Schedule, Notes/Handouts & Videos

In evolution, hybridization occurs when two distinct species merge genetically to create a new species. Recent advances in phylogenetic analyses of DNA have revealed that hybridization has played an important role in the evolutionary history of many species. Reconstructing evolutionary relationships is already challenging because of the many processes that shape species' histories, and the presence of hybridization  adds a layer of complexity. In this talk, we explore some of the challenges of inferring evolutionary relationships in the presence of hybridization under the Network Multispecies Coalescent model (NMSC).  Specifically, we discuss which aspects of evolutionary history can be reliably recovered from data (are identifiable) and also present recent advances in statistically consistent inference methods. Additionally, we  present some of the consequences of model misspecification when the true evolutionary process violates the assumptions of an inference model.

The Dirichlet problem for the real elliptic Monge-Ampère equation in two dimensions arises in many important applications including optimal transport, machine learning, and geometry. In this talk, I will discuss the performance of two numerical methods for the solution of this problem. The first method is an augmented Lagrangian based method that reformulates the problem as a saddle point problem. The second method is a relaxation algorithm using a least squares formulation. This work is part of an ongoing undergraduate research project, and I will present preliminary numerical experiments in two dimensions comparing the two methods with respect to accuracy, convergence behavior, and computational cost.

Work by J.C. Meza and Isaic Cruse, UC Merced.