Related papers: Circle packings, renormalizations and subdivision …

These are notes on the method of normalized graph cuts and its applications to graph clustering. I provide a fairly thorough treatment of this deeply original method due to Shi and Malik, including complete proofs. I include the necessary…

We formulate conditions for almost-commutative (spacetime) manifolds under which the asymptotically expanded spectral action is renormalizable. These conditions are of a graph-theoretical nature, involving the Krajewski diagrams that…

Let $M$ be a closed smooth connected spin manifold of even dimension $n$, let $g$ be a Riemannian metric of regularity $W^{1,p}$, $p > n$, on $M$ whose distributional scalar curvature in the sense of Lee-LeFloch is bounded below by…

Many biological tissues feature a heterogeneous network of fibers whose tensile and bending rigidity contribute substantially to these tissues' elastic properties. Rigidity percolation has emerged as a important paradigm for relating these…

We study the global behavior of the renormalization operator on a specially constructed Banach manifold that has cubic critical circle maps on its boundary and circle diffeomorphisms in its interior. As an application, we prove results on…

The Renormalisation Group (RG) is a systematic procedure used to regularise divergences appearing as artefacts when constructing solutions to a large class of differential problems, whether perturbatively or not. This paper is devoted to…

In this technical note we introduce a manifestly gauge-invariant and supersymmetric procedure to regularize and renormalize one-loop divergences of chiral multiplets in two-dimensional N=(2,2) theories in curved spacetime. We apply the…

Let P be a locally finite circle packing in the plane invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite, we construct an explicit Borel measure on the plane which…

Given a singular projective variety in some projective space, we characterize the smooth curves contracted by the Gauss map in terms of normal bundles. As a consequence, we show that if the variety is normal, then a contracted line always…

Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…

We prove two rigidity theorems for maps between Riemannian manifolds. First, we prove that a Lipschitz map $f:M\to N$ between two oriented Riemannian manifolds, whose differential is almost everywhere an orientation-preserving isometry, is…

The Euclidean renormalization bundle considered in QFT by Connes, Kreimer, and Marcolli has been extended, in a remarkable series of papers by S Agarwala, to Riemannian manifolds $(X,g)$: in particular by the construction of a flat…

Spin textures, i.e., the distribution of spin polarization vectors in reciprocal space, exhibit diverse patterns determined by symmetry constraints, resulting in a variety of spintronic phenomena. Here, we propose a universal theory to…

We develop the notion of a Kleinian Sphere Packing, a generalization of "crystallographic" (Apollonian-like) sphere packings defined by Kontorovich-Nakamura [KN19]. Unlike crystallographic packings, Kleinian packings exist in all…

The conformal boundary of a hyperbolic $3$-manifold $M$ is a union of Riemann surfaces. If any of these Riemann surfaces has a nontrivial Teichm\"uller space, then the hyperbolic metric of $M$ can be deformed quasi-isometrically. These…

In [10] it was shown that there is a mapping class group-equivariant deformation retraction of the Teichm\"uller space of a closed surface onto a CW complex with dimension equal to the virtual cohomological dimension of the mapping class…

There is a well developed renormalization theory of real analytic critical circle maps by de Faria, de Melo, and Yampolsky. In this paper, we extend Yampolsky's result on hyperbolicity of renormalization periodic points to a larger class of…

Recent general results on Hamiltonian reductions under polar group actions are applied to study some reductions of the free particle governed by the Laplace-Beltrami operator of a compact, connected, simple Lie group. The reduced systems…

We present a novel approach for deriving KAM-type linearization theorems directly -- and almost immediately -- from the existence of the stable foliation for a renormalization operator. We give a few illustrations in dynamics in one and…

We discuss some specializations of the frames of flat orthonormal frame bundles over geometries of indefinite signature, and the resulting symmetries of families of embedded Riemannian or pseudo-Riemannian geometries. The specializations…