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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