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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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.

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 ...