Title: Advances in Asymptotic and Computational Methods for Biological Transport
Speaker: Alan Lindsay, University of Notre Dame
Abstract: Asymptotic analysis remains one of the most powerful analytical tools for extracting interpretable information from mathematical models in science. These methods systematically exploit multiscale structure to reduce complex and often intractable problems to a sequence of tractable sub-problems. When coupled with modern numerical methods, they greatly expand the range and scope of scientific questions that can be addressed.
In this talk I will discuss the insights these tools have yielded into the role that geometry, dynamics and localization play in biological transport. For the diffusive delivery of cargoes to small reactive sites, they give precise information on how the spatial organization of those sites shapes function. This has led to new solutions to the long-standing Berg-Purcell problem and the narrow escape problem. Underpinning these results is a suite of high-order boundary integral solvers which pair with asymptotic methods to resolve multiscale features and massively expand the geometric scope of biological problems that can be investigated. Throughout the talk I will highlight where interactions with experimental science have guided the direction of the mathematics, and I will close with promising directions for future enquiry.
Zoom: https://northwestern.zoom.us/j/98486002568
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Natalie Masini
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