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Three viewpoints on semi-abelian homology
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticisEmmanuel College, 2009-11-17)
The main theme of the thesis is to present and compare three different viewpoints on semi-abelian homology, resulting in three ways of defining and calculating homology objects. Any two of these three homology theories ...
Deformations and gluing of asymptotically cylindrical manifolds with exceptional holonomy
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2008-10-14)
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 7-dimensional manifolds
with ...
Autonomous Pseudomonoids
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2009-04-25)
In this dissertation we generalise the basic theory of Hopf algebras to the context of autonomous pseudomonoids in monoidal bicategories.
...
The topology of terminal quartic 3-folds
(University of Cambridge, 2007-06-20)
Let Y be a quartic hypersurface in P^4 with terminal singularities. The Grothendieck-Lefschetz 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, 2007-10-23)
This thesis is chiefly concerned with a classical conjecture of Littlewood's regarding the L^1-norm of the Fourier transform, and the closely related idempotent theorem. The vast majority of the results regarding these ...
Comparing Grothendieck-Witt Groups of a Complex Variety to its Real Topological K-Groups
(Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 2009-01)
On a complex variety X, two different approaches to K-theory are available: the
algebraic K-theory of the variety, and the topological K-theory of the underlying
topological space. In this context, the algebraic variant ...
Arithmetic structure in sets of integers
(University of Cambridge, 2008-05-20)
This dissertation deals with four problems concerning arithmetic structures in dense
sets of integers. In Chapter 1 we give an exposition of the state-of-the-art technique
due to Pintz, Steiger and Szemer edi which yields ...
Computational modeling of the EGFR network elucidates control mechanisms regulating signal dynamics
(2009-12-22)
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 ...