Monday, February 20, 2023
02/20/2023 - 4:00pm
In the 1950s Phil Anderson made a prediction about the effect of random impurities on the conductivity properties of a crystal. Mathematically, these questions amount to the study of solutions of differential or difference equations and the associated spectral theory of self-adjoint operators obtained from an ergodic process. With the arrival of quasicrystals, in addition to random models, nonrandom lattice models such as those generated by irrational rotations or skew-rotations on tori have been studied over the past 30 years.
02/20/2023 - 4:30pm
Quantum groups are related to 3-dimensional topological quantum field theories. Downsizing from three dimensions to one but adding defects, I will explain a surprising relation between topological theories for one-dimensional manifolds with defects and values in the Boolean semiring and finite-state automata and their generalizations. I will then discuss the easier, linear case of these theories where symmetric Frobenius algebras appear, with connections to thin surface cobordisms. This is joint with Mikhail Khovanov.