### Recent Submissions

• #### 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 self-avoiding 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 π-part 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 ...