University of Connecticut

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Mathematics REU Talk Series- Self-Affine Curves And Parameterization Dimension

Thursday, July 14, 2022
1:30pm – 2:30pm

Storrs Campus
MONT 313

Professor Matthew Badger will be giving a talk titled: "Self-affine curves and parameterization dimension."

Abstract: There are many possible ways to describe the dimension of a set of points, which sometimes agree and sometimes disagree. I will describe an example of the latter type, discovered in recent joint work with Vyron Vellis. While every set of points in the Euclidean plane has Hausdorff / Minkowski / Assouad / topological dimension at most 2, there exist curves in the plane (connected Bedford-McMullen carpets) with parameterization dimension bigger than 2. I'll explain this phenomenon and describe open problems about the parameterization dimension of generalized Menger sponges.


Mathematics REU (primary), College of Liberal Arts and Sciences, UConn Master Calendar

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