Recent Submissions

• Embedded contact knot homology and a surgery formula ﻿

(2018-10-20)
Embedded contact homology is an invariant of closed oriented contact 3-manifolds first defined by Hutchings, and is isomorphic to both Heegard Floer homology (by the work of Colin, Ghiggini and Honda) and Seiberg-Witten ...
• 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, ...