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Balanced semisimple filtrations for tilting modules
(American Mathematical SocietyRepresentation Theory, 2017-03-08)
Let $ U_l$ be a quantum group at an $ l$th root of unity, obtained via Lusztig's divided powers construction. Many indecomposable tilting modules for $ U_l$ have been shown to have what we call a balanced semisimple ...
The half plane UIPT is recurrent
(SpringerProbability Theory and Related Fields, 2017-03-07)
We prove that the half plane version of the uniform infinite planar triangulation (UIPT) is recurrent. The key ingredients of the proof are a construction of a new full plane extension of the half plane UIPT, based on a ...
Topological cycle matroids of infinite graphs
(ElsevierEuropean Journal of Combinatorics, 2017-02-01)
We prove that the topological cycles of an arbitrary infinite graph together with its topological ends form a matroid. This matroid is, in general, neither finitary nor cofinitary.
Infinitesimal Models of Algebraic Theories
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsHomerton College, 2017-11-25)
Smooth manifolds have been always understood intuitively as spaces that are infinitesimally
linear at each point, and thus infinitesimally affine when forgetting about the base point. The
aim of this thesis is to develop ...
Comments on: High-dimensional simultaneous inference with the bootstrap
(Sociedad de Estadistica e Investigacion OperativaTest, 2017-12-01)
We congratulate the authors on their stimulating contribution to the burgeoning high-dimensional inference literature. The bootstrap offers such an attractive methodology in these settings, but it is well-known that its ...
Bounding cohomology for low rank algebraic groups
(University of CambridgeDPMMSHomerton, 2017-08-01)
Let G be a semisimple linear algebraic group over an algebraically closed field of prime characteristic. In this thesis we outline the theory of such groups and their cohomology. We then concentrate on algebraic groups in ...
K-stability for Kähler manifolds
(International PressMathematical Research Letters, 2017-09)
We formulate a notion of K-stability for Kähler manifolds, and prove one direction of the Yau–Tian–Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi functional being bounded below (resp. ...
On the Absence of Uniform Recovery in Many Real-World Applications of Compressed Sensing and the Restricted Isometry Property and Nullspace Property in Levels
(Society for Industrial and Applied MathematicsSiam Journal on Imaging Sciences, 2017-03-15)
The purpose of this paper is twofold. The first is to point out that the property of uniform recovery, meaning that all sparse vectors are recovered, does not hold in many applications where compressed sensing is successfully ...
Mobility of an axisymmetric particle near an elastic interface
(Cambridge University PressJournal of Fluid Mechanics, 2017-01-01)
Using a fully analytical theory, we compute the leading-order corrections to the translational, rotational and translation–rotation coupling mobilities of an arbitrary axisymmetric particle immersed in a Newtonian fluid ...
Nonlinear effects in buoyancy-driven variable-density turbulence
(Cambridge University PressJournal of Fluid Mechanics, 2017-01-01)
We consider the time dependence of a hierarchy of scaled L²ᵐ-norms D_m,ω and D_m,θ of the vorticity ω =∇ x u and the density gradient ∇θ, where θ = log.(ρ*/ ρ*₀), in a buoyancy-driven turbulent flow as simulated by Livescu ...