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A short proof that every finite graph has a tree-decomposition displaying its tangles
(ElsevierEuropean Journal of Combinatorics, 2016-06-08)
We give a short proof that every finite graph (or matroid) has a tree-decomposition that displays all maximal tangles.
This theorem for graphs is a central result of the graph minors project of Robertson and Seymour and ...
On Short Time Existence of Lagrangian Mean Curvature Flow
(SpringerMathematische Annalen, 2016)
We consider a short time existence problem motivated by a conjecture of Joyce in [8]. Specifically we prove that given any compact Lagrangian L ⊂ C^n with a finite number of singularities, each asymptotic to a pair of ...
Towards mirror symmetry for varieties of general type
(ElsevierAdvances in Mathematics, 2016)
Balanced metrics on twisted Higgs bundles
(SpringerMathematische Annalen, 2016)
SMOOTH PRINCIPAL COMPONENT ANALYSIS OVER TWO-DIMENSIONAL MANIFOLDS WITH AN APPLICATION TO NEUROIMAGING
(Institute of Mathematical StatisticsThe Annals of Applied Statistics, 2016-01-05)
Motivated by the analysis of high-dimensional neuroimaging signals located over the cortical surface, we introduce a novel Principal Component Analysis technique that can handle functional data located over a two-dimensional ...
Data processing for the sandwiched Rényi divergence: a condition for equality
(SpringerLetters in Mathematical Physics, 2016)
The $\alpha$-sandwiched Rényi divergence satisfies the data processing inequality, i.e. monotonicity under quantum operations, for $\alpha$ $\geq$ 1/2. In this article, we derive a necessary and sufficient algebraic condition ...
Asymptotics of Partial Density Functions for Divisors
(SpringerThe Journal of Geometric Analysis, 2016-09-19)
We study the asymptotic behaviour of the partial density function associated to sections of a positive hermitian line bundle that vanish to a particular order along a fixed divisor $Y$ . Assuming the data in question is ...
Non-Backtracking Loop Soups and Statistical Mechanics on Spin Networks
(SpringerAnnales Henri Poincaré, 2016-10-20)
We introduce and study a Markov field on the edges of a graph $\mathcal{G}$ in dimension $\textit{d}$ ≥ 2 whose configurations are spin networks. The field arises naturally as the edge-occupation field of a Poissonian model ...
Unstable mode solutions to the Klein-Gordon equation in Kerr-anti-de Sitter spacetimes
(SpringerCommunications in Mathematical Physics, 2016)
For any cosmological constant Λ = −3/$l^2$ < 0 and any $\alpha$ < 9/4, we find a Kerr-AdS spacetime ($M$, $g_{KAdS}$), in which the Klein-Gordon equation $\square g_{KAdS}$ ψ+$\alpha$/$l^2$ψ = 0 has an exponentially growing ...
Homogeneous Monge-Amp$\grave e$re Equations and Canonical Tubular Neighbourhoods in Kähler Geometry
(Oxford University PressInternational Mathematics Research Notices, 2016)
We prove the existence of canonical tubular neighbourhoods around complex submanifolds of Kähler manifolds that are adapted to both the holomorphic and symplectic structure. This is done by solving the complex Homogeneous ...