Browsing Department of Pure Mathematics and Mathematical Statistics (DPMMS) by Issue Date
Now showing items 120 of 248

Threedimensional manifolds
(University of CambridgeFaculty of MathematicsTrinity College, 19600803)In the postwar years, the theory of 3dimensional manifolds has developed tremendously. On the one hand, Bing and Moise have proved that 3manifolds can be triangulated, and that the Hauptvermutung (that any two triangulations ...

The classification of maps between the classifying spaces of Lie groups
(University of CambridgeGonville and Caius CollegeDepartment of Pure Mathematics and Mathematical Statistics, 19740801)

NF
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 19770727)A study Of Quine's Set Theory

Symmetric structures in Banach spaces
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsTrinity College, 19900220)

The topology of terminal quartic 3folds
(University of Cambridge, 20070620)Let Y be a quartic hypersurface in P^4 with terminal singularities. The GrothendieckLefschetz theorem states that any Cartier divisor on Y is the restriction of a Cartier divisor on P^4 . However, no such result holds ...

Topics in arithmetic combinatorics
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20071023)This thesis is chiefly concerned with a classical conjecture of Littlewood's regarding the L^1norm of the Fourier transform, and the closely related idempotent theorem. The vast majority of the results regarding these ...

Arithmetic structure in sets of integers
(University of Cambridge, 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 ...

Deformations and gluing of asymptotically cylindrical manifolds with exceptional holonomy
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 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 ...

Comparing GrothendieckWitt Groups of a Complex Variety to its Real Topological KGroups
(Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 200901)On a complex variety X, two different approaches to Ktheory are available: the algebraic Ktheory of the variety, and the topological Ktheory of the underlying topological space. In this context, the algebraic variant ...

Autonomous Pseudomonoids
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20090425)In this dissertation we generalise the basic theory of Hopf algebras to the context of autonomous pseudomonoids in monoidal bicategories. ...

Three viewpoints on semiabelian homology
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticisEmmanuel College, 20091117)The main theme of the thesis is to present and compare three different viewpoints on semiabelian homology, resulting in three ways of defining and calculating homology objects. Any two of these three homology theories ...

Computational modeling of the EGFR network elucidates control mechanisms regulating signal dynamics
(20091222)Abstract Background The epidermal growth factor receptor (EGFR) signaling pathway plays a key role in regulation of cellular growth and development. While highly studied, it is still not fully understood how the signal is ...

Maximum likelihood estimation of a multivariate logconcave density
(University of Cambridge, 20100112)Density estimation is a fundamental statistical problem. Many methods are either sensitive to model misspecification (parametric models) or difficult to calibrate, especially for multivariate data (nonparametric smoothing ...

Graphical representations of Ising and Potts models: stochastic geometry of the quantum Ising model and the spacetime Potts model
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsStatistical LaboratoryGonville & Caius College, 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 ...

On eigenvectors for semisimple elements in actions of algebraic groups
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20100209)Let $G$ be a simple simply connected algebraic group defined over an algebraically closed field $K$ and $V$ an irreducible module defined over $K$ on which $G$ acts. Let $E$ denote the set of vectors in $V$ which are ...

Models of genus one curves
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20100316)In this thesis we give insight into the minimisation problem of genus one curves defined by equations other than Weierstrass equations. We are interested in genus one curves given as double covers of P1, plane cubics, or ...

Iwasawa theory for modular forms at supersingular primes
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20100706)Let f=\sum a_nq^n be a normalised eigennewform of weight k\ge2 and p an odd prime which does not divide the level of f. We study a reformulation of Kato's main conjecture for f over the Zpcyclotomic extension of Q. In ...

Noncommutative Iwasawa theory of elliptic curves at primes of multiplicative reduction
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20100706)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], ...

Comparison of multimarker logistic regression models, with application to a genomewide scan of schizophrenia.
(20100909)Abstract Background Genomewide association studies (GWAS) are a widely used study design for detecting genetic causes of complex diseases. Current studies provide good coverage of common causal SNPs, but not rare ones. A ...

Two topics in financial mathematics : Forward utility and consumption functions & Hedging with variance swaps in infinite dimensions
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 201010)Financial Mathematics is often presented as being composed of two main branches: one dealing with investment and consumption, with the aim of answering the now ancient question of how people should invest and spend their ...