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Research Seminars: Applied and Computational Mathematics

Fall 2021

Time & Location: Typically talks will be Friday in Zoom Chat at 2:00 PM.
Organizers: Nathan Glatt-Holtz and Kun Zhao

Archives

 

 

September 3

Title: TBA

Beskos ? | Institution

Abstract: TBA

 

September 10

Title: TBA

Nisan Ben Gal | 3M

Abstract: TBA

 

September 17

Title: Almost-Periodic Schr\"odinger Operators with Thin Spectra

Jake Fillman | Texas Tech

Abstract: The determination of the spectrum of a Schr\"odinger operator is a fundamental problem in mathematical quantum mechanics. We will discuss a series of results showing that almost-periodic Schr\"odinger operators can exhibit spectra that are remarkably thin in the sense of Lebesgue measure and fractal dimensions: the spectrum can be a Cantor set of zero Lebesgue measure and zero Hausdorff dimension.  [joint work with D. Damanik, A. Gorodetski, and M. Lukic]

 

September 24

Title: TBA

Bravetti | Institution

Abstract: TBA

 

October 1

Title: Parameter Estimation in an SPDE Model for Cell Repolarisation

Josef Janak | Potsdam

Abstract: We propose a stochastic Meinhardt model for cell repolarisation and study how parameter estimation techniques developed for simple linear SPDE models apply in this situation. We pursue estimation of the diffusion term based on continuous time observations which are localised in space. We show asymptotic normality for our estimator as the space resolution becomes finer. We demonstrate the performance of the model and the estimator in numerical and real data experiments.

 

October 8

Title: Non-conservative H^{1/2-} weak solutions of the incompressible 3D Euler equations

Matthew Novack | Institute for Advanced Study

Abstract: We will discuss the motivation and techniques behind a recent construction of non-conservative weak solutions to the 3D incompressible Euler equations on the periodic box. The most important feature of this construction is that for any positive regularity parameter β < 1/2, it produces infinitely many solutions which lie in C^0_t H^β_x . In particular, these solutions have an L^2-based regularity index strictly larger than 1/3, thus deviating from the scaling of the Kolmogorov-Obhukov 5/3 power spectrum in the inertial range.

This is joint work with Tristan Buckmaster, Nader Masmoudi, and Vlad Vicol.

Time: 2:00

 

October 15

Title: Digital Twins and Efficient Clinical Trials

David Li-Bland | Unlearn.AI

Abstract: Clinical trials for a novel medical treatment measure the effect of the treatment by estimating the change in disease progression between a group of patients who receive the treatment, and a control group of patients who instead receive a placebo. One typically needs a large group of patients to accurately measure this treatment effect, which makes it very difficult to explore new treatments for rare diseases or diseases with a low quality of life (such as Alzheimers, MS, or ALS) where patients face practical challenges when participating in clinical trials.

In this talk, I will describe how we use machine learning to generate Digital Twins of patients. Such Digital Twins significantly reduce the number of patients needed for a clinical trial, and yet we can provide stastical guarantees that their use does not increase the odds that an ineffective or unsafe treatment would be wrongly approved.

 

October 22

Title: Modeling Immunity to Malaria with an Age-Structured PDE Framework

Zhuolin Qu | Department of Mathematics, University of Texas at San Antonio

Abstract: Malaria is one of the deadliest infectious diseases globally, causing hundreds of thousands of deaths each year. It disproportionately affects young children, with two-thirds of fatalities occurring in under-fives. Individuals acquire protection from disease through repeated exposure, and this immunity plays a crucial role in the dynamics of malaria spread. We develop a novel age-structured PDE model of malaria specifically tracking acquisition and loss of immunity across the population. Using our analytical calculation of the basic reproduction number (R0), we study the role of vaccination and immunity feedback on severe disease and malaria incidence. Using demographic and immunological data, we parameterized our model to simulate realistic scenarios. Thus, via a combination of analytic and numerical investigations, our work sheds new light on the role of acquired immunity in malaria dynamics and the impact on vaccination strategies in the presence of demographic effects.

This is a joint work with Lauren Childs, Christina Edholm, Denis Patterson, Joan Ponce, Olivia Prosper, and Lihong Zhao.

 

October 29

Title: TBA

Speaker | Institution

Abstract: TBA

 

November 5

Title: TBA

Speaker | Institution

Abstract: TBA

 

November 12

Title: TBA

Konstantinos ? | Institution

Abstract: TBA

 

November 19

Title: TBA

Weber ? | Institution

Abstract: TBA

 

December 3

Title: TBA

Chapouto ? | Institution

Abstract: TBA

 

December 10

Title: TBA

Aseel Farhat | Florida State University

Abstract: TBA