Related papers: Dynamics on the space of 2-lattices in 3-space

Noticing that the space of the solutions of a first order Hamiltonian field theory has a pre-symplectic structure, we describe a class of conserved charges on it associated to the momentum map determined by any symmetry group of…

In this article we propose a metric variation on the C^0-version of the Zimmer program for three manifolds. After a reexamination of the isometry groups of geometric three-manifolds, we consider homomorphisms defined on higher rank lattices…

We give the 3-dimensional Sklyanin algebras $S$ that are module-finite over their center $Z$ the structure of a Poisson $Z$-order (in the sense of Brown-Gordon). We show that the induced Poisson bracket on $Z$ is non-vanishing and is…

We demonstrate how different types of $SU(3)$ Heisenberg models can be implemented with the use of the $p$ orbitals of three dimensional optical lattices. By considering a Mott insulator with unit filling, the dynamics is well described by…

We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that embedded projective variety, known as its…

Finite temperature SU(2) lattice gauge theory is investigated in a 3D cubic box with fixed boundary conditions provided by a discretized, static BPS monopole solution with varying core scale $\mu$. Using heating and cooling techniques we…

The phase space of a gyrostat with a fixed point and a heavy top is the Lie-Poisson space $\textbf{e}(3)^*\cong \mathbb{R}^3\times \mathbb{R}^3$ dual to the Lie algebra $\textbf{e}(3)$ of Euclidean group $E(3)$. One has three naturally…

We prove many new cases of Zimmer's conjecture for actions by lattices in non-$\mathbb{R}$-split semisimple Lie groups $G$. By prior arguments, Zimmer's conjecture reduces to studying certain probability measures invariant under a minimal…

We formulate the Asymptotic Length-Saturation Conjecture on the length sets of closed geodesics on hyperbolic manifolds whose fundamental groups are subarithmetic, that is, contained in an arithmetic group. We prove the first instance of…

We classify all locally finite joinings of a horospherical subgroup action on \Gamma \ G when \Gamma is a Zariski dense geometrically finite subgroup of G=PSL_2(R) or PSL_2(C). This generalizes Ratner's 1983 joining theorem for the case…

We classify locally finite joinings with respect to the Burger-Roblin measure for the action of a horospherical subgroup $U$ on $\Gamma \backslash G$, where $G = \operatorname{SO}(n,1)^\circ$ and $\Gamma$ is a convex cocompact and Zariski…

The pressure of QCD admits at high temperatures a factorization into purely perturbative contributions from "hard" thermal momenta, and slowly convergent as well as non-perturbative contributions from "soft" thermal momenta. The latter can…

In this article we construct many examples of properly convex irreducible domains divided by Zariski dense relatively hyperbolic groups in every dimension at least 3. This answers a question of Benoist. Relative hyperbolicity and non-strict…

Under the generalized Riemann Hypothesis (GRH), Baluyot, Chandee, and Li nearly doubled the range in which the density of low lying zeros predicted by Katz and Sarnak is known to hold for a large family of automorphic $L$-functions with…

We study the limiting distribution of dense orbits of a lattice subgroup $\Gamma\le \text{SL}(m+1,\mathbb{R})$ acting on $H\backslash\text{SL}(m+1,\mathbb{R})$, with respect to a filtration of growing norm balls. The novelty of our work is…

We introduce a relaxation of stability, called almost sure stability, which is insensitive to perturbations by subsets of Loeb measure $0$ in a non-standard finite group. We show that almost sure stability satisfies a stationarity principle…

In this work it is studied the Schr\"odinger equation for a non-relativistic particle restricted to move on a surface $S$ in a three-dimensional Minkowskian medium $\mathbb{R}_1^3$, i.e., the space $\mathbb{R}^3$ equipped with the metric…

Let $\Gamma$ be a Zariski dense Kleinian Schottky subgroup of PSL2(C). Let $\Lambda(\Gamma)$ be its limit set, endowed with a Patterson-Sullivan measure $\mu$ supported on $\Lambda(\Gamma)$. We show that the Fourier transform…

Let $P_3(\mathbf{C}^{\infty})$ be the space of complex cubic polynomials in infinitely many variables. We show that this space is $\mathbf{GL}_{\infty}$-noetherian, meaning that any $\mathbf{GL}_{\infty}$-stable Zariski closed subset is cut…

Let N be a complete hyperbolic 3-manifold that is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We show N is homeomorphic to the interior of a compact 3-manifold, or tame, if one of the following conditions holds: (1) N…