Events
Department of Mathematics and Statistics
Texas Tech University
The Kuramoto-Sivashinsky equation (KSE) draws the attention of many mathematicians and scientists for its chaotic behavior and its similarity to Navier-Stokes equations. In this present study, Serrin-type regularity of two-dimensional Kuramoto-Sivashinsky equation is studied. PDF available Watch online on Tuesday the 1st at 4 PM via this Zoom link.
The progression of HIV infection to AIDS is unclear and under examined. Many mechanisms have been proposed, including a decline in immune response, increase in replication rate, involution of the thymus, syncytium inducing capacity, activation of the latently infected cell pool, chronic activation of the immune system, and the ability of the virus to infect other immune system cells. The significance of each mechanism in combination has not been studied. We develop a simple HIV viral dynamics model incorporating proposed mechanisms as parameters that are allowed to vary. In the entire parameter space, we derive two formulae for the basic reproduction number (R0) by considering the infection starting with a single infected CD4 T cell and a single virion, respectively. We show that both formulae are equivalent. We derive analytical conditions for the occurrence of backward and forward bifurcations. To investigate the influence of the proposed mechanisms to the HIV progression, we perform uncertainty and sensitivity analysis for all parameters and conduct a bifurcation analysis on all parameters that are shown to be significant, in combination, to explore various HIV/AIDS progression dynamics. PDF available
 | Wednesday
Sep. 2
3:00 PM
Online
|
| Algebra and Number Theory
No Seminar
|
In this talk, I give a particular example in which a deterministic approach seems hopeless and yet a stochastic approach successfully allows us to get a glimpse of physics underneath. The celebrated Helmholtz - Kelvin's conservation of circulation from 1858 states that for a smooth solution to the Euler equations, the circulation around a curve moving with the fluid is a constant in time. Its proof completely breaks down once we add diffusion to the Euler equations, which is the Navier-Stokes equations, and no precise statement could be made for the subsequent 150 years. Remarkably, Constantin and Iyer in 2008 (Iyer's Ph.D. thesis in 2006) showed that if we consider random characteristics (essentially characteristics from PDE graduate course but added by noise), then an analog of the circulation theorem for the Navier-Stokes equations holds and states that the circulation on the loop is given by the average over the circulations of the ensemble of loops at the earlier times. Analogous statements can be made for other equations of hydrodynamics such as magnetohydrodynamics, and Boussinesq systems.I will give an introduction to the language of simplicial presheaves, which lies at the foundation of modern differential and algebraic geometry. In particular, I will explain sheaf cohomology in this language.This semester, the Financial Math seminar series is concentrating on alternative financial indices. The first seminar will consist of an overview from various members of this working group. The agenda for the first seminar is
1. Davide Lauria: index on financial returns from U.S. movies
2. Brent Lindquist: real estate analytics indices
3. Thilini Mahanama: index on financial assets due to natural disasters; introduction of new index on crime
4. Abootaleb Shirvani: U.S. citizenry “well-being” index
5. Zari Rachev: Vol-of-vol indices
6. Dimitri Volchenkov: political risk index
7. Jiho Park and/or Yuan Hu: near riskless rate portfolios
All presentations in the first seminar will be kept to 10 minutes maximum. Watch online at 2 PM this Friday the 4th via this Zoom link.