Department of Pure Mathematics and Mathematical Statistics (DPMMS)
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Elliptic curves over Q$_{∞}$ are modular
We show that if $\textit{p}$ is a prime, then all elliptic curves de ned over the cyclotomic $\mathbb{Z}$$_{p}$extension of Q are modular. 
Connective constants and height functions for Cayley graphs
The connective constant $\mu$($\textit{G}$) of an infinite transitive graph $\textit{G}$ is the exponential growth rate of the number of selfavoiding walks from a given origin. In earlier work of Grimmett and Li, a locality ... 
On the GL$_{n}$eigenvariety and a conjecture of Venkatesh
Let π be a cuspidal, cohomological automorphic representation of GL$_{n}$(A). Venkatesh has suggested that there should exist a natural action of the exterior algebra of a certain motivic cohomology group on the πpart of ... 
Infinitely many monotone Lagrangian tori in del Pezzo surfaces
We construct almost toric fibrations (ATFs) on all del Pezzo surfaces, endowed with a monotone symplectic form. Except for CP$^{2}$#CP$^{2}$, CP$^{2}$#2CP$^{2}$, we are able to get almost toric base diagrams (ATBDs) of ...