Browsing 1 - Oberwolfach Preprints (OWP) by Title
Now showing items 130-149 of 408
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Geometric quantization of integrable systems with hyperbolic singularities
[OWP-2009-01] (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. ... -
Geometry of Free Loci and Factorization of Noncommutative Polynomials
[OWP-2017-23] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-02)The free singularity locus of a noncommutative polynomial f is defined to be the sequence $Z_n(f)=\{X\in M_n^g : \det f(X)=0\}$ of hypersurfaces. The main theorem of this article shows that f is irreducible if and only if ... -
Getzler rescaling via adiabatic deformation and a renormalized local index formula
[OWP-2016-18] (Mathematisches Forschungsinstitut Oberwolfach, 2016-10)We prove a local index theorem of Atiyah-Singer type for Dirac operators on manifolds with a Lie structure at infinity (Lie manifolds for short). After introducing a renormalized supertrace on Lie manifolds with spin ... -
Ghost Algebras of Double Burnside Algebras via Schur Functors
[OWP-2012-09] (Mathematisches Forschungsinstitut Oberwolfach, 2012-07-03)For a finite group $G$, we introduce a multiplication on the $\mathbb{Q}$-vector space with basis $\mathscr{S}_{G\times G}$, the set of subgroups of ${G \times G}$. The resulting $\mathbb{Q}$-algebra $\tilde{A}$ can be ... -
Gibbs measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation
[OWP-2015-04] (Mathematisches Forschungsinstitut Oberwolfach, 2015-05-18)We study the one dimensional periodic derivative nonlinear Schrödinger (DNLS) equation. This is known to be a completely integrable system, in the sense that there is an infinite sequence of formal integrals of motion $\int ... -
Global Solutions to Stochastic Wave Equations with Superlinear Coefficients
[OWP-2019-26] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-13)We prove existence and uniqueness of a random field solution $(u(t,x);(t,x)\in [0,T]\times \mathbb{R}^d)$ to a stochastic wave equation in dimensions $d=1,2,3$ with diffusion and drift coefficients of the form $|x| ... -
Global Variants of Hartogs' Theorem
[OWP-2018-24] (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-06)Hartogs' theorem asserts that a separately holomorphic function, defined on an open subset of $\mathbb{C}^n$, is holomorphic in all the variables. We prove a global variant of this theorem for functions defined on an open ... -
Gradient Canyons, Concentration of Curvature, and Lipschitz Invariants
[OWP-2017-35] (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-13)We find new bi-Lipschitz invariants of holomorphic functions of two variables by using the gradient canyons and by combining analytic and geometric viewpoints on the concentration of curvature. -
Graphical constructions for the sl(3), C2 and G2 invariants for virtual knots, virtual braids and free knots
[OWP-2015-13] (Mathematisches Forschungsinstitut Oberwolfach, 2015-07-31)We construct graph-valued analogues of the Kuperberg sl(3) and $G_2$ invariants for virtual knots. The restriction of the sl(3) and $G_2$ invariants for classical knots coincides with the usual Homflypt sl(3) invariant and ... -
A graphical interface for the Gromov-Witten theory of curves
[OWP-2016-06] (Mathematisches Forschungsinstitut Oberwolfach, 2016-05-10)We explore the explicit relationship between the descendant Gromov–Witten theory of target curves, operators on Fock spaces, and tropical curve counting. We prove a classical/tropical correspondence theorem for descendant ... -
Grassmannian connection between three- and four-qubit observables, Mermin's contextualities and black holes
[OWP-2013-17] (Mathematisches Forschungsinstitut Oberwolfach, 2013-07-23)We invoke some ideas from finite geometry to map bijectively 135 heptads of mutually commuting three-qubit observables into 135 symmetric four-qubit ones. After labeling the elements of the former set in terms of a ... -
Ground State of Bose Gases Interacting through Singular Potentials
[OWP-2023-18] (Mathematisches Forschungsinstitut Oberwolfach, 2023-11-27)We consider a system of $N$ bosons on the three-dimensional unit torus. The particles interact through repulsive pair interactions of the form $N^{3β-1} v (N^βx)$ for $β\in (0,1)$. We prove the next order correction to ... -
Group Algebras of Compact Groups. A New Way of Producing Group Hopf Algebras over Real and Complex Fields: Weakly Complete Topological Vector Spaces
[OWP-2019-06] (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-27)Weakly complete real or complex associative algebras $A$ are necessarily projective limits of finite dimensional algebras. Their group of units $A^{-1}$ is a pro-Lie group with the associated topological Lie algebra $A_{\rm ... -
Group-Graded Rings Satisfying the Strong Rank Condition
[OWP-2019-22] (Mathematisches Forschungsinstitut Oberwolfach, 2019-08-16)A ring $R$ satisfies the $\textit{strong rank condition}$ (SRC) if, for every natural number $n$, the free $R$-submodules of $R^n$ all have rank $\leq n$. Let $G$ be a group and $R$ a ring strongly graded by $G$ such that ... -
Groups with Spanier-Whitehead Duality
[OWP-2019-23] (Mathematisches Forschungsinstitut Oberwolfach, 2019-09-17)We introduce the notion of Spanier-Whitehead $K$-duality for a discrete group $G$, defined as duality in the KK-category between two $C*$-algebras which are naturally attached to the group, namely the reduced group ... -
Hecke duality relations of Jacobi forms
[OWP-2008-03] (Mathematisches Forschungsinstitut Oberwolfach, 2008-03-07)In this paper we introduce a new subspace of Jacobi forms of higher degree via certain relations among Fourier coefficients. We prove that this space can also be characterized by duality properties of certain distinguished ... -
Heisenberg-Weyl algebra revisited: combinatorics of words and paths
[OWP-2009-02] (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 ... -
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 ... -
Higher Finiteness Properties of Reductive Arithmetic Groups in Positive Characteristic: the Rank Theorem
[OWP-2011-05] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-8)We show that the finiteness length of an $S$-arithmetic subgroup $\Gamma$ in a noncommutative isotropic absolutely almost simple group $\mathcal{G}$ over a global function field is one less than the sum of the local ranks ... -
Hight functions on quaternionic Stiefel manifolds
[OWP-2015-10] (Mathematisches Forschungsinstitut Oberwolfach, 2015-07-29)In this note, we study height functions on quaternionic Stiefel manifolds and prove that all these height functions are Morse-Bott. Among them, we characterize the Morse functions and give a lower bound for their number ...