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On the Cauchy Problem for the Homogeneous Boltzmann-Nordheim Equation for Bosons: Local Existence, Uniqueness and Creation of Moments
(SpringerJournal of Statistical Physics, 2016)
The Boltzmann-Nordheim equation is a modification of the Boltzmann equation, based on physical considerations, that describes the dynamics of the distribution of particles in a quantum gas composed of bosons or fermions. ...
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 ...
Non-reductive automorphism groups, the Loewy filtration and K-stability
(l'Institut FourierAnnales de l'Institut Fourier, 2016-03-18)
We study the K-stability of a polarised variety with non-reductive automorphism group. We associate a canonical filtration of the co-ordinate ring to each variety of this kind, which destabilises the variety in several ...
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 ...
Alpha invariants and coercivity of the Mabuchi functional on Fano manifolds
(Université Paul SabatierAnnales de la Faculté des Sciences de Toulouse, 2016)
We give a criterion for the coercivity of the Mabuchi functional for general Kàhler classes on Fano manifolds in terms of Tian's alpha invariant. This generalises a result of Tian in the anti-canonical case implying the ...
On K-stability of finite covers
(Oxford University PressJournal of the London Mathematical Society, 2016)
We show that certain Galois covers of K-semistable Fano varieties are K-stable. We use this to give some new examples of Fano manifolds admitting Kähler-Einstein metrics, including hypersurfaces, double solids and threefolds.
Gaussian tree constraints applied to acoustic linguistic functional data
(ElsevierJournal of Multivariate Analysis, 2016-10-11)
Evolutionary models of languages are usually considered to take the form of trees. With the development of so-called tree constraints the plausibility of the tree model assumptions can be assessed by checking whether the ...
Exceptional collections, and the Néron–Severi lattice for surfaces
(ElsevierAdvances in Mathematics, 2017-01-10)
We work out properties of smooth projective varieties X over a (not necessarily algebraically closed) field $\textit{k}$ that admit collections of objects in the bounded derived category of coherent sheaves D$^{b}$(X) that ...
$\textit{K}$-Theory of Fermat Curves
(Department of Pure Mathematics and Mathematical Statistics, University of CambridgeUniversity of CambridgeChurchill College, 2017-01-10)
I investigate the $K_2$ groups of the quotients of Fermat curves given in projective coordinates by the equation $F_n:X^n+Y^n=Z^n$. On any quotient where the number of known elements is equal to the rank predicted by ...