Mathematical Foundations of Mechanical Biology (10w5056)


(University of Calgary)

Krishna Garikipati (University of Michigan)

Alain Goriely (Oxford University)


The Banff International Research Station will host the "Mathematical Foundations of Mechanical Biology" workshop from September 26 to October 1, 2010.

In the last decade, there has been tremendous advances in medicine, physiology, and biology which have transformed life sciences from a descriptive field into a quantitative field. In particular, many scientists have come to the realization than mechanics is an important aspect for the evolution of biological systems. Mechanics is the study of deformations and displacements of bodies subjected to forces. Therefore, it enters at every level of biology, from the elasticity of molecules to the circulation of blood and the structure of bones. Mechanics, as a scientific field, has always been at the interface between mathematics and science. While mechanics provides a quantitative framework for the study of bodies under forces it has also always been a great inspirational source for mathematical problems, and in many instances research in mathematics has evolved in parallel with mechanics (for instance, the dynamical systems was developed in symbiosis with celestial mechanics). Similarly recent advances in biology have challenged mechanicians and mathematicians. In particular, problems in continuum mechanics of both liquids and solids play an important role in the regular and pathological function of many biological systems as well as a mean to carry information between systems. Whereas, continuum mechanics has a long tradition, it has been mostly developed for engineering purpose where structures are static and in equilibrium and not for living systems which have the remarkable property of being in constant evolution and rarely in thermodynamic equilibrium. Therefore, many fundamental concepts must be revisited to devise a theory which is both mathematically rigorous but also suitable to answer important scientific questions (e.g. How do we model growing structure? How do singularity and patterns form? How do elastic networks transmit deformation and information?)

The workshop is on the Mathematical Foundations of Mechanical Biology. The experts from various fields (mathematics, mechanics, engineering, biologists) will gather to identify current scientific challenges in the mechanics of biological systems and develop the mathematical foundations and techniques relevant for these problems. There has been significant progress in this research field recently and bringing experts together will provide an excellent forum for discuss the current state of play and facilitate new collaborations to address outstanding problems, of which there are many, which is one of the reasons that it makes it an exciting area to work in.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí­a (CONACYT).