Thursday, September 20, 2018
09/20/2018 - 4:00pm to 5:00pm
What is the probability that an Erdős-Rényi random graph has exactly the average number of triangles? What if instead we ask K4’s or three term arithmetic progressions in a random set? We will outline some of our recent work exploring when we can extend central limit theorems to pointwise local limit theorems.
09/20/2018 - 4:15pm
The spectrum of an operator on Hilbert space is a closed subset of the complex plane. On the spectral complement, there is a family of analytic functions, called resolvent functions, associated to the operator. A natural inverse question follows: given a closed subset of the plane and a resolvent-type function on its complement, to what extent can we recover the associated operator? This question leads naturally to the study of Hardy spaces on multiply-connected domains. In this talk, we survey some results applying this perspective to Schroedinger and related operators.