The hyperbolic formal affine Demazure algebra

In the present paper we extend the construction of the formal (affine) Demazure algebra due to Hoffnung, Malag\'on-L\'opez, Savage and Zainoulline in two directions. First, we introduce and study the notion of an extendable weight lattice in the Kac-Moody setting and show that all the definitions and properties of the formal (affine) Demazure operators and algebras hold for such lattices. Second, we show that for the hyperbolic formal group law the formal Demazure algebra is isomorphic (after extending the coefficients) to the Hecke algebra.Comment: Final version. Accepted for publication in Algebras and Representation Theory. ALGE-D-15-0016

Parallel eigensolvers in plane-wave Density Functional Theory

We consider the problem of parallelizing electronic structure computations in plane-wave Density Functional Theory. Because of the limited scalability of Fourier transforms, parallelism has to be found at the eigensolver level. We show how a recently proposed algorithm based on Chebyshev polynomials can scale into the tens of thousands of processors, outperforming block conjugate gradient algorithms for large computations

Bounding the Heat Trace of a Calabi-Yau Manifold

The SCHOK bound states that the number of marginal deformations of certain two-dimensional conformal field theories is bounded linearly from above by the number of relevant operators. In conformal field theories defined via sigma models into Calabi-Yau manifolds, relevant operators can be estimated, in the point-particle approximation, by the low-lying spectrum of the scalar Laplacian on the manifold. In the strict large volume limit, the standard asymptotic expansion of Weyl and Minakshisundaram-Pleijel diverges with the higher-order curvature invariants. We propose that it would be sufficient to find an a priori uniform bound on the trace of the heat kernel for large but finite volume. As a first step in this direction, we then study the heat trace asymptotics, as well as the actual spectrum of the scalar Laplacian, in the vicinity of a conifold singularity. The eigenfunctions can be written in terms of confluent Heun functions, the analysis of which gives evidence that regions of large curvature will not prevent the existence of a bound of this type. This is also in line with general mathematical expectations about spectral continuity for manifolds with conical singularities. A sharper version of our results could, in combination with the SCHOK bound, provide a basis for a global restriction on the dimension of the moduli space of Calabi-Yau manifolds.Comment: 32 pages, 3 figure

On the seismic modelling of rotating B-type pulsators in the traditional approximation

The CoRoT and Kepler data revolutionised our view on stellar pulsation. For massive stars, the space data revealed the simultaneous presence of low-amplitude low-order modes and dominant high-order gravity modes in several B-type pulsators. The interpretation of such a rich set of detected oscillations requires new tools. We present computations of oscillations for B-type pulsators taking into account the effects of the Coriolis force in the so-called traditional approximation. We discuss the limitations of classical frequency matching to tune these stars seismically and show that the predictive power is limited in the case of high-order gravity mode pulsators, except if numerous modes of consecutive radial order can be identified.Comment: 8 pages, 4 figures. Paper submitted for publication in the Proceedings of the 61st Fujihara Seminar: Progress in solar/stellar physics with helio- and asteroseismology to appear in ASP Conference Serie

A note on some constants related to the zeta-function and their relationship with the Gregory coefficients

In this paper new series for the first and second Stieltjes constants (also known as generalized Euler's constant), as well as for some closely related constants are obtained. These series contain rational terms only and involve the so-called Gregory coefficients, which are also known as (reciprocal) logarithmic numbers, Cauchy numbers of the first kind and Bernoulli numbers of the second kind. In addition, two interesting series with rational terms are given for Euler's constant and the constant ln(2*pi), and yet another generalization of Euler's constant is proposed and various formulas for the calculation of these constants are obtained. Finally, in the paper, we mention that almost all the constants considered in this work admit simple representations via the Ramanujan summation