Browsing 1 - Oberwolfach Preprints (OWP) by MFO Scientific Program "Research in Pairs 2016"
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Alexander r-Tuples and Bier Complexes
[OWP-2016-17] (Mathematisches Forschungsinstitut Oberwolfach, 2016-10)We introduce and study Alexander $r$-Tuples $\mathcal{K} = \langle K_i \rangle ^r_{i=1}$ of simplicial complexes, as a common generalization of pairs of Alexander dual complexes (Alexander 2-tuples) and r-unavoidable ... -
Analysis and Simulation of a New Multi-Component Two-Phase Flow Model with Phase Transitions and Chemical Reactions
[OWP-2017-08] (Mathematisches Forschungsinstitut Oberwolfach, 2017-03-15)A class-II model for multi-component mixtures recently introduced in D. Bothe, W. Dreyer, Continuum thermodynamics of chemically reacting fluid mixtures, Acta Mech., 226 (2015), 1757–1805 is investigated for simple mixtures. ... -
The Berry-Keating Operator on a Lattice
[OWP-2016-23] (Mathematisches Forschungsinstitut Oberwolfach, 2016-11-17)We construct and study a version of the Berry-Keating operator with a built-in truncation of the phase space, which we choose to be a two-dimensional torus. The operator is a Weyl quantisation of the classical Hamiltonian ... -
The Colored Jones Polynomial and Kontsevich-Zagier Series for Double Twist Knots
[OWP-2017-29] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-20)Using a result of Takata, we prove a formula for the colored Jones polynomial of the double twist knots $K_{(-m,-p)}$ and $K_{(-m,p)}$ where $m$ and $p$ are positive integers. In the $(-m,-p)$ case, this leads to new ... -
Exceptional Legendrian Torus Knots
[OWP-2018-04] (Mathematisches Forschungsinstitut Oberwolfach, 2018-03-21)We present classification results for exceptional Legendrian realisations of torus knots. These are the first results of that kind for non-trivial topological knot types. Enumeration results of Ding-Li-Zhang concerning ... -
Finitary Proof Systems for Kozen's μ
[OWP-2016-26] (Mathematisches Forschungsinstitut Oberwolfach, 2016-12-30)We present three finitary cut-free sequent calculi for the modal $μ$-calculus. Two of these derive annotated sequents in the style of Stirling’s ‘tableau proof system with names’ (2014) and feature special inferences that ... -
Herbrand’s Theorem as Higher Order Recursion
[OWP-2018-01] (Mathematisches Forschungsinstitut Oberwolfach, 2018-02-19)We provide a means to compute Herbrand disjunctions directly from sequent calculus proofs with cuts. Our approach associates to a first-order classical proof $\pi \vdash \exists v F$, where $F$ is quantifier free, an ... -
Holonomy Groups of $G_2^*$-Manifolds
[OWP-2017-07] (Mathematisches Forschungsinstitut Oberwolfach, 2017-03-07)We classify the holonomy algebras of manifolds admitting an indecomposable torsion free $G_2^*$-structure, i.e. for which the holonomy representation does not leave invariant any proper non-degenerate subspace. We realize ... -
The Initial and Terminal Cluster Sets of an Analytic Curve
[OWP-2016-25] (Mathematisches Forschungsinstitut Oberwolfach, 2016-12-21)For an analytic curve $\gamma : (a,b) \to \mathbb{C}$, the set of values approaches by $\gamma(t)$, as $t ↘a$ and as $t↗b$ can be any two continuua of $\mathbb{C} \cup \{\infty\}$. -
Killing Tensors on Tori
[OWP-2016-20] (Mathematisches Forschungsinstitut Oberwolfach, 2016-11-10)We show that Killing tensors on conformally at n-dimensional tori whose conformal factor only depends on one variable, are polynomials in the metric and in the Killing vector fields. In other words, every first integral ... -
Late-Time Behaviour of Israel Particles in a FLRW Spacetime with Λ>0
[OWP-2016-19] (Mathematisches Forschungsinstitut Oberwolfach, 2016-10)In this paper we study the relativistic Boltzmann equation in a spatially flat FLRW space-time. We consider Israel particles, which are the relativistic counterpart of the Maxwellian particles, and obtain global-in-time ... -
Legendrian Lens Space Surgeries
[OWP-2016-10] (Mathematisches Forschungsinstitut Oberwolfach, 2016-06-17)We show that every tight contact structure on any of the lens spaces $L(ns^2 - s + 1,s^2)$ with $n\geq 2, s \geq 1$, can be obtained by a single Legendrian surgery along a suitable Legendrian realisation of the negative ... -
Non-Extendability of Holomorphic Functions with Bounded or Continuously Extendable Derivatives
[OWP-2017-30] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-21)We consider the spaces $H_{F}^{\infty}(\Omega)$ and $\mathcal{A}_{F}(\Omega)$ containing all holomorphic functions $f$ on an open set $\Omega \subseteq \mathbb{C}$, such that all derivatives $f^{(l)}$, $l\in F \subseteq ... -
Numerical Invariants and Moduli Spaces for Line Arrangements
[OWP-2017-02] (Mathematisches Forschungsinstitut Oberwolfach, 2017-02-01)Using several numerical invariants, we study a partition of the space of line arrangements in the complex projective plane, given by the intersection lattice types. We offer also a new characterization of the free plane ... -
On Local Combinatorial Formulas for Chern Classes of Triangulated Circle Bundle
[OWP-2016-16] (Mathematisches Forschungsinstitut Oberwolfach, 2016-08-17)Principal circle bundle over a PL polyhedron can be triangulated and thus obtains combinatorics. The triangulation is assembled from triangulated circle bundles over simplices. To every triangulated circle bundle over a ... -
On the L2 Markov Inequality with Laguerre Weight
[OWP-2016-15] (Mathematisches Forschungsinstitut Oberwolfach, 2016-08-17) -
On the Markov inequality in the $L_2$-norm with the Gegenbauer weight
[OWP-2017-05] (Mathematisches Forschungsinstitut Oberwolfach, 2017-02-22)Let $w_{\lambda}(t) := (1-t^2)^{\lambda-1/2}$, where ${\lambda} > -\frac{1}{2}$, be the Gegenbauer weight function, let $\|\cdot\|_{w_{\lambda}}$ be the associated $L_2$-norm, $$ |f\|_{w_{\lambda}} = \left\{\int_{-1}^1 ... -
On Weak Weighted Estimates of Martingale Transform
[OWP-2016-22] (Mathematisches Forschungsinstitut Oberwolfach, 2016-11-12)We consider several weak type estimates for singular operators using the Bellman function approach. We disprove the $A_1$ conjecture, which stayed open after Muckenhoupt-Wheeden's conjecture was disproved by Reguera-Thiele. -
Overlap Synchronisation in Multipartite Random Energy Models
[OWP-2017-13] (Mathematisches Forschungsinstitut Oberwolfach, 2017-04-29)In a multipartite random energy model, made of coupled GREMs, we determine the joint law of the overlaps in terms of the ones of the single GREMs. This provides the simplest example of the so-called synchronisation of the ... -
Regularity and energy conservation for the compressible Euler equations
[OWP-2016-04] (Mathematisches Forschungsinstitut Oberwolfach, 2016-05-10)We give sufficient conditions on the regularity of solutions to the inhomogeneous incompressible Euler and the compressible isentropic Euler systems in order for the energy to be conserved. Our strategy relies on commutator ...