Geometric and Analytic Inequalities (16w5047)

The Banff International Research Station will host the "Geometric and Analytic Inequalities" workshop from July 10th to July 15th, 2016.

Why does "roundness" look so pleasing and attractive? And why is it so common in nature?

The answer probably relies in the Isoperimetric inequality, one of the best known and most intriguing result in mathematics, already familiar to ancient Greeks.

The classical statement of the Isoperimetric Inequality in the plane sounds as follows: among all sets with given area, the disk has the smallest perimeter or, equivalently, among all closed planar curves with given length, the circle encloses the biggest area. This property generalizes to the space: among sets with given volume, balls have the smallest surface area (equivalently, among all sets with given surface area, the ball has the biggest volume). This optimality property of circle and sphere has many physical applications, making the sphere the most convenient shape in many natural situations. This explains the natural "beauty of roundness". Although even a child can understand its statement, to obtain a full proof of the Isoperimetric Inequality has been a challenging problem that stretched mathematicians along many centuries, stimulating a lot of new ideas and techniques up to nowadays. The isoperimetric inequality is the prototype
of what we call geometric-analytic inequalities, that are the subject of this workshop: geometric-looking inequalitieas which have a deep analytic nature.

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)..