TETRAHEDRAL GEOMETRY/TOPOLOGY SEMINAR

         ANNOUNCEMENT

DATE:               Friday, November 3, 2006             

LOCATION:     Hempfield High School, Room 213 (directions attached)                

                           followed by dinner at a place to be determined.

4:30 TALK:       Jim Stasheff, University of Pennsylvania

                           “A gentle introduction to the homotopy algebra of string field theory”

Abstract: String theory regards particles as (tiny) one-dimensional objects in space-time - paths or loops.  String FIELD theory deals with functions defined on the space of all such strings.   String field theory is multi-layered. The bottom layer is the topology of string configurations which in turn gives rise to `convolution' algebras of fields.  This fits naturally in to the existing framework in algebraic topology developed for studying spaces of the homotopy type of (iterated) loop spaces.  Various moduli spaces are involved; in particular, the moduli spaces of configurations of points in $R^n$  as well as the more traditionalmoduli spaces of configurations of points on a Riemann surface.

A traditional mathematical approach to particle physics considers particles as mathematical points which, as time goes by, trace out world lines - curves in space-time. Attempts to unite the fundamental forces of physics in a quantum theoretical context have lead to the idea that particles may in fact be `strings' ,extended one dimensional objects but of such a small extent that we can not observe the extent directly. Physicists deal with two kinds of strings: open strings are paths in space and closed strings are free loops in space.  Physical properties of such strings such as vibrations could have physically observable effects, even though our instruments do not permit direct resolution of these  minute objects themselves.  As such strings move or evolve over time, they would trace out a world sheet instead of a world line, but life (the mathematics) gets really interesting when particles interact..

     EVERYONE WELCOME

       PLEASE FORWARD THIS ANNOUNCEMENT TO ANYONE INTERESTED

           The Tetrahedral Geometry/Topology Seminar is sponsored jointly by

Elizabethtown College, Franklin & Marshall College, Lebanon Valley College and Millersville University.