In this talk, we will present the nature of inverse problems in ocean acoustics. We will focus on localizing a sound-transmitting source and on estimating properties related to the propagation medium. New work in our group features denoising acoustic signals for better inversion results, implementing optimal transport methods to improve the convexity of the implicit misfit minimization, and developing Machine Learning algorithms for seabed classification. We will describe open problems in the field and seek solutions.
Phylogenetic trees and networks provide mathematical representations of evolutionary history while raising a wide range of mathematical questions. In this talk, I will introduce phylogenetics through three problems that highlight different mathematical perspectives.
First, I will discuss probabilistic models of lateral gene transfer and the resulting questions of identifiability and statistical inference. Second, I will consider the combinatorics of phylogenetic networks, focusing on how many evolutionary trees a network can display and the resulting extremal questions. Finally, I will describe a divide-and-conquer approach to reconstructing evolutionary networks from data on small subsets of taxa.
No background in phylogenetics is assumed. The goal is to illustrate how questions arising from evolutionary biology can lead to interesting problems in several areas of mathematics.