Mathematics Colloquium

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Beyond the Elliptic Genus

Speaker: I. M. Singer, MIT

Location: Warren Weaver Hall 1302

Date: Monday, April 19, 2010, 3:45 p.m. CANCELLED

Synopsis:

A genus is a homomorphism Phi from a cobordism ring to a commutative ring R with unit. I'll begin with examples of F. Hirzebruch where R is the ring of integers. Then I'll describe some of the work of S. Ochanine and P.S. Landweber where R is the ring of modular forms for an elliptic curve, i.e., a Riemann surface with genus g=1; Phi is the elliptic genus.

I'll explain the physics derivation of the elliptic genus using the Dirac‐Ramond operator on loop space. That leads to a new cobordism ring, string cobordism, and a new genus with values in the ring of modular forms for surfaces with genus g>1.

I'll end with speculations on possible applications of this generalized string genus.

(Joint work with Orlando Alvarez.)