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


Monday, May 2, 2016
2:10 p.m.

PhD Candidate:  Parker Glynn-Adey
Supervisor:  Rina Rotman
Thesis title: Width, Ricci Curvature, and Bisecting Surfaces


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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