Emil Prodan
(Yeshiva University)
January 22, 2021
14:00
(EST)
Organized by Americas GNCG Seminar.

Non-Commutative Geometry and Materials Science


Starting with the pioneering works of Jean Bellissard in the 1980’s,
Non-Commutative Geometry has emerged as one of sharpest tools in the arsenal of a theoretical materials scientist. Perhaps for this audience, the most important questions are why Non-Commutative Geometry and how much of it?
Using well understood examples, where specially designed materials display extraordinary behaviours in extreme conditions, I will try to convince the audience that one has to walk the entire sequence: algebra of observables → K-theory →pairing with cyclic cohomology → local index formula, plus one additional step which I call “pushing into the Sobolev.” Furthermore, among such extraordinary behaviours is a certain relation between the dynamics of degrees of freedominside the bulk and at the boundary of a sample, dubbed the bulk-boundary correspondence principle. It is captured by a certain extension of C∗-algebras and, as such, KK-theory offers a natural framework and supplies the necessary tools to investigate such phenomena. If the time permits, I will also discuss recent efforts trying to steer these tools from their usual use of explaining observed behaviours towards the discovery of new dynamical behaviours in materials science.

Share on email
Share on facebook
Share on google
Share on twitter
Share on linkedin