Taylor Brysiewicz

University of Notre Dame

Thursday, September 23, 2021

3:30 pm - 4:30 pm

154 Hurley Hall

Title: Maximum Likelihood Degrees of Point Configurations

Abstract:

The goal of likelihood inference in statistics is to maximize a monomial z^u over some statistical model M. The number of critical points of this optimization problem measures its complexity and is called the maximum likelihood degree of the model. When M is the configuration space of points on a projective line, the critical equations are known in the physics literature as scattering equations. The number of solutions to these equations is well-known, but the analogous numbers for higher dimensional projective spaces remain elusive.

Using techniques from algebraic geometry, topology, tropical geometry, combinatorics, and numerics, we discuss a computational framework for counting, computing, and understanding the solutions to these generalized scattering equations.