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On the number of non-zero elements of joint degree vectors
(Electronic Journal of CombinatoricsThe Electronic Journal of Combinatorics, 2017-03-31)
Joint degree vectors give the number of edges between vertices of degree i and degree j for 1 ≤ i ≤ j ≤ n-1 in an n-vertex graph. We find lower and upper bounds for the maximum number of nonzero elements in a joint degree ...
A Liouville hyperbolic souvlaki
(Institute of Mathematical StatisticsElectronic Journal of Probability, 2017-04-25)
We construct a transient bounded-degree graph no transient subgraph of which embeds in any surface of finite genus.
Moreover, we construct a transient, Liouville, bounded-degree, Gromov–hyperbolic graph with trivial ...
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. ...
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 ...