Theses  Pure Mathematics and Mathematical Statistics
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Instabilities in asymptotically AdS spacetimes
(20180428)In recent years, more and more efforts have been expended on the study of $n$dimensional asymptotically antide Sitter spacetimes $(\mathcal{M},g)$ as solutions to the Einstein vacuum equations \begin{align*} \mathrm{ ... 
Topics in metric geometry, combinatorial geometry, extremal combinatorics and additive combinatorics
(20180301)In this thesis, we consider several combinatorial topics, belonging to the areas appearing in the thesis title. Given a nonempty complete metric space $(X,d)$, a family of $n$ continuous maps $f_1,f_2,\dots,f_n\colon X\to ... 
Semisimple filtrations of tilting modules for algebraic groups
(20180207)Let $G$ be a reductive algebraic group over an algebraically closed field $k$ of characteristic $p > 0$. The indecomposable tilting modules $\{T(\lambda)\}$ for $G$, which are labeled by highest weight, form an important ... 
Tilings and other combinatorial results
In this dissertation we treat three tiling problems and three problems in combinatorial geometry, extremal graph theory and sparse Ramsey theory. We first consider tilings of $\mathbb{Z}^n$. In this setting a tile $T$ ...