Theses  Pure Mathematics and Mathematical Statistics
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Extremal Combinatorics and Universal Algorithms
(20181015)In this dissertation we solve several combinatorial problems in different areas of mathematics: automata theory, combinatorics of partially ordered sets and extremal combinatorics. Firstly, we focus on some new automata ... 
Dcap modules on rigid analytic spaces
(20180720)Following the notion of $p$adic analytic differential operators introduced by ArdakovWadsley, we establish a number of properties for coadmissible $\wideparen{\mathcal{D}}$modules on rigid analytic spaces. Our main ... 
Automorphism Groups of Quadratic Modules and Manifolds
(20180720)In this thesis we prove homological stability for both general linear groups of modules over a ring with finite stable rank and unitary groups of quadratic modules over a ring with finite unitary stable rank. In particular, ... 
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{ ...