Virtual Master’s Defense: Stephen Liu

Thursday, March 19, 2020 | 4:30pm (EST) | Zoom

Title: On the Asymptotic Behavior of the Magnitude Function for Odd-Dimensional Euclidean Balls


Magnitude is a numerical invariant of metric spaces with origins in the notion of the Euler characteristic of a category. To this day the only convex sets in Euclidean space for which we can compute magnitude are the odd-dimensional Euclidean balls. Recent results have shed light on the asymptotic behavior of the magnitude function for these Euclidean balls, and in particular recent work by Meckes showed that the first order small-t asymptotics of the magnitude function recovers its first intrinsic volume. The aim of this thesis is to survey work done to understand the magnitude function for these balls and to compute its second order small-t asymptotics.


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