Algebraic Topology and Geometric Metaphors in Biology | Schmuel Weinberger

Описание: Recorded on 01/21/2026
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Title: Algebraic Topology and Geometric Metaphors in Biology
Speaker: Schmuel Weinberger

This talk was recorded as part of the 'Expanding the Palette of Mathematics in Biology' workshop

Workshop Overview:
Mathematical Biology tends to involve a very small and specific (albeit extremely important and useful) branch of math, namely differential equations and dynamical systems. The vast majority of publications in which something biological is modeled present the model as a system of differential equations which are then solved, simulated, or otherwise analyzed for features like stability, limit cycles, hysteresis, etc. Meanwhile, huge swaths of mathematics are seldom if ever discussed in the context of biological problems. Examples include group theory, category theory, differential geometry, algebraic topology, number theory, the list goes on and on. For many important biological problems, differential equations may not be the correct representation. Such problems could be addressed in new ways by formulating the problem in different mathematical terms, allowing different mathematical approaches to be brought to bear while, at the same time, giving rise to new, interesting mathematical problems. Some of these problems might, in turn, serve as biological motivating exercises for teaching different areas of math to non-major students.

This workshop will bring together mathematicians working on areas not traditionally associated with "mathematical biology" and biologists interested in exploring their biological questions in new theoretical ways. The goal is to identify specific biological questions that could be viewed from different mathematical lenses, and to foster mutual interactions between the two groups in such a way that the mathematical attendees go away with new math problems to think about, i.e. problems that are interesting from a mathematical point of view, while the biologists go away with new perspectives on their problems and maybe an appreciation that there is much more in math besides solving equations.

NITMB Overview:
The NSF-Simons National Institute for Theory and Mathematics in Biology (NITMB) aims to integrate the disciplines of mathematics and biology in order to transform the practice of biological research and to inspire new mathematical discoveries. NITMB is a partnership between Northwestern University and the University of Chicago. It is funded by the National Science Foundation DMS-2235451 and the Simons Foundations MP-TMPS-00005320.

The mission of the NITMB is to create a nationwide collaborative research community that will generate new mathematical results and uncover the “rules of life” through theories, data-informed mathematical models, and computational and statistical tools.