Department of Pure Mathematics and Mathematical Statistics (DPMMS)
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Level raising for automorphic representations of GL(2n)
(20190518)To each regular algebraic, conjugate selfdual, cuspidal automorphic representation $\Pi$ of $\mathrm{GL}(N)$ over a CM number field $E$ (or, more generally, to a regular algebraic isobaric sum of conjugate selfdual, ... 
Ricciflat deformations of orbifolds and asymptotically locally Euclidean manifolds
(20190719)In this thesis we study Ricciflat deformations of Ricciflat Kähler metrics on compact orbifolds and asymptotically locally Euclidean(ALE) manifolds. In both cases we also study the moduli space of Ricciflat structures. ... 
Rigid Analytic Quantum Groups
(20190427)Following constructions in rigid analytic geometry, we introduce a theory of $p$adic analytic quantum groups. We first define Fréchet completions $\wideparen{U_q(\mathfrak{g})}$ and $\wideparen{\mathcal{O}_q(G)}$ of the ... 
Tropical Intersection Theory on Moduli Stack of Curve Coverings
(20190601)We construct the moduli cone stack $\mathfrac{M}_\eta^\text{trop}$ of tropical \'{e}tale covers (i.e., coverings of twisted tropical curves). We define the tropical intersection theory on $\mathfrac{M}_\eta^\text{trop}$ ...