### Recent Submissions

• #### $\textit{K}$-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 ...
• #### Computations in monotone Floer theory ﻿

(Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 2016-06-28)
Floer theory is a rich collection of tools for studying symplectic manifolds and their Lagrangian submanifolds with the help of holomorphic curves. Its origins lie in estimating the numbers of equilibria in Hamiltonian ...
• #### Spectral methods and computational trade-offs in high-dimensional statistical inference ﻿

(Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 2016-10-04)
Spectral methods have become increasingly popular in designing fast algorithms for modern highdimensional datasets. This thesis looks at several problems in which spectral methods play a central role. In some cases, we ...
• #### Categories of spaces built from local models ﻿

(2016-06-28)
Many of the classes of objects studied in geometry are defined by first choosing a class of nice spaces and then allowing oneself to glue these local models together to construct more general spaces. The most well-known ...