Orateur
Description
The past four decades have witnessed a vibrant and profound dialog between mathematics and quantum physics. The fundamental driving challenge here is how to reconcile the rigid algebraic structures of quantum physics with the geometric fluidity of relativistic spacetime. It turns out that such questions, and their as yet woefully incomplete answers, are as illuminating within pure mathematics as they are in quantum physics.
In this talk I will highlight one key aspect of this dialog: symmetry. Our traditional mathematical notions of symmetry -- think groups, matrices, diffeomorphisms, etc. -- always exist and compose discretely and linearly through time: first f then g, then h. By contrast, symmetries of quantum fields permeate both time and space, where they can wiggle, bend and break. This challenges us as mathematicians to rethink our whole notion of symmetry! Wandering down this path leads us deep into purely mathematical terrain -- to the heart of modern category theory, representation theory, even number theory.