Department of Pure Mathematics and Mathematical Statistics (DPMMS)
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Finite Metric Subsets of Banach Spaces
(2019-01-31)The central idea in this thesis is the introduction of a new isometric invariant of a Banach space. This is Property AI-I. A Banach space has Property AI-I if whenever a finite metric space almost-isometrically 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
(2018-11-24)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
(2019-03-30)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 ...
