9 citations · 14 across the 9 of their papers we have counts for
11 papers
On globally hypoelliptic abelian actions and their existence on homogeneous spaces
Danijela Damjanovic, James Tanis, Zhenqi Wang
We define globally hypoelliptic smooth actions as actions whose leafwise Laplacian along the orbit foliation is a globally hypoelliptic differential operator. When $k…
Transversal local rigidity of discrete Abelian actions on Heisenberg nilmanifolds
Danijela Damjanovic, James Tanis
In this paper we prove a perturbative result for a class of actions on Heisenberg nilmanifolds, which have Diophantine properties. Along the way we prove cohomologica…
Cohomological equation and cocycle rigidity of discrete parabolic actions
James Tanis, Zhenqi Jenny Wang
We study the cohomological equation for discrete horocycle maps on and via representation theory. Specifically, we pro…
Cohomological equation and cocycle rigidity of discrete parabolic actions in some higher rank Lie groups
James Tanis, Zhenqi Jenny Wang
Let denote a higher rank -split simple Lie group of the following type: , , , and , where $m\geq…
Effective equidistribution of twisted horocycle flows and horocycle maps
Livio Flaminio, Giovanni Forni, James Tanis
We prove bounds for twisted ergodic averages for horocycle flows of hyperbolic surfaces, both in the compact and in the non-compact finite area case. From these bounds we derive ef…
Uniform bounds for period integrals and sparse equidistribution
James Tanis, Pankaj Vishe
Let be a compact manifold, and let be a function of zero average. We use spectral methods to get uniform (i.e. independ…
Effective equidistribution for some unipotent flows in mod cocompact, irreducible lattice
James Tanis
Let , and let be an irreducible, cocompact lattice. We prove a sharp estimate up to a logarithmic factor on the rate of equidistribution o…
Kaczmarz Algorithm and Frames
Wojciech Czaja, James Tanis
Sequences of unit vectors for which the Kaczmarz algorithm always converges in Hilbert space can be characterized in frame theory by tight frames with constant 1. We generalize thi…
Cocycle Rigidity and Splitting for some Discrete Parabolic Actions
Danijela Damjanovic, James Tanis
We prove trivialization of the first cohomology with coefficients in smooth vector fields, for a class of parabolic actions on $(SL(2, \mathbb R)\times SL(2, \mathbb…
The distribution of -integral points on -orbit closures of binary forms
Sho Tanimoto, James Tanis
We study the distribution of -integral points on -orbit closures of binary forms and prove an asymptotic formula for the number of -integral points of bounded…
The Cohomological Equation and Invariant Distributions for Horocycle Maps
James Tanis
We study the invariant distributions for the horocycle map on and prove Sobolev estimates for the cohomological equation of the horocycle map. As an…