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Homology and $K$-Theory of Torsion-Free Ample Groupoids and Smale Spaces
[OWP-2020-20] (Mathematisches Forschungsinstitut Oberwolfach, 2020-10-09)
Given an ample groupoid, we construct a spectral sequence with groupoid homology with integer coefficients on the second sheet, converging to the $K$-groups of the groupoid C*-algebra when the groupoid has torsion-free ...
l-Torsion Bounds for the Class Group of Number Fields with an l -Group as Galois Group
[OWP-2020-11] (Mathematisches Forschungsinstitut Oberwolfach, 2020-05-04)
We describe the relations among the $\ell$-torsion conjecture for $\ell$-extensions, the discriminant multiplicity conjecture for nilpotent extensions and a conjecture of Malle giving an upper bound for the number of ...
Space-Time Euler Discretization Schemes for the Stochastic 2D Navier-Stokes Equations
[OWP-2020-12] (Mathematisches Forschungsinstitut Oberwolfach, 2020-05-06)
We prove that the implicit time Euler scheme coupled with finite elements space discretization for the 2D Navier-Stokes equations on the torus subject to a random perturbation converges in $L^2(\Omega)$, and describe the ...
Generating Finite Coxeter Groups with Elements of the Same Order
[OWP-2020-07] (Mathematisches Forschungsinstitut Oberwolfach, 2020-03-16)
Supposing $G$ is a group and $k$ a natural number, $d_k(G)$ is defined to be the minimal number of elements of $G$ of order $k$ which generate $G$ (setting $d_k(G) = 0$ if $G$ has no such generating sets). This paper ...
Multivariate Hybrid Orthogonal Functions
[OWP-2020-04] (Mathematisches Forschungsinstitut Oberwolfach, 2020-03-12)
We consider multivariate orthogonal functions satisfying hybrid orthogonality conditions
with respect to a moment functional. This kind of orthogonality means that the product of
functions of different parity order ...
On Weakly Complete Universal Enveloping Algebras of pro-Lie Algebras
[OWP-2020-10] (Mathematisches Forschungsinstitut Oberwolfach, 2020-04-27)
Hopf Algebras in Combinatorics, Volume 1
[OWP-2020-14] (Mathematisches Forschungsinstitut Oberwolfach, 2020-07-29)
Nondegenerate Invariant Symmetric Bilinear Forms on Simple Lie Superalgebras in Characteristic 2
[OWP-2020-02] (Mathematisches Forschungsinstitut Oberwolfach, 2020-02-04)
As is well-known, the dimension of the space of non-degenerate invariant symmetric bilinear forms (NISes) on any simple finite-dimensional Lie algebra or Lie superalgebra is equal to at most 1 if the characteristic of the ...
The Pelletier-Ressayre Hidden Symmetry for Littlewood-Richardson Coefficients
[OWP-2020-18] (Mathematisches Forschungsinstitut Oberwolfach, 2020-09-08)
We prove an identity for Littlewood–Richardson coefficients conjectured by Pelletier and Ressayre. The proof relies on a novel birational involution defined over any semifield.
Nonexistence of Subcritical Solitary Waves
[OWP-2020-06] (Mathematisches Forschungsinstitut Oberwolfach, 2020-03-15)
We prove the nonexistence of two-dimensional solitary gravity water waves with subcritical wave speeds and an arbitrary distribution of vorticity. This is a longstanding open problem, and even in the irrotational case there ...