For a graph G, we construct two algebras whose dimensions are both equal to the number of spanning trees of G. One of these algebras is the quotient of the polynomial ring modulo certain monomial… (More)

We characterize all linear operators on finite or infinite-dimensional polynomial spaces that preserve the property of having the zero set inside a prescribed region C for arbitrary closed circular… (More)

Let C(X) be the algebra generated by the curvature two-forms of standard holomorphic hermitian line bundles over the complex homogeneous manifold X = G/B. The cohomology ring of X is a quotient of… (More)

We discuss the problem of finding an upper bound for the number of equilibrium points of a potential of several fixed point charges in Rn. This question goes back to J. C. Maxwell and M. Morse. Using… (More)

In this short survey we recall some basic results and relations between the qualitative theory of linear ordinary differential equations with real time and the reality problems in Schubert calculus.… (More)

To any real rational function with generic ramification points we assign a combinatorial object, called a garden, which consists of a weighted labeled directed planar chord diagram and of a set of… (More)

The gravitational-wave signal GW150914 was first identified on September 14, 2015, by searches for short-duration gravitational-wave transients. These searches identify time-correlated transients in… (More)

Preprint This is the submitted version of a paper published in Linear Algebra and its Applications. Around multivariate Schmidt-Spitzer theorem. Access to the published version may require… (More)

In this paper we study the topology of the configuration space of a device with d legs (“centipede”) under some constraints, such as the impossibility to have more than k legs off the ground. We… (More)

Consider a homogenized spectral pencil of exactly solvable linear differential operators Tλ = Pk i=0 Qi(z)λ k−i d i dzi , where each Qi(z) is a polynomial of degree at most i and λ is the spectral… (More)