Spring 2023 Southern Regional Algebra Conference 2023, March 24-26, 2023
Scientific Computing Around Louisiana (SCALA) March 10-11
Spring 2023 Math For All February 24-25, 2023
Week of February 3 - January 30
Topic: Analysis of solitonic interactions, and an initial connection to random matrix theory
Ken McLaughlin | Tulane University
Abstract:
I will describe the interaction between a single soliton and a gas of solitons, providing for the first time a mathematical justification for the kinetic theory as posited by Zakharov in the 1970s. Then, if time permits, I will explain an initial connection to random matrix theory, in order to introduce randomness into a large collection of solitons. This is joint work with Manuela Girotti, Tamara Grava, Robert Jenkins, and Alexander Minakov.
Location: TBA
Time: 3:00pm
Week of January 27 - January 24
Topic: The hydrodynamics of dinoflagellate motility
Rudi Shuech | Tulane
Abstract:
Flagella are crucial to the interactions of many microorganisms with their surrounding fluid environment. The single-celled dinoflagellates have a unique but remarkably conserved flagellation morphology: a trailing longitudinal flagellum and an exquisitely complex transverse flagellum that encircles the cell. What are the selective advantages offered by this arrangement? We investigated the dinoflagellate design in silico using a high-performance regularized Stokeslet boundary element method, comparing to µPIV observations of swimming cells and quantifying how the morphology affects swimming performance. We found that the helical transverse flagellum provides most forward thrust and, despite its near-cell position, is more hydrodynamically efficient than the trailing flagellum; however, the latter is nonetheless required to enable steering. Flagellar hairs and the sheet-like structure of the transverse flagellum allow dinoflagellates to exert strong propulsive forces and maintain high clearance rates without extending a long conventional flagellum far into the surroundings. This unique morphology has thus been essential to the evolution of the generally large, fast-swimming dinoflagellates.
Location: Stanley Thomas 316
Time: 3:00pm
Monday, February 24
Topic: Spherical Tropicalization and Berkovich Analytification
Desmond Coles | University of Texas, Austin
Abstract:
Tropicalization is the process by which algebraic varieties are assigned a "combinatorial shadow". I will review the notion of the tropicalization of a toric variety and recent work on extending this construction to spherical varieties. I will then present how one can construct a deformation retraction from the Berkovich analytification of a spherical variety to its tropicalization.
Location: Temporary location: GI 126
Time: 3:00pm
Week of January 20 - January 16
Topic: Graduate Algebra III: Linguistics
Melanie Tian | Tulane University
Abstract:
We introduce the field of mathematical linguistics in two flavors. First we introduce mathematical methods in linguistics, where we give examples on verifying equivalences and non-equivalences using tools such as lambda calculus and determiners as relations. Then we look at two problems on deciphering unfamiliar writing systems: numeral system in Nahuatl, and Transcendental Algebra constructed by Jakob Linzbach.
Location: Stanley Thomas 316
Time: 4:00pm
Week of January 20 - January 16
Topic: Modeling microswimmers: the effects of cell shape and complex environments
Rudi Shuech | Tulane
Abstract:
In this two-part talk, first I will summarize my previous work on the effects of curved-rod bacterial shapes on swimming performance and other ecologically important tasks. We used a regularized Stokeslet boundary element method to compute the motion of curved-rod microswimmers propelled by rotating helical flagella. We then showed that Pareto-optimal tradeoffs between efficient swimming, chemotaxis, and cell construction cost can explain the morphological diversity of extant curved bacterial species.
In the second part, I will transition to thinking about the complex environments that microorganisms swim through, which are often composed of a viscous fluid with suspended microstructures such as elastic polymers and filamentous networks. These microstructures can have similar length scales to the microorganisms, leading to complex swimming dynamics. Some microorganisms are also known to remodel the viscoelastic networks they move through. To gain insight into the coupling between the dynamics of the swimmer and the network, we combined our computational framework for microswimmer motion with a model of a discrete viscoelastic network. The network is represented by a cloud of points with virtual Maxwell element links, whose properties (i.e., stiffness, relaxation time) can have non-obvious effects on the swimmer dynamics. We model enzymatic dissolution of the network by bacteria or microrobots by breaking links based on their distance to the microswimmer. We investigate how swimming performance is affected by properties of the network and swimmer.
If time allows, I will also introduce our new work on microswimmers penetrating thin, membrane-like interfaces.
Location: Stanley Thomas 316
Time: 3:00pm
Week of December 9 - December 5
Topic: TBA
Speaker | University
Abstract:
TBA
Location: TBA
Time: 3:00 pm
Topic: TBA
Speaker - University (Host: TBA )
Abstract:
TBA
Location: TBA
Time: 3:30 pm
Topic: TBA
Speaker | University
Abstract:
TBA
Location: TBA
Time: 4:00 PM
Topic: TBA
Speaker | Tulane University
Abstract:
TBA
Location: Stanley Thomas 316
Time: 5:00pm
Monday, February
Topic: TBA
Speaker | Tulane University
Abstract:
TBA
Location: TBA
Time: 3:00pm
