Related papers: Note on the structure constants for the diffeomorp…
We study the couplings of discrete states that appear in the string theory embedded in two dimensions, and show that they are given by the structure constants of the group of area preserving diffeomorphisms. We propose an effective action…
We prove the existence of common fixed points for commuting homeomorphisms of the plane R^2 or the sphere S^2, which preserve a probability measure. For example: some commuting C^1-diffeomorphisms of S^2, which are sufficiently close to the…
We present a representation formula for discrete indefinite affine spheres via loop group factorizations. This formula is derived from the Birkhoff decomposition of loop groups associated with discrete indefinite affine spheres. In…
This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…
For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group,…
We study the geometric structure of the statistical models for two-by-two contingency tables. One or two odds ratios are fixed and the corresponding models are shown to be a portion of a ruled quadratic surface or a segment. Some pointers…
We give an explicit, positive, and type-uniform formula for all equivariant structure constants of the Peterson Schubert calculus in arbitrary Lie types, using only the Cartan matrix of the corresponding root system $\Phi$. This solves an…
We provide lower and upper bounds on the minimum size of a maximum stable set over graphs of flag spheres, as a function of the dimension of the sphere and the number of vertices. Further, we use stable sets to obtain an improved Lower…
We give a general description of the structure of a discrete double groupoid (with an extra, quite natural, filling condition) in terms of groupoid factorizations and groupoid 2-cocycles with coefficients in abelian group bundles. Our…
We discuss the current state of knowledge of stable homotopy groups of spheres. We describe a new computational method that yields a streamlined computation of the first 61 stable homotopy groups, and gives new information about the stable…
We present an adaptation of the so-called structural method \cite{CMM23} for Hamiltonian systems, and redesign the method for this specific context, which involves two coupled differential systems. Structural schemes decompose the problem…
I describe various aspects of the construction of a dual standard model including how it may be possible to obtain the charge spectrum, the family structure and spin of the known matter particles. I summarize the encouraging features of the…
This paper presents a set of general strategies for the analysis of structure in amorphous materials and a general approach to assessing the utility of a selected structural description. Measures of structural diversity and utility are…
This paper is devoted to introduce new geometric constants that quantify the difference between Roberts orthogonality and Birkhoff orthogonality in normed planes. We start by characterizing Roberts orthogonality in two different ways: via…
We provide an alternative proof that Crosscaps are diffeomorphically stable.
In this paper we show that in the case of noncommutative two-tori one gets in a natural way simple structures which have analogous formal properties as Hopf algebra structures but with a deformed multiplication on the tensor product.
We give a simple parametrization of the $G_2$ group, which is consistent with the structure of $G_2$ as a SU(3) fibration. We also explicitly compute the (bi)invariant measure, which turns out to have a simple expression.
We prove a stability theorem for spaces of smooth concordance embeddings. From it we derive various applications to spaces of concordance diffeomorphisms and homeomorphisms.
We define 2-calibrated structures, which are analogs of symplectic structures in odd dimensions. We show the existence of differential topological constructions compatible with the structure.
In the present paper we survey the most recent classification results for proper biharmonic submanifolds in unit Euclidean spheres. We also obtain some new results concerning geometric properties of proper biharmonic constant mean curvature…