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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 ...
Quiver algebras as Fukaya categories
(Mathematical Sciences PublishersGeometry & Topology, 2015-10-20)
We embed triangulated categories defined by quivers with potential arising from ideal triangulations of marked bordered surfaces into Fukaya categories of quasiprojective 3–folds associated to meromorphic quadratic ...
The 1-2 model
(American Mathematical SocietyIn the Tradition of Ahlfors–Bers, VII, 2017)
The current paper is a short review of rigorous results for the 1-2 model. The 1-2 model on the hexagonal lattice is a model of statistical mechanics in which each vertex is constrained to have degree either 1 or 2. It was ...
Variation of Gieseker moduli spaces via quiver GIT
(Mathematical Sciences PublishersGeometry & Topology, 2016)
We introduce a notion of stability for sheaves with respect to several polarisations that generalises the usual notion of Gieseker-stability. We prove, under a boundedness assumption, which we show to hold on threefolds ...