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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

We investigate the correspondence between holomorphic automorphic forms on the upper half-plane with complex weight and parabolic cocycles. For integral weights at least 2 this correspondence is given by the Eichler integral. ...

We consider a domain $\Omega_\varepsilon\subset\mathbb{R}^N$, $N\geq2$, with a very rough boundary depending on~$\varepsilon$. For instance, if $N=3$ the domain $\Omega_\varepsilon$ has the form of a brush with an ...

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 ...