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The Fukaya category, exotic forms and exotic autoequivalences
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2012-04-10)
A symplectic manifold is a smooth manifold M together with a choice of a
closed non-degenerate two-form. Recent years have seen the importance of associating
an A∞-category to M, called its Fukaya category, in helping ...
Stability of charged rotating black holes for linear scalar perturbations
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsCambridge Centre for Analysis, 2015-03-03)
In this thesis, the stability of the family of subextremal Kerr-Newman space- times is studied in the case of linear scalar perturbations.
That is, nondegenerate energy bounds (NEB) and integrated local energy decay ...
Unifying Amplitude and Phase Analysis Unifying Amplitude and Phase Analysis. A Compositional Data Approach to Functional Multivariate Mixed-Effects Modeling of Mandarin Chinese
(Taylor & FrancisJournal of the American Statistical Association, 2015-07-06)
Mandarin Chinese is characterized by being a tonal language; the pitch (or F0) of its utterances carries considerable linguistic information. However, speech samples from different individuals are subject to changes in ...
Characterisation of gradient flows on finite state Markov chains
(Institute of Mathematical StatisticsElectronic Communications in Probability, 2015-03-29)
In his 2011 work, Maas has shown that the law of any time-reversible continuoustime
Markov chain with finite state space evolves like a gradient flow of the relative
entropy with respect to its stationary distribution. ...
Invariant distributions, Beurling transforms and tensor tomography in higher dimensions
(SpringerMathematische Annalen, 2015-02-01)
In the recent articles [PSU13, PSU14c], a number of tensor tomography results were proved on two-dimensional manifolds. The purpose of this paper is to extend some of these methods to manifolds of any dimension. A central ...
Groups and embeddings in SL(2, C)
(Taylor & FrancisCommunications in Algebra, 2015-10-19)
We give results on when a finitely generated torsion free group does
or does not embed in SL(2, C). For instance if we glue two copies of
the figure 8 knot along its torus boundary then the fundamental group
of the resulting ...
The Triviality problem for profinite completions
(SpringerInventiones Mathematicae, 2015-02-24)
We prove that there is no algorithm that can determine whether or not a finitely presented group has a non-trivial finite quotient; indeed, this property remains undecidable among the fundamental groups of compact, ...
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.