31 citations · 63 across the 9 of their papers we have counts for
13 papers
Periodic orbit theory of Bethe-integrable quantum systems: an -particle Berry-Tabor trace formula
Juan Diego Urbina, Michael Kelly, Klaus Richter
One of the fundamental results of semiclassical theory is the existence of trace formulae showing how spectra of quantum mechanical systems emerge from massive interference among a…
Pattern Equivariant Mass Transport in Aperiodic Tilings and Cohomology
Michael Kelly, Lorenzo Sadun
Suppose that we have a repetitive and aperiodic tiling of , and two mass distributions and on , each pattern equivariant with respec…
The Beurling-Selberg Box Minorant Problem via Linear Programming Bounds
Jacob Carruth, Noam Elkies, Felipe Gonçalves +1
In this paper we investigate a high dimensional version of Selberg's minorant problem for the indicator function of an interval. In particular, we study the corresponding problem o…
Separated Nets in Nilpotent Groups
Tullia Dymarz, Michael Kelly, Sean Li +1
In this paper we generalize several results on separated nets in Euclidean space to separated nets in connected simply connected nilpotent Lie groups. We show that every such group…
Effective equidistribution of translates of maximal horospherical measures in the space of lattices
Kathryn Dabbs, Michael Kelly, Han Li
Recently Mohammadi and Salehi-Golsefidy gave necessary and sufficient conditions under which certain translates of homogeneous measures converge, and they determined the limiting m…
Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices, II
Alan Haynes, Michael Kelly, Henna Koivusalo
Recent results of several authors have led to constructions of parallelotopes which are bounded remainder sets for totally irrational toral rotations. In this brief note we explain…
One-sided Band-limited Approximations of Some Radial Functions
Felipe Gonçalves, Michael Kelly, José Madrid
We construct majorants and minorants of a Gaussian function in Euclidean space that have Fourier transforms supported in a box. The majorants that we construct are shown to be extr…
Pattern Equivariant Cohomology and Theorems of Kesten and Oren
Michael Kelly, Lorenzo Sadun
In 1966 Harry Kesten settled the Erd\H os-Szüsz conjecture on the local discrepancy of irrational rotations. His proof made heavy use of continued fractions and Diophantine analysi…
Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices
Alan Haynes, Henna Koivusalo
For any irrational cut-and-project setup, we demonstrate a natural infinite family of windows which gives rise to separated nets that are each bounded distance to a lattice. Our pr…
A Variation on Selberg's Approximation Problem
Michael Kelly
Let in the upper half-plane and let be an interval. We construct an analogue of Selberg's majorant of the characteristic function of that vanishes at the p…
The Blaschke-Santalo Inequality
Gabriele Bianchi, Michael Kelly
The Blaschke-Santaló Inequality is the assertion that the volume product of a centrally symmetric convex body in Euclidean space is maximized by (and only by) ellipsoids. In this p…
Equivalence relations on separated nets arising from linear toral flows
Alan Haynes, Michael Kelly, Barak Weiss
In 1998, Burago-Kleiner and McMullen independently proved the existence of separated nets in which are not bi-Lipschitz equivalent (BL) to a lattice. A finer equival…
Uniform Dilations in Higher Dimensions
Michael Kelly, Thai Hoang Le
A theorem of Glasner says that if is an infinite subset of the torus , then for any , there exists an integer such that the dilation $nX=\{nx: x \in \mathb…