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Exact Lagrangian immersions with a single double point
(American Mathematical Society, 2015-01-09)
We show that if a closed orientable 2k-manifold K, k > 2, with Euler characteristic χ(K) ≠ -2 admits an exact Lagrangian immersion into C2k with one transverse double point and no other self intersections, then K is ...
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.
Detecting and Localizing Differences in Functional Time Series Dynamics: A Case Study in Molecular Biophysics
(Taylor & FrancisJournal of the American Statistical Association, 2016-03-22)
Motivated by the problem of inferring the molecular dynamics of DNA in solution, and linking them with its base-pair composition, we consider the problem of comparing the dynamics of functional time series (FTS), and of ...
Free groups and the axiom of choice
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2016-01-05)
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 ...
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.
Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs
(SpringerPublications mathématiques de l'IHÉS, 2016-01-18)
For every smooth complex projective variety W of dimension d and nonnegative Kodaira dimension, we show the existence of a universal constant m depending only on d and two natural invariants of the very general fibres of ...