*Everyone is welcome to attend. Refreshments will be served in the Math Lounge before the exam.*

Monday, May 2, 2016

2:10 p.m.

BA6183

PhD Candidate: Parker Glynn-Adey

Supervisor: Rina Rotman

Thesis title: Width, Ricci Curvature, and Bisecting Surfaces

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Abstract:

In this thesis we studied width-volume inequalities, bisecting surfaces in three spheres, and the planar case of Larry Guth’s sponge problem. Our main result is a width-volume inequality for conformally non-negatively Ricci curved manifolds. We obtain several estimates on the size of minimal hypersurfaces in such manifolds. Concerning geometric subdivision and 3-spheres, we give a positive answer to a question of Papasoglu. Regarding the sponge problem, we show that any open bounded Jordan measurable set in the plane of small area admits an expanding embedding in to a strip of unit height. We also prove that a generalization of the planar sponge problem is NP-complete. This thesis is partially based on joint work with Ye. Liokumovich [G-ALiokumovich2014] and Z. Zhu [G-AZhu2015]

A copy of the thesis can be found here: ut-thesis

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