Title: Three 10 min talks (titles below)
Speaker: Nico Cooper, Curtis Grant, Catherine Ray
Speaker Info: Northwestern University
Schedule:Date: Friday, February 18, 2022
4:15 – Speaker: Nico Cooper Title: The KdV Hierarchy: From water waves to quantum gravity in 10 minutes Abstract: In this talk, I'll speed through the vast landscape of topics related to the KdV hierarchy. We'll start with the basic motivation for the ordinary KdV equation in hydrodynamics, constructing higher order equations, and the infinite dimensional symmetry that arises as a consequence. To talk about the hierarchy in general, we'll introduce the tau function, and its relationship to the funny representation theory of GL(∞). In searching for more solutions, we can find operators that take us from n-soliton solutions to (n+1)-soliton solutions. In particular, these operators happen to be the exact same vertex operators from 2D conformal field theory. From here, we may be able to fit in a few words about Witten's conjecture relating the KdV hierarchy and intersection numbers of moduli spaces via 2D quantum gravity.
4:30 – Speaker: Curtis Grant Title: Counting Eigenvalues of the Laplacian Abstract: What are the eigenvalues of the Laplacian on a domain? In general this is computationally difficult, so instead let's determine how fast the number of eigenvalues below a given threshold grows. A result of Weyl provides the answer to this question, and I aim to present a proof of a simple case of this remarkable result.
~~~ 5 min break ~~~
4:50 – Speaker: Catherine Ray Title: Triangle Time Abstract: In an equilateral triangle, what can you find? By drawing lines to a point inside, we'll untwine a K3 surface -- divine!