Series: Mathematics Colloquium

Date: Thursday, October 31, 2002

Time: 4:30 - 5:30 PM

Place: 102 McAllister Building

Host: Ping Xu

Refreshments: 4:00 - 4:30 PM, in 212 McAllister

Speaker: James Stasheff, University of North Carolina, Chapel Hill

Title: An Introduction to Operads With Applications to Physics

Abstract: 

Operads were originally studied as a tool in homotopy theory,
specifically for studying iterated loop spaces.  The notion of operad
involves an abstraction of a family of composable functions of several
variables together with an action of permutations of variables and
provides an efficient machinery for employing such families.  Today
operads have a wide range of applications in algebra, topology and
mathematical physics.  The talk will introduce operads, both formally
and in terms of the most basic examples: 1) multi-variable functions
and 2) trees under grafting.  More subtle examples involve the
`geometry' of configuration spaces and moduli spaces with their
compactifications and decorations.  Applications, especially to
mathematical physics, include conformal field theory and string field
theory.