### Recent Submissions

• #### 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, 2016-12-01)
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, 2017-01-10)
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 W-cycles conjecture ﻿

We prove Wise’s W-cycles 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 ...