Scholarly Works  Pure Mathematics and Mathematical Statistics
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Undecidability and the developability of permutoids and rigid pseudogroups
(Cambridge University Press, 20170320)A $\textit{permutoid}$ is a set of partial permutations that contains the identity and is such that partial compositions, when defined, have at most one extension in the set. In 2004 Peter Cameron conjectured that there ... 
FourDimensional Weakly Selfavoiding Walk with Contact Selfattraction
(Springer, 20170401)We consider the critical behaviour of the continuoustime weakly selfavoiding walk with contact selfattraction on $\mathbb{Z}$$^{4}$, for sufficiently small attraction. We prove that the susceptibility and correlation ... 
Elliptic curves over Q$_{∞}$ are modular
We show that if $\textit{p}$ is a prime, then all elliptic curves de ned over the cyclotomic $\mathbb{Z}$$_{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 ...