Mathematics Colloquium- Featuring UA Math Postdocs

Title: Movement patterns reveal dolphin identity through social dynamics

Abstract: Animal interactions are often understood through how individuals move together. However, we often observe movement without knowing who is who. In this work, movement data are obtained from drone-based imagery, where individuals are observed only for limited period as they move in and out of camera’s field of view. As individuals leave and re-enter the observation frame, trajectories become fragmented and the same animal may be assigned multiple labels, making it difficult to draw reliable conclusions about group behavior. In species such as dolphins, social relationships are reflected in patterns of attraction and alignment that shape how movement evolves over time. These patterns provide a way to recover identity and characterize interactions without relying on uncertain labels. In this talk, I present a Bayesian hierarchical state-space model for jointly inferring identity and social interactions from movement data. I apply this framework to Risso’s dolphins to examine how sonar exposure alters social interactions within the group.

 

Title: Rational Chow groups of Hurwitz spaces

Abstract: The Hurwitz space, parametrizing degree d genus g covers of the projective line up to automorphisms of the target, is a fundamental tool in the study of moduli spaces of curves. In this talk, we shift the focus to the intersection theory on the Hurwitz space itself, and its admissible covers compactification. We will discuss various intersection-theoretic techniques used in computing their rational Chow rings, particularly in the context of triple and quadruple covers.

 

Title: Crowding Effects in Collective Cell Movement under Self-Generated Aerotactic Gradients.

Abstract: Using a self-generated hypoxic assay, it is shown that Acanthamoeba displays a remarkable collective aerotactic behavior: when a cell colony is covered, cells quickly consume the available oxygen and the population spreads outwards at constant speed, which is reminiscent of a similar behavior in Dictyostelium discoideum that we have studied. Yet, at high density only, we observe the emergence of an additional dense ring in Acanthamoeba, unlike in the latter experiment. By proposing a mesoscopic model for Acanthamoeba accounting for collisions, we are able to infer a new density-dependent macroscopic model, which shines light on the characterizing difference between the two experiments. The modeling inferences are confirmed by an experimental investigation of the cell behavior.