Colloquium

Current contacts: Jaclyn Lang and Katrina Morgan

Francesca Bernardi, Worcester Polytechnic Institute

Understanding microscale fluid and particle transport is critical to perfecting the manufacturingand use of microfluidic technologies in medical, industrial, and environmental engineeringapplications. In this talk, I will focus on the microfiltration systems utilized by municipal facilitiesin the US performing water purification for potable water reuse. In these systems, as wastewateris pushed through the filters, foulants and pollutants are captured by the membrane allowingclean, drinkable water to exit. 

I will introduce two 2D mathematical approaches to model filters with different geometries: (1)a flat-sheet membrane model tackled via Monte Carlo simulations to qualitatively capture foulingand cleaning mechanisms. And (2) a single hollow-fiber membrane model approximatedanalytically through the fluid dynamics in a semi-infinite channel with permeable walls. Resolvingthe solute and particle transport details of the microfiltration process would allow for bettercontrol of fouling and cleaning mechanisms and could improve its efficiency. Open questions andpossible next steps will be discussed.

Mathematical approaches to microfiltration

Event Date
2025-02-03
Event Time
04:00 pm ~ 05:00 pm
Event Location
Wachman 617

Models of social and biological systems

Event Date
2025-02-17
Event Time
04:00 pm ~ 05:00 pm
Event Location
Wachman Hall 617

Olivia Chu, Bryn Mawr College

Abstract: Evolutionary dynamics shape social and biological systems across scales, from the evolution of multicellularity to the emergence of underground fungal symbioses to the formation and maintenance of animal groups and human societies. In these complex adaptive systems, small-scale interactions and associations can lead to emergent, large-scale phenomena. These interactions are often greatly influenced by various forms of heterogeneity, such as personality differences in human populations and variation in altruistic tendencies in animals. In this talk, I will present several models of complex social and biological systems, motivated by real-world phenomena and observations. These models are driven by evolutionary game theory, opinion dynamics frameworks, and agent-based modeling, and employ tools from stochastic processes, differential equations, and dynamical network analysis. I will discuss applications such as the evolution of cooperation, social group formation, the effects of environmental shocks on political opinions and activism, and altruistic tensions in social insect populations.

Using logic to investigate homeomorphism groups (Thomas Koberda)

Event Date
2025-03-17
Event Time
04:00 pm ~ 05:00 pm
Event Location
Wachman Hall 617

Thomas Koberda, University of Virginia

Abstract: It is a difficult and deep problem to understand countable groups that can act by homeomorphisms on compact manifolds, especially in dimension two or more. I will discuss some new ways of investigating groups acting on manifolds through ideas from mathematical logic. This talk will include work that is joint with Sang-hyun Kim and J. De la Nuez Gonzalez.

Noncommutative tensor triangular geometry

Event Date
2025-03-31
Event Time
04:00 pm ~ 05:00 pm
Event Location
Wachman 617

Milen Yakimov, Northeastern University

One of the major approaches to representation theory is via support theories. They come in different flavors and have different origins. The talk will be a gentle introduction to noncommutative tensor triangular geometry, which is designed as a universal approach to support varieties. No algebraic or categorical background will be assumed. The talk is based on joint works with Dan Nakano (Univ Georgia) and Kent Vashaw (UCLA).