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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| ...
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 ...
Hölder Continuity of the Spectra for Aperiodic Hamiltonians
[OWP-2019-05] (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-26)
We study the spectral location of a strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are "close to each other" if, up to a translation, ...
Minimal Codimension One Foliation of a Symmetric Space by Damek-Ricci Spaces
[OWP-2019-11] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-07)
In this article we consider solvable hypersurfaces of the form $N \exp(\mathbb{R} H)$ with induced metrics in the symmetric space $M = SL(3,\mathbb{C})/SU(3)$, where $H$ a suitable unit length vector in the subgroup $A$ ...
A Function Algebra Providing New Mergelyan Type Theorems in Several Complex Variables
[OWP-2019-02] (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-11)
For compact sets $K\subset \mathbb C^{d}$, we introduce a subalgebra $A_{D}(K)$ of $A(K)$, which allows us to obtain Mergelyan type theorems for products of planar compact sets as well as for graphs of functions.
The Becker-Gottlieb Transfer: a Geometric Description
[OWP-2019-13] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-14)
In this note, we examine geometric aspects of the Becker-Gottlieb transfer in terms of the Umkehr and index maps, and rework some classic index theorems, using the cohomological formulae of the Becker-Gottlieb transfer. ...
On a Cheeger Type Inequality in Cayley Graphs of Finite Groups
[OWP-2019-20] (Mathematisches Forschungsinstitut Oberwolfach, 2019-07-22) - (7 July - 7 October 2017)
Let $G$ be a finite group. It was remarked by Breuillard-Green-Guralnick-Tao that if the Cayley graph $C(G,S)$ is an expander graph and is non-bipartite then the spectrum of the adjacency operator $T$ is bounded away from ...
Weighted Surface Algebras: General Version
[OWP-2019-07] (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-28)
We introduce general weighted surface algebras of triangulated surfaces with arbitrarily oriented triangles and describe their basic properties. In particular, we prove that all these algebras, except the singular disc, ...
Applications of BV Type Spaces
[OWP-2019-04] (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-13)
Experimenting with Symplectic Hypergeometric Monodromy Groups
[OWP-2019-15] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-22)
We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results ...