and Physics Seminar
Elliptic cohomology, Witten genus, and applications to physics
Nora Ganter
Colby College
Friday, October 19, 2007, 4:00 p.m.
Room 6635 South Hall
Abstract: Elliptic cohomology is a field at the intersection of number theory,
algebraic geometry and algebraic topology. Its definition is very technical and highly
homotopy theoretic. While its geometric definition is still an open question, elliptic
cohomology exhibits striking formal similarities to string theory, and it is strongly
expected that a geometric interpretation will come from there.
To illustrate the interaction between the two fields, I will speak about my work on
orbifold genera and product formulas: After a very informal introduction to elliptic
cohomology, I will discuss string theory on orbifolds and explain how a formula by
Dijkgraaf, Moore, Verlinde and Verlinde on the orbifold elliptic genus of symmetric
powers of a manifold motivated my work in elliptic cohomology. I will proceed to
explain why elliptic cohomology provides a good framework for the study of orbifold
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