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Non-commutative Iwasawa theory of elliptic curves at primes of multiplicative reduction
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2010-07-06)
Let E be an elliptic curve defined over the rationals Q, and p be a prime at least 5 where E has multiplicative reduction. This thesis studies the Iwasawa theory of E over certain false Tate curve extensions F[infinity], ...
Witt groups of complex varieties
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsTrinity Hall, 2011-07-12)
The thesis Witt Groups of Complex Varieties studies and compares two related cohomology theories that arise in the areas of algebraic geometry and topology: the algebraic theory of Witt groups, and real topological K-theory. ...
Response to: DNA identification by pedigree likelihood ratio accommodating population substructure and mutations
(2011-03-25)
Abstract Mutation models are important in many areas of genetics including forensics. This letter criticizes the model of the paper 'DNA identification by pedigree likelihood ratio accommodating population substructure and ...
The contact property for magnetic flows on surfaces
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsTrinity College, 2015-01-06)
This work investigates the dynamics of magnetic flows on closed orientable Riemannian surfaces. These flows are determined by triples (M, g, σ), where M is the surface, g is the metric and σ is a 2-form on M . Such dynamical ...
Hidden states, hidden structures: Bayesian learning in time series models
(University of CambridgeDepartment of Engineering, 2014-06-10)
This thesis presents methods for the inference of system state and the learning of model structure for a number of hidden-state time series models, within a Bayesian probabilistic framework. Motivating examples are taken ...
Algebraic boundaries of Hilbert's SOS cones
(Cambridge University PressCompositio Mathematica, 2012-10-15)
We study the geometry underlying the difference between nonnegative
polynomials and sums of squares. The hypersurfaces that discriminate
these two cones for ternary sextics and quaternary quartics are shown
to be ...
Hypergraph containers
(SpringerInventiones Mathematicae, 2015-01-08)
We develop a notion of containment for independent sets in hypergraphs. For every r-uniform hypergraph G, we find a relatively small collection C of vertex subsets, such that every independent set of G is contained within ...
Trading to stops
(Society for Industrial and Applied MathematicsSiam Journal on Financial Mathematics, 2014-12-16)
The use of trading stops is a common practice in financial markets for a variety of reasons: it reduces the frequency of trading and thereby transaction costs; it provides a simple way to control losses on a given trade, ...
On the Boltzmann equation, quantitative studies and hydrodynamical limits
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsCambridge Centre for Analysis, 2014-11-11)
The present thesis deals with the mathematical treatment of kinetic theory and focuses more
precisely on the Boltzmann equation. We investigate several properties of the solutions to the latter equation: their positivity ...
Ample subvarieties and q-ample divisors
(ElsevierAdvances in Mathematics, 2012-03-20)
We introduce a notion of ampleness for subschemes of any codimension
using the theory of q-ample line bundles. We also investigate certain geometric
properties satisfied by ample subvarieties, e.g. the Lefschetz ...