We formulate and report on the problem of the Bass-Note 

Spectrum of an invariant operator as one varies over locally uniform 

geometries. In the Euclidean setting this recasts classical problems of

Mahler from the geometry of numbers in a new light. For certain operators 

homogeneous dynamics can be used decisively. In the non-Euclidea setting 

of hyperbolic manifolds we review some recent developments using the

conformal bootstrap method and of random covers to study the Bass- Note

spectra. We highlight the theme and impact of rigidity.

The small quantum connection of a Fano variety is among the most accessible and fundamental objects in enumerative geometry. In this talk, I’ll survey recent results on the structure of the quantum connection, with an emphasis on bounds for the sizes of Jordan blocks of the “regularized monodromy”. These bounds can be viewed as mirror analogues of classical results by Borel, Katz, and Varchenko concerning the Jordan blocks of monodromy for Gauss–Manin connections associated to families of varieties. This is joint work—partially in progress—with P. Seidel.

A relaxed-pace seminar on impromptu subjects related to the interests of the audience. Everyone is welcome. The subjects are geometry, probability, combinatorics, dynamics, and more!