Department of Pure Mathematics and Mathematical Statistics (DPMMS)
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On Problems in the Representation Theory of Symmetric Groups
(20200125)In this thesis, we study the representation theory of the symmetric groups $\mathfrak{S}_n$, their Sylow $p$subgroups $P_n$ and related algebras. For all primes $p$ and natural numbers $n$, we determine the maximum number ... 
Internal enriched categories
This dissertation introduces and develops the theory of internal enriched categories, arising from the internalization of the theory of enriched categories. Given an internal monoidal category V in an ambient category E, ... 
Statistical inference in highdimensional matrix models
(20200717)Matrix models are ubiquitous in modern statistics. For instance, they are used in finance to assess interdependence of assets, in genomics to impute missing data and in movie recommender systems to model the relationship ... 
Geometric Functional Data Analysis
(20191026)In this thesis, we introduce a comprehensive framework for the analysis of statistical samples that are functional data with nontrivial geometry. Geometry can interplay with functional data in different forms. The most ...