Related papers: The Gromov-Lawson index and the Baum-Connes assemb…
This paper has a double goal, the first one is to make a slight survey of some theoretical results about the existence of positively invariant curves that allow to describe important properties of the set of bounded orbits and its boundary…
We survey results for Cameron-Liebler sets and low degree Boolean functions for Hamming graphs, Johnson graphs and Grassmann graphs from the point of view of association schemes. This survey covers selected results in finite geometry,…
This article surveys results for Riemannian manifolds of positive and non-negative sectional curvature with symmetries.
This is a revised form of the previous paper in which we study cones of positive maps of B(H) into itself. We add the result that the dual cone of a symmetric mapping cone is itself a symmetric mapping cone. As applications we obtain…
This is a survey article on Newton-Okounkov bodies in projective geometry focusing on the relationship between positivity of divisors and Newton-Okounkov bodies.
The main goal of this paper is to present the application of structural sums, mathematical objects originating from the computational materials science, in construction of a feature space vector of 2D random composites simulated by…
Gromov and Lawson developed a codimension 2 index obstruction to positive scalar curvature for a closed spin manifold M, later refined by Hanke, Pape and Schick. Kubota has shown that also this obstruction can be obtained from the Rosenberg…
The goal of this article is to motivate and describe how Gromov-Witten theory can and has provided tools to understand the moduli space of curves. For example, ideas and methods from Gromov-Witten theory have led to both conjectures and…
We follow a stream of the history of positive matrices and positive functionals, as applied to algebraic sums of squares decompositions, with emphasis on the interaction between classical moment problems, function theory of one or several…
A method to compute several scalar quantities of Cosmic Microwave Background maps on the sphere is presented. We consider here four type of scalars: the Hessian matrix scalars, the distortion scalars, the gradient related scalars and the…
This work presents a mathematical treatment of the relation between Self-Organizing Maps (SOMs) and Gaussian Mixture Models (GMMs). We show that energy-based SOM models can be interpreted as performing gradient descent, minimizing an…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
We obtain two types of results on positive scalar curvature metrics for compact spin manifolds that are even dimensional. The first type of result are obstructions to the existence of positive scalar curvature metrics on such manifolds,…
In this article we briefly survey some developments in gauged linear sigma models (GLSMs). Specifically, we give an overview of progress on constructions of GLSMs for various geometries, GLSM-based computations of quantum cohomology,…
Conjecture 1 of Stanley Chang: "Positive scalar curvature of totally nonspin manifolds" asserts that a closed smooth manifold M with non-spin universal covering admits a metric of positive scalar curvature if and only if a certain…
Modern sampling methods create ensembles of district maps that score well on discrete compactness scores, whereas the Polsby-Popper and other shape-based scores remain highly relevant for building fair maps and litigating unfair ones. The…
There are several interrelated notions of discrete curvature on graphs. Many approaches utilize the optimal transportation metric on its probability simplex or the distance matrix of the graph. In this survey article, we compute formulas…
We study conjugacy invariants for completely positive maps that are inspired by the concept of curvature introduced for commuting d-tuples of contractions by Arveson
Between the category of exact metric spaces with bounded geometry (about which much is known) and the larger category of arbitrary exact metric spaces (about which little is known) lies the intermediate category of asymptotically exact…
This paper provides some technical results needed in "Formalism for Relative Gromov-Witten Invariants." We study line-bundles on the moduli stacks of relative stable and rubber maps that are used to define relative Gromov-Witten invariants…