## Departmental PhD Thesis Exam – Dominic Dotterrer

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

Thesis Title:  The (co)isoperimetric problem in (random) polyhedra

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.