The de Rham functor for logarithmic D-modules

In the first part we deepen the six-functor theory of (holonomic) logarithmic D-modules, in particular with respect to duality and pushforward along projective morphisms. Then, inspired by work of Ogus, we define a logarithmic analogue of the de Rham functor, sending logarithmic D-modules to certain graded sheaves on the so-called Kato-Nakayama space. For holonomic modules we show that the associated sheaves have finitely generated stalks and that the de Rham functor intertwines duality for D-modules with a version of Poincar\'e-Verdier duality on the Kato-Nakayama space. Finally, we explain how the grading on the Kato-Nakayama space is related to the classical Kashiwara-Malgrange V-filtration for holonomic D-modules.Comment: 37 page

Beyond Standard Model Higgs

Recent LHC highlights of searches for Higgs bosons beyond the Standard Model are presented. The results by the ATLAS and CMS collaborations are based on 2011 and 2012 proton-proton collision data at centre-of-mass energies of 7 and 8 TeV, respectively. They test a wide range of theoretical models.Comment: Presented at the XXXIV Physics in Collision Symposium, Bloomington, Indiana, September 16-20, 2014. 9 pages, 9 figure

An elementary representation of the higher-order Jacobi-type differential equation

We investigate the differential equation for the Jacobi-type polynomials which are orthogonal on the interval $[-1,1]$ with respect to the classical Jacobi measure and an additional point mass at one endpoint. This scale of higher-order equations was introduced by J. and R. Koekoek in 1999 essentially by using special function methods. In this paper, a completely elementary representation of the Jacobi-type differential operator of any even order is given. This enables us to trace the orthogonality relation of the Jacobi-type polynomials back to their differential equation. Moreover, we establish a new factorization of the Jacobi-type operator which gives rise to a recurrence relation with respect to the order of the equation.Comment: 17 page