TSVP Talk: "Metric Spaces: Navigating in a World Without Directions" by Jana Björn

Title: Metric Spaces: Navigating in a World Without Directions

Abstract: We are all used to the left-right, forward-backward and up-down directions of our 3-dimensional space. They can be used to define partial derivatives and appear in the differential equations which describe many real-world phenomena. But how much are they really needed?
When navigating between motorway exits, subway stations or airport terminals, we easily loose the sense of directions. In these situations we usually care about the total travel time and the fastest route is not always the same as the shortest one. Distances can be measured in different ways, by time, kilometers, ticket cost or fuel consumption. All these different ways have often one thing in common, namely, going from A to B is usually faster, shorter or cheaper than first going from A to C and then from C to B. This useful property is called the triangle inequality and lies behind the definition of metric spaces.
In this talk I shall in an elementary way and by examples introduce metric spaces and show how various seemingly different real-world problems can be treated simultaneously by means or different metric spaces. In particular we shall consider harmonic functions in this setting, without directions and partial derivatives.

Profile: Jana Björn is a Professor of Mathematics at Linköping University, Sweden, where she also received her PhD in 1996. She was a postdoc at University of Michigan, Ann Arbor, and then at Lund University. She has also spent longer research periods at Charles University in Prague, University of Cincinnati and the Mittag-Leffler Institute in Stockholm. Her research is in analysis on metric spaces, mainly in collaboration with Anders Björn. In particular, she is interested in p-harmonic functions, partial differential equations and various minimization problems. She studies various solving methods and properties of the solutions, such as their interior and boundary regularity and growth estimates. This is research in pure mathematics and its aim is to provide rigorous fundamentals for and a better understanding of some problems, which could come from natural sciences and other fields. Analysis on metric spaces makes it possible to study such questions simultaneously in many different settings, for example on very rough sets and for highly nonhomogeneous media. It also brings new insight into which properties and assumptions are really essential for the theory and which are the main obstructions. A popular-scientific description of Jana's research is at this website.

Language: English, no interpretation.

Target audience: General audience / everyone at OIST and beyond.
Freely accessible to all OIST members and guests without registration.

This talk will also be broadcast online via Zoom:

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Meeting ID: 973 1993 9023
Passcode: 387020 

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