### Recent Submissions

• #### Extremal Combinatorics and Universal Algorithms ﻿

(2018-10-15)
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 ...
• #### D-cap modules on rigid analytic spaces ﻿

(2018-07-20)
Following the notion of $p$-adic analytic differential operators introduced by Ardakov--Wadsley, 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 ﻿

(2018-07-20)
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 ﻿

(2018-04-28)
In recent years, more and more efforts have been expended on the study of $n$-dimensional asymptotically anti-de Sitter spacetimes $(\mathcal{M},g)$ as solutions to the Einstein vacuum equations \begin{align*} \mathrm{ ...