Analysis and Geometry of Metric Spaces - a Bridge between Smooth and Fractal Views (20w5105)

Organizers

(Kyoto University)

Mario Bonk (University of California, Los Angeles)

Description

The Banff International Research Station will host the "Analysis and Geometry of Metric Spaces - a Bridge between Smooth and Fractal Views" workshop in Banff from April 5 to April 10, 2020.


The notion of fractals was introduced by Mandelbrot as new models of the shapes of objects in nature like the coastline, trees and the surface of rocks, which can not be represented by combinations of smooth objects such as lines, rectangles, circles and spheres. Since there happens natural phenomena such as waves and heat diffusions on those objects modeled by fractals, we need to develop the theory to treat such natural phenomena on fractals, which are included in the category of metric spaces. This direction of study is called analysis and geometry on metric spaces. In this area of research, there have been two groups, one has tried to extend the existing theory for smooth spaces and the other has tried to use the complicated structure of the object itself. These two groups have been working separately for more than 20 years and both have obtained fruitful results. However, recently, evidences of strong connection between those two approaches. So the main purpose of this workshop is to gather people from both sides, to promote interaction and to create a common ground for deeper study in this area.


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).