• Geometric quantization of integrable systems with hyperbolic singularities 

      [OWP-2009-01] Hamilton, Mark D.; Miranda, Eva (Mathematisches Forschungsinstitut Oberwolfach, 2009)
      We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. ...
    • Heisenberg-Weyl algebra revisited: combinatorics of words and paths 

      [OWP-2009-02] Blasiak, Pawel; Duchamp, Gérard H. E.; Horzela, Andrzej; Penson, Karol A.; Solomon, Allan I. (Mathematisches Forschungsinstitut Oberwolfach, 2009)
      The Heisenberg–Weyl algebra, which underlies virtually all physical representations of Quantum Theory, is considered from the combinatorial point of view. We provide a concrete model of the algebra in terms of paths on a ...
    • Minimal Riesz energy on the sphere for axis-supported external fields 

      [OWP-2009-04] Brauchart, Johann S.; Dragnev, Peter D.; Saff, Edward B. (Mathematisches Forschungsinstitut Oberwolfach, 2009)
      Abstract. We investigate the minimal Riesz $s$-energy problem for positive measures on the d-dimensional unit sphere $\mathbb{S}^d$ in the presence of an external field induced by a point charge, and more generally by ...
    • On the Directionally Newton-non-degenerate Singularities of Complex Hypersurfaces 

      [OWP-2008-16] Kerner, Dmitry (Mathematisches Forschungsinstitut Oberwolfach, 2008)
      We introduce a minimal generalization of Newton-non-degenerate singularities of hypersurfaces. Roughly speaking, an isolated hypersurface singularity is called directionally Newton-non-degenerate if the local embedded ...
    • On the δ=const Collisions of Singularities of Complex Plane Curves 

      [OWP-2008-15] Kerner, Dmitry (Mathematisches Forschungsinstitut Oberwolfach, 2008)
      We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equi-normalizable or ...
    • Urn Models & Operator Ordering Procedures 

      [OWP-2008-06] Blasiak, Pawel (Mathematisches Forschungsinstitut Oberwolfach, 2008-03-10)
      Ordering of operators is purely combinatorial task involving a number of commutators shuffling components of operator expression to desired form. Here we show how it can be illustrated by simple urn models in which normal ...
    • Weyl-Titchmarsh Functions of Vector-Valued Sturm-Liouville Operators on the Unit Interval 

      [OWP-2008-13] Chelkak, Dmitry; Korotyaev, Evgeny (Mathematisches Forschungsinstitut Oberwolfach, 2008)
      The matrix-valued Weyl-Titchmarsh functions $M(\lambda)$ of vector-valued Sturm-Liouville operators on the unit interval with the Dirichlet boundary conditions are considered. The collection of the eigenvalues (i.e., poles ...