Department of Pure Mathematics and Mathematical Statistics (DPMMS)
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Shadows of Teichmüller Discs in the Curve Graph
We consider several natural sets of curves associated to a given Teichmüller disc, such as the systole set or cylinder set, and study their coarse geometry inside the curve graph. We prove that these sets are quasiconvex ... 
An upper bound for the pseudoisotopy stable range
(Springer, 20161201)We prove that the pseudoisotopy stable range for manifolds of dimension 2n can be no better than (2n  2). In order to do so, we define new characteristic classes for block bundles, extending our earlier work with Ebert, ... 
$\textit{K}$Theory of Fermat Curves
(Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 20170110)I investigate the $K_2$ groups of the quotients of Fermat curves given in projective coordinates by the equation $F_n:X^n+Y^n=Z^n$. On any quotient where the number of known elements is equal to the rank predicted by ... 
Stackings and the Wcycles conjecture
We prove Wise’s Wcycles conjecture: Consider a compact graph Γ′ immersing into another graph Γ. For any immersed cycle Λ : S¹ → Γ, we consider the map Λ′ from the circular components S of the pullback to Γ′. Unless Λ′ is ...