Theses  Pure Mathematics and Mathematical Statistics
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Monoid Extensions, Relaxed Actions and Cohomology
In this thesis a particular class of monoid extensions are studied and characterized, the weakly Schreier split extensions. It is demonstrated that both Artin glueings of frames and λsemidirect products of inverse semigroups ... 
Topological and geometric inference of data
The overarching problem under consideration is to determine the structure of the subspace on which a distribution is supported, given only a finite noisy sample thereof. The special case in which the subspace is an embedded ... 
Capitulation Discriminants of Genus One Curves
In this thesis we study genus one curves of degree n embedded in projective space P n−1 . We are speci cally interested in the curves de ned over Q that are counterexamples to the Hasse principle, that is the curves that ... 
Topics in shapeconstrained inference
This thesis consists of three chapters. The first of these surveys the field of nonparametric inference under shape constraints, focussing in particular on the topics of shaperestricted regression and shapeconstrained ...