Theses  Pure Mathematics and Mathematical Statistics
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Cubulating CAT(0) groups and Property (T) in random groups
(20210916)This thesis considers two properties important to many areas of mathematics: those of cubulation and Property (T). Cubulation played a central role in Agol’s proof of the virtual Haken conjecture, while Property (T) has ... 
Computationally Efficient Methods for HighDimensional Statistical Problems
With the everincreasing amount of computational power available, so broadens the horizon of statistical problems that can be tackled. However, many practitioners have only an ordinary personal computer on which to do their ... 
Advanced Bayesian Monte Carlo Methods for Inference and Control
Monte Carlo methods are are an ubiquitous tool in modern statistics. Under the Bayesian paradigm, they are used for estimating otherwise intractable integrals arising when integrating a function $h$ with respect to a ... 
Extremal problems in the cube and the grid and other combinatorial results
This dissertation contains results from various areas of combinatorics. In Chapters 2, 3 and 4 we consider questions in the area of isoperimetric inequalities. In Chapter 2, we find the exact classification of all subsets ...