Related papers: Partitions of Unity and New Obstructions for Gabor…
We consider Gabor frames generated by a Gaussian function and describe the behavior of the frame constants as the density of the lattice approaches the critical value.
A conjecture regarding the structure of expander graphs is discussed.
We study cohomological obstructions to the existence of global conserved quantities. In particular, we show that, if a given local variational problem is supposed to admit global solutions, certain cohomology classes cannot appear as…
The recent proof of the Boij-Soederberg conjectures reveals new structure about Betti diagrams of modules, giving a complete description of the cone of Betti diagrams. We begin to expand on this new structure by investigating the semigroup…
Latent fibrations are an adaptation, appropriate for categories of partial maps (as presented by restriction categories), of the usual notion of fibration. The paper initiates the development of the basic theory of latent fibrations and…
We present the first detailed computations of wave optics effects in the gravitational lensing of binary systems. The field is conceptually rich, combining the caustic singularities produced in classical gravitational lensing with quantum…
In this paper we extend the work of Rautenbach and Szwarcfiter by giving a structural characterization of graphs that can be represented by the intersection of unit intervals that may or may not contain their endpoints. A characterization…
We suggest a reduction of the combinatorial problem of hypergraph partitioning to a continuous optimization problem.
We obtain the generating functions for partial matchings avoiding neighbor alignments and for partial matchings avoiding neighbor alignments and left nestings. We show that there is a bijection between partial matchings avoiding three…
These lecture notes give an introduction to the Brauer-Manin obstruction to the existence of rational points, focusing on the interplay between theory and computation.
The paper studies the structure of restricted Leibniz algebras. More specifically speaking, we first give the equivalent definition of restricted Leibniz algebras, which is by far more tractable than that of a restricted Leibniz algebras in…
We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which ``controls'' deformations of the structure bracket of the algebroid. We also have a closer look at various special cases…
We review the motivation for Gauge-Mediated Supersymmetry Breaking and discuss some recent advances.
Consider the semisimple mod p reduction of the Galois representation associated to a Hilbert newform f by Carayol and Taylor. This paper discusses how, under certain conditions on f, the universal ring for deformations of this residual…
Over the past twenty years, lecture hall partitions have emerged as fundamental combinatorial structures, leading to new generalizations and interpretations of classical theorems and new results. In recent years, geometric approaches to…
We show that various natural algebro-geometric moduli stacks, including the stack of curves, have the property that every Deligne-Mumford gerbe over a field appears as the residual gerbe of one of their points. These gerbes are universal…
Approximately dual frames as a generalization of duality notion in Hilbert spaces have applications in Gabor systems, wavelets, coorbit theory and sensor modeling. In recent years, the computing of the associated deviations of the canonical…
We develop an obstruction theory for the extension of truncated minimal $A$-infinity bimodule structures over truncated minimal $A$-infinity algebras. Obstructions live in far-away pages of a (truncated) fringed spectral sequence of…
We exhibit examples of pairs $(X,D)$ where $X$ is a smooth projective variety and $D$ is an anticanonical reduced simple normal crossing divisor such that the deformations of $(X,D)$ are obstructed. These examples are constructed via toric…
We introduce, and propagate wave-packet solutions of, a single qubit system in which geometric gauge forces and phases emerge. We investigate under what conditions non-trivial gauge phenomena arise, and demonstrate how symmetry breaking is…