Pacific Institute for the Mathematical Sciences - PIMS

Broken Symmetries

Abstract:

There is a remarkable connection pioneered by Alain Connes
between operator algebras, which originated as the mathematical models
for quantum mechanical systems, and abstract structures arising from
number theory. This connection is based on the fact that systems of
numbers and of sub-atomic particles share some common features that make
them tractable with the same mathematical tools.

One of these features is the prominent role that symmetries play in both
cases; another is the relevance of pairs of operations that do not
commute with each other. For quantum systems, the non-commuting
operations are the measurements of position and momentum of particles;
for number systems, they are addition and multiplication.

I will give a nontechnical overview of the subject, discussing its
motivations and implications, and then briefly report some recent
developments.

Location: Education Building 191

For more information please visit University of Regina Department of Mathematics