Events
Department of Mathematics and Statistics
Texas Tech University
Abstract pdf
The Statistics seminar may be attended in person on Wednesday at 3:00 PM CDT (UT-5).
The Kauffman bracket skein module of a lens space was determined by
Hoste and Przytycki. It can be obtained as the tensor product of two
skein modules of solid tori over the algebra of the cylinder over the
torus. We examine this tensor product structure in detail.
Abstract. An amazing property of Hermite interpolation is that it is a projection
in a Sobolev seminorm. As a result, in constrast with the usual Lagrange
interpolant, Hermite interpolation has a smoothing effect. We show how to
exploit this projection property to develop Hermite-based solvers for differen-
tial equations with novel properties. For hyperbolic pdes, Hermite methods
admit order-independent time steps and highly localized evolution processes
which can be exploited on modern computer architectures. For initial value
problems one can develop implicit schemes of arbitrary order for which the
system size is also order-independent.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math Basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 915 2866 2672
* Passcode: applied
 | Thursday
Oct. 9
6:30 PM
MA 108
|
| Mathematics Education
Math Circle
Stone Fields
Mathematics and Statistics, Texas Tech University
|
Math Circle Fall Flyer
Continuous-time deterministic compartmental mathematical models are often used to simulate and analyze the course of epidemic outbreaks in time. Whereas modelling of control measures in the context of mathematical epidemiology has focused on optimal resource allocation, an important problem is the study of transient dynamic behaviour under state and input constraints for the dynamical system. These constraints normally reflect limitations in the intervention measures due to budget, capacity of healthcare system, or public policy goals.
We address the problem of viability, or existence of solutions of the controlled dynamical system that share a given set of properties, namely solutions that respect a given upper bound on the phase variable (in our case the size of the infected human compartment) subject to the control function taking values in a given compact set. Such transient dynamic behaviour of the solutions can be studied using viability kernels, which represent the largest set of initial states of the dynamical system such that the proportion of infected individuals is sustained below a given ceiling for all future times. Our goal is to characterise the viability kernel, and we focus on a level-set approach based on Bellman's value function satisfying a dynamic programming principle. This approach allows kernels with positive Lebesgue measure to be approximated numerically even for systems of higher dimensions.
As examples we study several models for vector-borne diseases of Susceptible-Infected or Susceptible-Infected-Recovered type for the human host, and Susceptible-Infected for the mosquito vector, as well as a two-patch system with human mobility based on the Lagrangian modelling framework. The epidemic control is based on the use of mosquito repellents in clothing and the control function takes values constrained by the maximum proportion of the host population employing the repellent-treated clothes. The inspiration for this work originates from COST Action 16227 Investigation and mathematical analysis of the effects of avantgarde disease control via mosquito nano-tech-repellents (2017-2022), funded by EU Horizon 2020 Framework Programme.
The Biomath seminar may be attended virtually Friday at 11:00 AM CDT (UT-5) via this Zoom link.
Meeting ID: 938 8653 3169
Passcode: 883472
abstract noon CDT (UT-5)
Zoom link available from Dr. Brent Lindquist upon request.