Printer-friendly versionAbstracts
Week of February 18, 2024
| Group Actions, Geometry and Dynamics | Prime number theorems for polynomials from homogeneous dynamics |
4:00pm -
KT205
|
The Bateman-Horn conjecture gives a prediction for how often an irreducible polynomial takes on prime values. In this talk, I will discuss the proof of Bateman-Horn for two new polynomials – the determinant polynomial on nxn matrices and the determinant polynomial on nxn symmetric matrices. A key tool in the proof is the input of homogeneous dynamics to count the number of integral points on level sets. This talk is based on joint work with Giorgos Kotsovolis. |
| Analysis | Invariant Gibbs measures for (1+1)-dimensional wave maps into Lie groups. | 4:00pm - |
We consider the wave maps equation for maps from $(1+1)$-dimensional Minkowski space into a compact Lie group. The Gibbs measure of this model corresponds to a Brown- ian motion on the Lie group, which is a natural object from stochastic differential geometry. Our main result is the invariance of the Gibbs measure under the wave maps equation and is the first result of this kind for any geometric wave equation. The proof combines techniques from differential geometry, partial differential equations, and probability theory. |
| Friday Morning Seminar | Friday Morning Seminar |
10:00am -
KT801
|
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! |