Applied math seminar: Shelby Cox (University of Michigan) @ Keller 303
Feb 28 @ 3:30 pm – 4:30 pm

Title: Maximum Likelihood Degree of Brownian motion tree models

Abstract: A Brownian motion tree model is a Gaussian model whose associated set of covariance matrices is linearly constrained according to common ancestry in a phylogenetic tree. In joint work with Jane Coons, Aida Maraj, and Ikenna Nometa, we study the complexity of inferring the maximum likelihood (ML) estimator for a Brownian motion tree model by computing its ML-degree. Our main result is that the ML-degree of the BMT model on a star tree with n + 1 leaves is 2^(n+1) – 2n – 3, which was previously conjectured by Amendola and Zwiernik. We also prove that the ML-degree of a Brownian motion tree model is independent of the choice of root and we find a combinatorial formula for the likelihood function. In this talk, I will introduce Brownian motion tree models and the tools from computational algebraic geometry that we use to compute the ML-degree.

Applied math seminar: Shilpa Khatri (UC Merced) @ Keller 303
Mar 6 @ 3:30 pm – 4:30 pm

Title: Fluid dynamics within symbiotic systems

Abstract: To understand the fluid dynamics of marine symbiotic systems, systems composed of multiple organisms, fluid-structure interaction problems must be solved. Challenges exist in developing numerical methods to solve these flow problems with boundary conditions at fluid-structure interfaces. We are studying the impact of fluid flow on symbiotic systems within two different biological systems. (1) Pulsing soft corals, Xeniidae corals, that have internal algal endosymbionts, zooxanthellae, which provide them with much of their energy and (2) the bobtail squid, Euprymna scolopes, that depend on the luminous bacteria, Vibrio fischeri, to protect them from predators through counterillumination. Both of these problems are motivated by field and experimental work in the marine sciences. I will discuss these related data, mathematical models and numerical methods developed to study these problems and provide comparisons with the modeling.

Colloquium talk. @ Keller 303
Apr 5 @ 3:30 pm – 4:30 pm

Speaker: Dr. Kamuela Yong, UH West Oahu.

3:30-4:30PM, Keller 303.

Title: When Mathematicians Don’t Count

Abstract: A systemic issue of Indigenous invisibility within the mathematical community persists, rooted in practices that obscure Indigenous individuals in demographic data. Whether through aggregation with broader groups, categorization as “other,” or complete omission due to identifiability concerns, they remain statistically invisible. This not only impedes accurate representation but also perpetuates the false narrative that mathematics is devoid of Indigenous presence.

Simultaneously, Indigenous voices remain critically absent within educational spaces.

In this talk, I will not only address these challenges but also share our ongoing efforts to build a thriving community of Indigenous mathematicians. Furthermore, I will discuss my personal journey in transforming my curriculum, infusing it with examples of ancestral knowledge and Indigenous perspectives integrated into mathematical concepts.

By shedding light on these issues and offering actionable strategies for change, this presentation seeks to inspire hope and promote a more inclusive and welcoming environment for Indigenous individuals within the mathematical community.

Benson Farb public lecture
Apr 23 @ 5:30 pm – 6:30 pm
Benson Farb colloquium
Apr 25 @ 3:30 pm – 4:30 pm
Benson Farb seminar
Apr 26 @ 3:30 pm – 4:30 pm
Lynette Agcaoili MA presentation
Apr 30 @ 3:00 pm – 4:00 pm

Lynette Agcaoili’s MA presentation is scheduled for April 30, 2024.  Everyone is welcome and graduate students are especially encouraged to attend.

Tuesday, April 30, 2024, 3:00 – 5:00 pm, Keller 404

Title:  An Introduction to Inverse Limits

Abstract:  The goal of this presentation is to give an introduction to inverse limits in a way that is (hopefully) accessible to advanced undergraduates/incoming graduate students. We will, of course, define what inverse limits are, and then construct injective resolutions for both abelian groups and inverse systems. We will then talk about flasque resolutions and some properties of flasque to construct a short exact sequence of inverse systems. Finally we will give explicit constructions of the inverse limit of a system and its first derived functor (i.e. varprojlim_{leftarrow}^(1) A_i), and show that if our indexing set is the natural numbers, then the second derived functor and higher are all 0 (i.e. varprojlim_{leftarrow}^(n) A_i = 0 for any n>1).

Last day of instruction
May 1 all-day