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SUMMARY

Project “Mathematical Methods for Ecology and Industrial Management”

IP Kurusch Ebrahimi-Fard

This project is supported by a 2014 "BBVA Foundation Grant to Researchers, Innovators and Cultural Creators". It may be considered a nice example for the “unreasonable effectiveness” of mathematics in the sciences. Its central theme are control systems, which are ubiquitous in modern technology. Indeed, they can be found in virtually all modes of transportation, power generation and distribution systems, automated manufacturing plants, medical devices, and communication systems. Among others, the project addresses the problem of trajectory generation, which aims at determining the inputs for a given system in order to make the outputs follow some desired trajectory. As control methodologies are now being adapted for biological systems, new versions of the trajectory generation problem are emerging. For example, a population of fish species is known to be controlled by a number of factors such as water temperature, the availability of food, the number of predators, harvesting, and the presence of disease and pollution. Given that some of these inputs can be controlled and a certain population profile as a function of time is desired, what are the suitable system inputs to produce this profile? The general goal of the research program is to adapt and apply recent advances in trajectory generation for nonlinear control systems, based on techniques and methods coming from advanced algebraic combinatorics, to ecological management problems.

Workshop on Mathematical Perspectives in Biology