We propose an algebraic combinatorial framework for the problem of completing partially observed low-rank matrices. We show that the intrinsic properties of the problem, including which entries can be reconstructed, and ...

The Lichnerowicz conjecture asserts that all harmonic manifolds are either flat or locally symmetric spaces of rank 1. This conjecture has been proved by Z.I. Szab ́o [Sz] for harmonic manifolds with compact universal ...

Using Szenes formula for multiple Bernoulli series, we explain how to compute Witten series associated to classical Lie algebras. Particular instances of these series compute volumes of moduli spaces of flat bundles over ...

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 ...

Let $G(q)$ be a finite Chevalley group, where $q$ is a power of a good prime $p$, and let $U(q)$ be a Sylow $p$-subgroup of $G(q)$. Then a generalized version of a conjecture of Higman asserts that the number $k(U(q))$ of ...

We classify Legendrian rational unknots with tight complements in the lens spaces $L(p,1)$ up to coarse equivalence. As an example of the general case, this classification is also worked out for $L(5, 2)$. The knots are ...

We explore consequences of the triviality of the monodromy group, using the condition of purity of the mixed Hodge structure on the cohomology of the surface X.

In this paper we present an algorithm for determining whether a subgroup $H$ of a non-connected reductive group $G$ is $G$-completely reducible. The algorithm consists of a series of reductions; at each step, we perform ...