Recent Advances in Comparison Geometry (24w5226)


Virginia Agostiniani (Università di Trento)

Mattia Fogagnolo (Università di Padova)

Pengzi Miao (University of Miami)


The Institute for Advanced Study in Mathematics will host the “Recent Advances in Comparison Geometry” workshop in Hangzhou, China from February 25 - March 1, 2024.

The aim of the conference is bringing together international experts who are currently working on comparison geometry and related problems. The fundamental idea of comparison geometry is that of trying to understand the shape of some geometric objects in terms of the shape of suitable model configurations, which are in general simpler objects, sometimes explicit, equipped with a remarkable number of symmetries. Typical outcomes of this profound idea are geometric inequalities. Among the most basic and earliest examples there certainly is the classical Isoperimetric Inequality, where a suitable scaling invariant area-to-volume ratio is compared with that of the ball in the Euclidean space (model situation).

In the last century, this mythological inequality has known several extensions and generalisations. It also possesses a relativistic counterpart known as the Riemannian Penrose Inequality where, roughly speaking,
the mass-to-area ratio of a Black Hole is compared with that of the Schwarzschild solution. This is not surprising after all: General Relativity has in fact been defined as a geometric theory of gravity. As such, it is a big source of inspiration of deep geometric problems. Viceversa, deep advances in geometry provides fruitful insights in our understanding of the physical universe.

The Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide 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 in Banff is supported by Canada’s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), and Alberta Technology and Innovation.