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Mathematical Sciences



Math Colloquium

Thursday, December 3, 2020


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Speaker: Kevin Sweet

Title: Modeling the Effect of Quorum-Sensing Regulated T6SS-Mediated Killing on Biofilms

Abstract: Bacterial interactions heavily impact how a biofilm forms, and how bacteria communicate impacts how they interact. One way that bacteria can communicate is through the production and sensing of quorum sensing molecules which regulate certain genetic expressions. It was our focus to model and analyze the relationship between quorum sensing regulated Type VI Secretion System (T6SS) mediated killing in two strains of Agrobacterium tumefaciens and biofilm structure. We constructed a deterministic two dimensional model that held the rate of quorum sensing molecule production constant in order to illustrate basic interactions between two bacterial strains and the effect that such interactions have on the biofilm’s development. By adding another dimension to our model we can more realistically show the effects that quorum sensing regulated T6SS mediated killing has on the biofilm’s structure based on the current state of the biofilm. This work illustrates how quorum sensing T6SS mediated killing contributes to overall biofilm structure.

Speaker: Abby Brauer

Title: Numerical Analysis of the 1-Dimensional Parabolic Optimal Transport Problem

Abstract: Numerical methods for the optimal transport problem is an active area of research. Recent work of Kitagawa and Abedin shows that the solution of a time-dependent equation converges exponentially fast, as time goes to infinity, to the solution of the optimal transport problem. This suggests a fast numerical algorithm for computing optimal maps; we investigate such an algorithm here in the 1-dimensional case. Specifically, we use a finite-difference scheme to solve the time-dependent optimal transport problem and carry out an error analysis of the scheme. A collection of numerical examples is also presented and discussed.






Visit the Past Colloquia page for a list of talks from recent semesters.