# Junior Colloquium – 2020-2021

April 4, 2021

Title: Structure-imposed constraints make Brownian walkers efficient searchers

Speaker: Vitaly V. Ganusov (UTK)

Abstract: T lymphocytes, cells of the adaptive immune system, face the challenge of finding rare targets in various tissues. To optimize the search for rare targets it has been proposed that T cells might perform a random walk with long displacements called Levy walks enabling superdiffusive behavior and shorter search times. However, whether the observed random walk patterns are driven by agent-intrinsic programs or being shaped by environmental factors remains largely unknown. I will present our recent work in which we used intravital microscopy to track movement of T cells in the liver. By combining the analysis of experimental data with computational modeling we provide evidence that liver structure has a major influence on the movement patterns of T cells and their efficiency at locating the infection.

March 18, 2021

Title: Drugs, Sex, Rock’n-Roll and a Rational Basis for Hope: What’s Math got to do with it?

Speaker: Lou Gross (UTK)

Abstract: Mathematics underlies much of everyday experience, even if most people don’t realize it. I’ll discuss the process of mathematical modeling and point out how each of us use models regularly. Modeling approaches will be described for some biological examples that illustrate the utility of taking a quantitative perspective in the evolution of sex, gender inequity (including at UTK), drug dosing, and concert sound engineering. Finally, I will summarize recent work to link models of human behavior and global climate that provide some basis for hope regarding projected increases in global temperature.

March 11, 2021

Title: A Stroll Through the Garden of Number Theory

Speaker: Ricardo Conceição (Gettysburg College)

Abstract: Have you ever wondered: What is Number Theory? What is a typical day of work for a number theorist? Can Number Theory save the world? In this talk, I will wonder out loud about these questions and guide you on a brief journey around this rich and traditional field of study. In our stroll, we will spend some time observing a particular problem in Number Theory that I stumbled upon in one of my visits to this beautiful garden.

(Full disclaimer: In this talk no definite answers to the above or similar questions will be given!)

November 12, 2020

Title: Random Walks

Speaker: Joan Lind (UTK)

Abstract:  Suppose you decide to go for a walk, and each time you reach a corner, you randomly choose the direction to take for the next block.  Your path will be an example of a simple random walk.  In this talk, we will take a look at this and other random walks, and we will discuss Schramm-Loewner Evolution, a ground-breaking random process which is related to these random walks.  There will be plenty of pictures and simulations along the way.

October 15, 2020

Title: Why should (1/2)! be something like 0.886227 (aka sqrt(pi)/2)) ?

Speaker: Jochen Denzler (UTK)

Abstract: This presentation gives a well-motivated proof of a theorem by Bohr and Mollerup according to which there is only one good’ way of interpolating n! for non-integers n (and this includes motivating the proper definition of good’). Other properties of this interpolation, the Gamma function, will be discussed. While complex variable techniques like analytic continuation will be referenced, the exposition will not depend on familiarity with complex variables.