Jan
11
Everyone welcome. Refreshments will be served in the Math Lounge before the exam. DEPARTMENTAL PHD THESIS EXAM Tuesday, January 22, 2013, 4:10 p.m., in Room BA 1240, 40 St. George St. PhD Candidate: Dominic Dotterrer PhD Advisor: Larry Guth Thesis Title: The (co)isoperimetric problem in (random) polyhedra (http://www.math.toronto.edu/graduate/Dotterrer-thesis.pdf) Thesis Abstract: Isoperimetric distortion of simplicial complexes in space: Taking inspiration from the theory of metric embeddings of graphs, we will propose a notion of higher dimensional 'distortion' for simplicial complexes embedded in Euclidean space. The notion is based on comparing the areas of combinatorially minimal surfaces to the areas of minimal surfaces in space. Using a probabilistic construction, we will show that the geometric picture is significantly worse than it is for graphs (where distortion is at worst logarithmic). This work represents a significant fraction of my Ph.D. dissertation.
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