Department of Pure Mathematics and Mathematical Statistics (DPMMS)
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Finite Metric Subsets of Banach Spaces
(20190131)The central idea in this thesis is the introduction of a new isometric invariant of a Banach space. This is Property AII. A Banach space has Property AII if whenever a finite metric space almostisometrically embeds into ... 
Structure in Machine Learning: Graphical Models and Monte Carlo Methods
This thesis is concerned with two main areas: approximate inference in discrete graphical models, and random embeddings for dimensionality reduction and approximate inference in kernel methods. Approximate inference is a ... 
Detecting topological properties of boundaries of hyperbolic groups
(20181124)In general, a finitely presented group can have very nasty properties, but many of these properties are avoided if the group is assumed to admit a nice action by isometries on a space with a negative curvature property, ... 
Extremal and Structural Problems of Graphs
(20190330)In this dissertation, we are interested in studying several parameters of graphs and understanding their extreme values. We begin in Chapter~$2$ with a question on edge colouring. When can a partial proper edge colouring ...