Browsing Theses  Pure Mathematics and Mathematical Statistics by Title
Now showing items 120 of 59

A concentration inequality based statistical methodology for inference on covariance matrices and operators
(20170623)In the modern era of high and infinite dimensional data, classical statistical methodology is often rendered inefficient and ineffective when confronted with such big data problems as arise in genomics, medical imaging, ... 
Arithmetic structure in sets of integers
(20080520)This dissertation deals with four problems concerning arithmetic structures in dense sets of integers. In Chapter 1 we give an exposition of the stateoftheart technique due to Pintz, Steiger and Szemer edi which yields ... 
Automorphisms of free products of groups
(20130205)The symmetric automorphism group of a free product is a group rich in algebraic structure and with strong links to geometric configuration spaces. In this thesis I describe in detail and for the first time the (co)homology ... 
Autonomous Pseudomonoids
(20090425)In this dissertation we generalise the basic theory of Hopf algebras to the context of autonomous pseudomonoids in monoidal bicategories. ... 
Bounding cohomology for low rank algebraic groups
(20170801)Let G be a semisimple linear algebraic group over an algebraically closed field of prime characteristic. In this thesis we outline the theory of such groups and their cohomology. We then concentrate on algebraic groups in ... 
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 ... 
Cliques in graphs
(20101012)The main focus of this thesis is to evaluate $k_r(n,\delta)$, the minimal number of $r$cliques in graphs with $n$ vertices and minimum degree~$\delta$. A fundamental result in Graph Theory states that a trianglefree graph ... 
Collaborating queues: large service network and a limit order book
(20121009)We analyse the steadystate behaviour of two different models with collaborating queues: that is, models in which "customers" can be served by many types of "servers", and "servers" can process many types of "customers". The ... 
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 ... 
Computing the CasselsTate pairing
(20151110) 
The contact property for magnetic flows on surfaces
(20150106)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 2form on M . Such dynamical ... 
Deformations and gluing of asymptotically cylindrical manifolds with exceptional holonomy
(20081014)In Berger's classification of Riemannian holonomy groups there are several infinite families and two exceptional cases: the groups Spin(7) and G_2. This thesis is mainly concerned with 7dimensional manifolds with ... 
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 ... 
Excitations in superfluids of atoms and polaritons
(20141111)This thesis is devoted to the study of excitations in atomic and polariton BoseEinstein condensates (BEC). These two specimens are prime examples for equilibrium and non equilibrium BEC. The corresponding condensate wave ... 
Exploring Random Geometry with the Gaussian Free Field
(20161001)This thesis studies the geometry of objects from 2dimensional statistical physics in the continuum. Chapter 1 is an introduction to SchrammLoewner evolutions (SLE). SLEs are the canonical family of nonselfintersecting, ... 
Extremal and probabilistic bootstrap percolation
(20131112)In this dissertation we consider several extremal and probabilistic problems in bootstrap percolation on various families of graphs, including grids, hypercubes and trees. Bootstrap percolation is one of the simplest ... 
Free groups and the axiom of choice
(20160105)The Nielsen–Schreier theorem states that subgroups of free groups are free. As all of its proofs use the Axiom of Choice, it is natural to ask whether the theorem is equivalent to the Axiom of Choice. Other questions arise ... 
The Fukaya category, exotic forms and exotic autoequivalences
(20120410)A symplectic manifold is a smooth manifold M together with a choice of a closed nondegenerate twoform. Recent years have seen the importance of associating an A∞category to M, called its Fukaya category, in helping ... 
Graphical representations of Ising and Potts models: stochastic geometry of the quantum Ising model and the spacetime Potts model
(20100209)Statistical physics seeks to explain macroscopic properties of matter in terms of microscopic interactions. Of particular interest is the phenomenon of phase transition: the sudden changes in macroscopic properties as ...