School of Mathematical Sciences
Monday, February 28, 2011
Schreiber 006, 12:15
Ben Gurion University
Nonabelian Multiplicative Integration on Surfaces
Nonabelian multiplicative integration on curves is a classical
theory, going back to Volterra in the 19-th century. In differential
geometry this operation can be interpreted as the holonomy of a connection
along a curve.
This talk is about the 2-dimensional case. A rudimentary nonabelian
multiplicative surface integration was known since the 1920's (work of
Schlesinger). I will present a much more sophisticated construction. My
main result is a 3-dimensional nonabelian Stokes Theorem. This result is
completely new; only a special case of it was predicted (without proof)
in papers in mathematical physics.
The talk is fairly elementary, requiring only some knowledge of Lie groups
and their Lie algebras. And there are many color pictures!
My motivation for this work has to do with a problem in twisted deformation
quantization. I will say a few words about this at the end of the talk.
For full details see the lecture notes
or the preprint
arXiv:1007.1250 at http://arix.org.
Coffee will be served at 12:00 before the lecture
at Schreiber building 006