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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 ...
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 ...
Computations in monotone Floer theory
(Department of Pure Mathematics and Mathematical Statistics, University of CambridgeUniversity of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2016-06-28)
Floer theory is a rich collection of tools for studying symplectic manifolds and their Lagrangian submanifolds with the help of holomorphic curves. Its origins lie in estimating the numbers of equilibria in Hamiltonian ...
Spectral gap in the group of affine transformations over prime fields
(University of ToulouseAnnales de la Faculte des Sciences de Toulousehttp://afst.cedram.org/item?id=AFST_2016_6_25_5_969_0, 2016-11-01)
We study random walks on the groups $\Bbb F^d_p \rtimes$ SL$_d$($\Bbb F_p$). We estimate the spectral gap in terms of the spectral gap of the projection to the linear part SL$_d$($\Bbb F_p$). This problem is motivated by ...
INVARIANT DISTRIBUTIONS AND THE GEODESIC RAY TRANSFORM
(Mathematical Science PublishersAnalysis & PDE, 2016-12-11)
We establish an equivalence principle between the solenoidal injectivity of the geodesic ray transform acting on symmetric $\textit{m}$-tensors and the existence of invariant distributions or smooth first integrals with ...
Exploring Random Geometry with the Gaussian Free Field
(University of CambridgeDPMMSPeterhouse, 2016-10-01)
This thesis studies the geometry of objects from 2-dimensional statistical physics in the continuum.
Chapter 1 is an introduction to Schramm-Loewner evolutions (SLE). SLEs are the canonical family of non-self-intersecting, ...
Pairwise Markov properties for regression graphs
(WileyStat, 2016-11-13)
With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ...
Non-relativistic twistor theory and Newton-Cartan geometry
(SpringerCommunications in Mathematical Physics, 2016-01-14)
We develop a non-relativistic twistor theory, in which Newton-Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle O ⊕ O(2). We ...