The one-component Coulomb gas on the sphere, consisting on $ N $ unit charges
interacting via a logarithmic potential, and in the presence of two external charges each of …

We make a systematic investigation of quadrature properties for quadrics, namely
integration of holomorphic functions over planar domains bounded by second degree …

We study the equilibrium measure on the two-dimensional sphere in the presence of an
external field generated by r+ 1 equal point charges that are symmetrically located around …

A physicist, a mathematician and a computer engineer look at a simple drawing. The
physicist immediately sees it as the shape of a melting material, with fjords in formation, with …

Hyperbolic homogeneous polynomials with real coefficients, ie, hyperbolic real projective
hypersurfaces, and their determinantal representations, play a key role in the emerging field …

Given a finite family of compact subsets of the complex plane we propose a certificate of
mutual non-overlapping with respect to area measure. The criterion is stated as a couple of …

With the sphere S^ 2 ⊂ R^ 3 S 2⊂ R 3 as a conductor holding a unit charge with logarithmic
interactions, we consider the problem of determining the support of the equilibrium measure …

This book grew out of investigations on the Polubarinova-Galin equation, describing the
conformal map onto a growing Hele-Shaw fluid blob, by one of the authors (Lin); see [69 …

Classically, the Bezout matrix or simply Bezoutian of two polynomials is used to locate the
roots of the polynomial and, in particular, test for stability. In this paper, we develop the …

For conformal maps defined in the unit disk one can define a certain Poisson bracket that
involves the harmonic moments of the image domain. When this bracket is applied to the …