Entropies, the Geometry of Nonlinear Flows, and their Applications (18w5069)


Jose A. Carrillo (University of Oxford)

Eric Carlen (Rutgers University)

(Université Paris-Dauphine)


Dejan Slepcev (Carnegie Mellon University)


The Banff International Research Station will host the "Entropies, the Geometry of Nonlinear Flows, and their Applications" workshop from April 8th to April 13th, 2018.

Many natural processes involving the interaction of a very large number of particles, such as conduction of heat, fluid flows and chemical reactions, possess an entropy, a quantity that increases during the evolution. A powerful strategy for quantitatively understanding the properties of such systems is to establish mathematical relations between entropies and other quantities characterizing the state of the system. The investigation of these relations has been extremely successful explaining and predicting the properties of the dynamics of such large and complicated systems, and to draw the sharpest conclusions it is important to establish the optimal relations between relevant quantities.

There is also an important geometric aspect to the evolutions of such systems. Mathematically, many nonlinear evolution equations can be interpreted as gradient flows of entropy functionals; i.e., steepest ascent or descent over the entropy/energy landscape with respect to an appropriate notion of distance. This interpretation is useful not only to understand the abstract geometric framework of the nonlinear equations, but also to deal, for instance, with particle approximations and handle mass conservative models in connection with mass transport theory.

A large scientific community has been involved in this area since the first meeting held in Banff in 2006, which played an important role in the development of the topic, and entropy methods have now reached a certain maturity through the geometric interpretation of nonlinear flows. The area is now more vibrant than ever involving a growing network of interaction between branches of mathematics, physics, biology and the social sciences. This meeting is intended to consolidate this progress and set the stage for new advances.

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 U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).