Related papers: Ratner's theorem on SL(2,R)-invariant measures

We prove some ergodic-theoretic rigidity properties of the action of SL(2,R) on moduli space. In particular, we show that any ergodic measure invariant under the action of the upper triangular subgroup of SL(2,R) is supported on an…

In this note, we consider applications of Ratner's theorem to constructions of families of polynomials with dense values on the set of primitive integer points from the viewpoint of invariant theory.

We give explicit versions for some of Ratner's estimates on the decay of matrix coefficients of SL(2,R)-representations.

We expose here a short proof of Cramer's theorem in R based on convex duality.

We formulate a second adjoint theorem in the context of tempered representations of real reductive groups, and prove it in the case of SL(2,R).

We prove Beurling's theorem for the full group $SL(2,\R)$. This is the {\em master theorem} in the quantitative uncertainty principle as all the other theorems of this genre follow from it.

This is an elementary observation that the symmetry properties of the Riemann curvature tensor can be (efficiently) expressed as SL(2)-invariance.

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)

We prove a genuine analogue of Wiener Tauberian theorem for integrable functions on $\mathrm {SL}(2, \R).$

A very short proof of Kneser's theorem via transversal is given.

This is the second of two papers that describe a compactness theorem for sequences of solutions of certain SL(2;C) analogs of the anti-self dual equations on oriented, 4-dimensional Riemannian manifolds. This paper proves theorems that…

A reparametrization invariant model, introduced by Montesinos, Rovelli and Thiemann, possessing an SL(2,R) gauge symmetry is treated along the guidelines of an algebraic constraint quantization scheme that translates the vanishing of the…

We give a short Wiener measure proof of the Riemann hypothesis based on a surprising, unexpected and deep relation between the Riemann zeta $\zeta(s)$ and the trivial zeta $\zeta_{t}(s):=Im(s)(2Re(s)-1)$.

In this article, we close a gap in the literature by proving existence of invariant measures for reflected SPDEs with only one reflecting barrier. This is done by arguing that the sequence (u(t, .)) is tight in the space of probability…

We prove existence of an invariant measure on a hypergroup.

Nonlinear ODEs invariant under the group SL(2,R) are solved numerically. We show that solution methods incorporating the Lie point symmetries provide better results than standard methods.

We define an $SL_2(\mathbb{R})$-Casson invariant of closed 3-manifolds. We also observe procedures of computing the invariants in terms of Reidemeister torsions. We discuss some approach of giving the Casson invariant some gradings.

We give a short and relatively elementary proof of the Hilton-Milner Theorem.

The Wigner-Eckart theorem is a well known result for tensor operators of su(2) and, more generally, any compact Lie algebra. In this paper the theorem will be generalized to the particular non-compact case of sl(2,R). In order to do so,…