Related papers: Non-arithmetic hybrid lattices in $\mathrm{PU}(2,1…
We study upper bounds for the torsion in homology of nonuniform arithmetic lattices. Together with recent results of Calegari-Venkatesh, this can be used to obtain upper bounds on K2 of the ring of integers of totally imaginary fields.
The full lattices in a finite dimensional commutative ${\mathbb Q}$-algebra form a commutative semigroup. In the case of an algebraic number field the top part of a certain quotient semigroup is the class group. For a separable algebra some…
We study binary mixtures of hard particles, which exclude up to their $k$th nearest neighbors ($k$NN) on the simple cubic lattice and have activities $z_k$. In the first model analyzed, point particles (0NN) are mixed with 1NN ones. The…
We present natural families of coordinate algebras of noncommutative products of Euclidean spaces. These coordinate algebras are quadratic ones associated with an R-matrix which is involutive and satisfies the Yang-Baxter equations. As a…
We show non-integrability of the nonlinear lattice of Fermi-Pasta-Ulam type via the singularity analysis(Picard-Vessiot theory) of normal variational equations of Lam\'e type.
In this article we introduce the study of the number of pairs of non-comparable elements in a distributive lattice $\L$. We give several tight lower and upper bounds for the number and give as an application the lattices precisely for which…
In this survey article we give an overview of how noncongruence modular curves can be viewed as Hurwitz moduli spaces of covers of elliptic curves at most branched above the origin. We describe some natural questions that arise, and…
We study the multiplicative lattices L which satisfy the condition a = (a : (a : b))(a : b) for all a,b in L.
We establish character rigidity for all non-uniform higher-rank irreducible lattices in semisimple groups of characteristic other than 2. This implies stabilizer rigidity for probability measure preserving actions and rigidity of invariant…
In this paper we calculate a number of integrals over SU(N) of interest in Hamiltonian Lattice Gauge Theory calculations.
Materials science and the study of the electronic properties of solids are a major field of interest in both physics and engineering. The starting point for all such calculations is single-electron, or non-interacting, band structure…
In this paper we consider Property (FA) for lattices in SU(2,1). First, we prove that SU(2,1;O_3) has Property (FA). We then prove that the arithmetic lattices in SU(2,1) of second type arising from congruence subgroups studied by…
The Fermi-Pasta-Ulam (FPU) lattice with periodic boundary conditions and $n$ particles admits a large group of discrete symmetries. The fixed point sets of these symmetries naturally form invariant symplectic manifolds that are investigated…
Let $\Gamma$ be a non-uniform lattice in $PU(p,1)$ without torsion and with $p\geq2 $. We introduce the notion of volume for a representation $\rho:\Gamma \rightarrow PU(m,1)$ where $m \geq p$. We use this notion to generalize the…
We investigate non-perturbative supersymmetry breaking in various models of quantum mechanics, including an interesting class of $PT$-invariant models, using lattice path integrals. These theories are discretized on a temporal Euclidean…
The problem of computing the index of a coincidence isometry of the hyper cubic lattice $\mathbb{Z}^{n}$ is considered. The normal form of a rational orthogonal matrix is analyzed in detail, and explicit formulas for the index of certain…
Given any poset $P$ and chain $\phi$ in $P$, we define the $(P,\phi)$-Tamari lattice. We study in depth these lattices and prove in particular that they are join-semidistributive, join-congruence uniform and left modular. We prove that the…
Besides the oscillator group, there is another four-dimensional non-abelian solvable Lie group that admits a bi-invariant pseudo-Riemannian metric. It is called split oscillator group (sometimes also hyperbolic oscillator group or Boidol's…
A gauge invariant Hamiltonian representation for SU(2) in terms of a spin network basis is introduced. The vectors of the spin network basis are independent and the electric part of the Hamiltonian is diagonal in this representation. The…
For any subfield K of the complex numbers which is not contained in an imaginary quadratic number field, we construct conjugate varieties whose algebras of K-rational (p,p)-classes are not isomorphic. This compares to the Hodge conjecture…