Mathematical Sciences Colloquium Series, Thursday, December 1, 2022

November 23, 2022

We hope you will join us as Sylvester Eriksson-Bique presents his research for the Department of Mathematical Sciences Colloquium Series.

“Modulus on Networks - What is it?"

December 1, 10:00 a.m., RB 113

Abstract:  I will discuss and define a concept called “modulus of a (path) family”, and how it relates to differentiability.  First, I want to give you an intuitive sense of what this concept measures and what sort of features of the space it captures. In this portion, I will mention some applied work, that I am aware of. Second, I want to give some indications of the mathematical significance of this tool, and how it has shown up in our recent work. The reason why the concept is important, is that is seems to capture key geometric and analytic information of the space. Specifically, the property of having positive modulus families of curves, allows one to differentiate functions, and, in some cases, to determine if some types of maps can exist. Part of the talk will discuss joint work with Guy C. David.

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