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February 5, 2018 | 2:45 p.m. - 4:00 p.m.
Category: Lecture
Location: Education, College of #179 | Map
5425 Gullen Mall
Detroit, MI 48202
Cost: Free

Speaker:  Carl McTague, University of Rochester

Title: A New Approach to Euler Calculus for Continuous Integrands 

Abstract: The Euler characteristic satisfies an inclusion-exclusion principle χ(X∪Y)=χ(X)+χ(Y)-χ(X∩Y), which lets one regard it as a measure – a peculiar one where a point has measure 1 while a circle has measure 0. One can use it to integrate simple functions (in the sense of measure theory), and the resulting integral calculus has deep roots in algebraic geometry and has recently found surprising applications to data analysis. However, since it is only finitely – not countably – additive, it does not fit into the framework of Lebesgue integration, and there are problems integrating even the most elementary non-simple functions. I will describe a new approach to this calculus, based on differential geometry, which makes it possible to integrate a large class of non-simple functions, and which hints at new ways to apply differential geometry to data analysis.

 

 

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For more information about this event, please contact Department of Mathematics at 3135772479 or math@wayne.edu.