Fall 2026 Mathematics Colloquia Schedule

Colloquium Date Colloquium Details
September 25, 2026 Dr. Panayotis Panayotaros
Mode Interactions of Surface Gravity Waves in Triangular Domains
September 25 abstract

We present a model of nonlinear mode interactions of 2-D gravity surface water waves in a domain with inclined lateral boundaries, assuming free surface potential flow. We consider an isosceles triangular domain with known linear modes and frequencies, and describe a preliminary analysis of the lowest nonlinear mode using normal forms. We also discuss theoretical and numerical work in progress on linear waves in more general domains. This is joint work with Eddaly Guerra Velasco, Boris A. Percino Figueroa, and Rosa M. Vargas Magaña.


4:30–5:30 pm | FLN 2.01.02
October 2, 2026 Dr. Rayanne Luke
Mathematical Models of Contact Lens Drug Delivery: Blinking and Lens Design
October 2 abstract

Drug-eluting contact lenses are an ophthalmic drug delivery alternative to eye drops. Such lenses can significantly increase drug residence time and therefore effectiveness. We design models of contact lens drug delivery to align with experimental systems and consider blinking and lens design. Our approach couples partial differential equations for linear diffusion of drug inside the contact lens with compartment models for the pre- and post-lens tear films and the eyelid region. To study blinking, we model the effect of a blink on the pre- and post-lens tear film drug concentrations, investigating mechanisms such as partial or full sweep out of drug by the eyelid, and squeezing or sliding of the lens. The most likely scenario is identified by comparing to model eye data. To study lens design, we model drug-polymer films encapsulated in hydrogel lenses, where the drug-laden region appears as an annulus in a top-down view. We investigate the dependence of drug release time on lens material and geometric properties and identify drug delivery transport mechanisms by comparing to in vivo data. In both cases, we recover drug cumulative release profiles from experimental systems, and determine the effects of blinking and lens design properties on cumulative release. This can inform our understanding of the mechanics of contact lens drug delivery and predict targeted tissue transport of drug. This is joint work with Dan Anderson (GMU).


3–4 pm | BSB 3.03.02
November 13, 2026 Dr. Claudia Rodriguez
Understanding Rural Mathematics Education Ecosystems: Connections, Collaboration, and Sustainability
November 13 abstract

How do universities, schools, teachers, students, and communities work together to create and sustain meaningful mathematics learning opportunities in rural settings? While professional development, teacher preparation, and student enrichment are often examined as separate educational initiatives, the connections among these experiences may offer valuable insights into how rural mathematics education ecosystems function.

This presentation draws on two initiatives at Tarleton State University. The first is a collaborative professional development project focused on artificial intelligence and mathematical modeling, bringing together in-service mathematics teachers, preservice teachers, a graduate student mentor, and university faculty. Grounded in Communities of Practice theory, the project examines how participation in authentic professional learning activities may support preservice teachers’ developing professional identities and instructional practices. The second initiative, Tarleton Math Scholars, is a mathematics enrichment program for rural high school students supported by pre-service mathematics teachers serving as tutors.

Preliminary research and evaluation efforts across these initiatives provide an emerging empirical foundation for examining mathematics education in rural contexts. Qualitative data from the professional development project explore participants' experiences, perceptions of artificial intelligence, and engagement with mathematical modeling, while ongoing data collection examines the implementation of instructional practices. Additionally, program evaluation data from Tarleton Math Scholars offer initial insights into students’ mathematics experiences and perceptions.

Although developed independently, these initiatives revealed connections among participants, instructional practices, and institutional settings that extend beyond each program's original objectives. Recognizing these connections has prompted a broader research agenda to systematically investigate how professional knowledge, relationships, and resources move across rural mathematics education settings, and how these interactions may contribute to the long-term sustainability of educational initiatives.


4–5 pm | FLN 2.01.02