Theses  Pure Mathematics and Mathematical Statistics
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Computations in monotone Floer theory
(Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 20160628)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 tradeoffs in highdimensional statistical inference
(Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 20161004)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
(20160628)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 wellknown ... 
Deformations of Cayley submanifolds
(20160301)Cayley submanifolds of R^8 were introduced by Harvey and Lawson as an instance of calibrated submanifolds, extending the volumeminimising properties of complex submanifolds in Kähler manifolds. More generally, Cayley ...