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Workshop

Random Dynamical Systems, with Applications in Biology

875 North Michigan Avenue
Chicago, IL 60611 United States

Workshop Organizers

Stefano Allesina

Antonio Auffinger

Nisha Chandramoorthy

Brent Doiron

Mary Silber

Overview

Mathematical models in the form of deterministic, autonomous dynamical systems have played a foundational role in all branches of mathematical biology, particularly in ecology, epidemiology, and neuroscience. Environmental fluctuations, heterogeneity, and processes like mutations, adaptation, and learning are often incorporated by adding some random and possibly time-dependent elements to the model framework. Randomness may also be incorporated when model parameters are uncertain, or to initialize some complex network structure, or as part of an algorithm that speeds up model computations. While some of these mathematical models remain amenable to rigorous analysis, many pose new mathematical and computational challenges. There is an opportunity here to develop new robust approaches to analyze these random dynamical systems in order to gain a more comprehensive understanding of the biological phenomena they model.

This workshop will convene mathematical scientists, working on random dynamical systems, and biological scientists who incorporate these frameworks in their research. The goal is to foster an exchange of ideas between these different research communities. The workshop is structured  to help participants identify the most promising opportunities for developing mathematics, at this interface between dynamical systems and probability theory, in a way that is informed by the biological questions. The program includes overview talks, structured problem formulation sessions, and will have ample time for small groups to work together to refine the questions to pursue through further collaboration.

An (AI) artist’s impression of the mathematics of fluctuations and randomness in cell biology