The genus spectrum of a hyperbolic 3-manifold

In this article we study the spectrum of totally geodesic surfaces of a finite volume hyperbolic 3-manifold. We show that for arithmetic hyperbolic 3-manifolds that contain a totally geodesic surface, this spectrum determines the commensurability class. In addition, we show that any finite volume hyperbolic 3-manifold has many pairs of non-isometric finite covers with identical spectra. Forgetting multiplicities, we can also construct pairs where the volume ratio is unbounded

Absolute profinite rigidity and hyperbolic geometry

We construct arithmetic Kleinian groups that are profinitely rigid in the absolute sense: each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. The Bianchi group $\mathrm{PSL}(2,\mathbb{Z}[\omega])$ with $\omega^2+\omega+1=0$ is rigid in this sense. Other examples include the non-uniform lattice of minimal co-volume in $\mathrm{PSL}(2,\mathbb{C})$ and the fundamental group of the Weeks manifold (the closed hyperbolic $3$-manifold of minimal volume).Comment: v2: 35 pages. Final version. To appear in the Annals of Mathematics, Vol. 192, no. 3, November 202

Discovery of a Magnetic DZ White Dwarf with Zeeman-Split Lines of Heavy Elements

A spectroscopic survey of previously-unstudied Luyten Half Second proper motion stars has resulted in the discoveries of two new cool magnetic white dwarfs. One (LHS 2273) is a routine DA star, T= 6,500K, with Zeeman-split H alpha and H beta, for which a simple model suggests a polar field strength of 18.5 MG viewed close to equator-on. However, the white dwarf LHS 2534 proves to be the first magnetic DZ showing Zeeman-split Na I and Mg I components, as well as Ca I and Ca II lines for which Zeeman components are blended. The Na I splittings result in a mean surface field strength estimate of 1.92 MG. Apart from the magnetic field, LHS 2534 is one of the most heavily-blanketed and coolest DZ white dwarfs at T ~ 6,000K.Comment: 7 pages, Astrophysical Journal (Letters), in pres

Collisions at infinity in hyperbolic manifolds

For a complete, finite volume real hyperbolic n-manifold M, we investigate the map between homology of the cusps of M and the homology of $M$. Our main result provides a proof of a result required in a recent paper of Frigerio, Lafont, and Sisto

Non-parametric comparison of histogrammed two-dimensional data distributions using the Energy Test

When monitoring complex experiments, comparison is often made between regularly acquired histograms of data and reference histograms which represent the ideal state of the equipment. With the larger HEP experiments now ramping up, there is a need for automation of this task since the volume of comparisons could overwhelm human operators. However, the two-dimensional histogram comparison tools available in ROOT have been noted in the past to exhibit shortcomings. We discuss a newer comparison test for two-dimensional histograms, based on the Energy Test of Aslan and Zech, which provides more conclusive discrimination between histograms of data coming from different distributions than methods provided in a recent ROOT release.The Science and Technology Facilities Council, U

A numerical study of the correspondence between paths in a causal set and geodesics in the continuum

This paper presents the results of a computational study related to the path-geodesic correspondence in causal sets. For intervals in flat spacetimes, and in selected curved spacetimes, we present evidence that the longest maximal chains (the longest paths) in the corresponding causal set intervals statistically approach the geodesic for that interval in the appropriate continuum limit.Comment: To the celebration of the 60th birthday of Rafael D. Sorki

Violations of Bell Inequalities for Measurements with Macroscopic Uncertainties: What does it Mean to Violate Macroscopic Local Realism?

We suggest to test the premise of ``macroscopic local realism'' which is sufficient to derive Bell inequalities when measurements of photon number are only accurate to an uncertainty of order $n$ photons, where $n$ is macroscopic. Macroscopic local realism is only sufficient to imply, in the context of the original Einstein-Podolsky-Rosen argument, fuzzy ``elements of reality'' which have a macroscopic indeterminacy. We show therefore how the violation of local realism in the presence of macroscopic uncertainties implies the failure of ``macroscopic local realism''. Quantum states violating this macroscopic local realism are presented.Comment: 28 pages, 5 figures- new version is unchanged but tightened-20 pages, 5 figure

Method for fabricating a low stress x-ray mask using annealable amorphous refractory compounds

X‐ray masks have been fabricated by depositing a compressively stressed refractory material on a wafer, annealing to a zero stress state, and then forming the membrane. Amorphous TaSiN and TaSi alloys deposited with a magnetron sputter tool have been extensively characterized in terms of resistivity, composition, defectivity, surface roughness, and crystalline state. Optimization in terms of these parameters has resulted in base line selection of absorber films of the following compositions: Ta_(61)Si_(17)N_(21) and Ta_(75)Si_(23). The process is shown to be extendable to an entire class of amorphous annealable refractory materials. Careful studies of deposition and annealing conditions have resulted in a 4× reduction of image placement to the 30 nm maximum vector level. Finally, the importance of stress gradients is experimentally verified