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Automorphy of some residually dihedral Galois representations
(Springer, 2015-05-08)
We establish the automorphy of some families of 2-dimensional representations of the absolute Galois group of a totally real field, which do not satisfy the so-called ‘Taylor–Wiles hypothesis’. We apply this to the problem ...
Equidistribution of Frobenius eigenvalues
(Oxford JournalsInternational Mathematics Research Notices, 2015-02-09)
We study the problem of variation of Frobenius eigenvalues on the cohomology of families of local systems of algebraic curves over finite fields.
Kriging prediction for manifold-valued random fields
(ElsevierJournal of Multivariate Analysis, 2015-12-25)
The statistical analysis of data belonging to Riemannian manifolds is becoming increasingly important in many applications, such as shape analysis, diffusion tensor imaging and the analysis of covariance matrices. In many ...
Abelian quotients of mapping class groups of highly connected manifolds
(SpringerMathematische Annalen, 2015-10-12)
We compute the abelianisations of the mapping class groups of the manifolds W²ⁿ_g = g(Sⁿ × Sⁿ) for n ≥ 3 and g ≥ 5. The answer is a direct sum of two parts. The first part arises from the action of the mapping class group ...
Turán-type results for complete h-partite graphs in comparability and incomparability graphs
(SpringerOrder, 2015-01-05)
We consider an h-partite version of Dilworth's theorem with multiple partial orders. Let P be a fi nite set, and let <₁, ..., <ᵣ be partial orders on P. Let G(P, <₁, ..., <ᵣ) be the graph whose vertices are the elements ...
Problems in Ramsey theory, probabilistic combinatorics and extremal graph theory
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2015-11-10)
In this dissertation, we treat several problems in Ramsey theory, probabilistic combinatorics and extremal graph theory.
Bayesian regularization of the length of memory in reversible sequences
(WileyJournal of the Royal Statistical Society: Series B (Statistical Methodology), 2015-10-16)
Variable order Markov chains have been used to model discrete sequential data in a variety of fields. A host of methods exist to estimate the history-dependent lengths of memory which characterize these models and to predict ...
On the Subadditivity of the Entropy on the Sphere
(SpringerThe Journal of Geometric Analysis, 2015-11-17)
We present a refinement of a known entropic inequality on the sphere, finding suitable conditions under which the uniform probability measure on the sphere behaves asymptomatically like the Gaussian measure on Rᴺ with ...
Uniform Stability of Twisted Constant Scalar Curvature Kähler Metrics
(Oxford University PressInternational Mathematics Research Notices, 2015-10-14)
We introduce a norm on the space of test configurations, called the minimum norm. We conjecture that uniform K-stability is equivalent to the existence of a constant scalar curvature Kähler metric. This uniformity is ...
Delay-independent asymptotic stability in monotone systems
(IEEEAmerican Control Conference (ACC), 2015-07-03)
Monotone systems comprise an important class of dynamical systems that are of interest both for their wide applicability and because of their interesting mathematical properties. It is known that under the property of ...