# Entropy Methods, PDEs, Functional Inequalities, and Applications (14w5109)

## Organizers

(Rutgers University)

(Université Paris-Dauphine)

(TU-Munich)

(Carnegie Mellon University)

## Description

The Banff International Research Station will host the "Entropy Methods, PDEs, Functional Inequalities, and Applications" workshop from June 29th to July 4th, 2014.

Many of the processes that play a role in everyday life
--- from the movement of the air around us to the conduction of electricity in our cell phone ---
can be modeled by systems composed of many particles.
In physics many'' typically means a number of the order of 10 to the 23;
in studies of the collective behaviour of animals in biology, numbers are much lower but still huge.
So naturally, the dynamics of these models is extremely complex in most situations,
and a good understanding of at least some of the system's characteristic features is of crucial importance.

emph{Entropies} are a key tool from this point of view:
they measure, in a sense, how far the system is from its equilibrium configuration,
and they never increase as time goes by, which means that they also capture the system's trend towards equilibrium.
In this spirit, emph{entropy methods}/ provide guiding lines both for the modeling and for the analysis of complex systems.
This workshop will bring together pure and applied mathematicians in order to discuss
how to identify an entropy for a given complex system,
how to analyze the temporal properties of that entropy mathematically,
and to draw conclusions on the original problem,
which is related, emph{e.g.}, to fluid dynamics, material sciences or biology.

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).