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Ask not what algebra can do for biology - ask what biology can do for algebra

Banff International Research Station for Mathematical Innovation and Discovery

Discrete models, such as Boolean networks, are an increasingly popular modeling framework in systems biology, with many hundreds of published models. The advantages are, among others, that they are intuitive and don't require detailed quantitative knowledge such as kinetic parameters. One disadvantage is that there are relatively few mathematical and computational tools available for this model type. As a basic example, given a model, how can we compute all its steady states The basic mathematical framework they can be cast in is polynomial dynamical systems over finite fields. There is a rich convergence of dynamic, algebraic, combinatorial, and graph-theoretic features that come together within this type of mathematical object. Yet very little of this convergence has been used to study a mathematically rich class of objects, with important applications to problems in the life sciences and elsewhere. This talk will discuss several mathematical and computational problems, inspired but not directly connected to applications in biology, that can stimulate interesting research in algebra, broadly defined.

Mathematics; Mathematical logic and foundations; Algebraic geometry

video/mp4

Author affiliation: University of Connecticut School of Medicine

2020-12-03

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/76645

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/