Tropical varieties play an important role in algebraic geometry. The Bergman complex B(M) and the positive Bergman complex B+(M) of an oriented matroid M generalize to matroids the notions of the tropical variety and positive tropical variety associated to a linear ideal. Our main result is that if A is a Coxeter arrangement of type Φ with corresponding oriented matroid MΦ, then B (MΦ) is dual ...

We study the condition that characterizes the symbols of bounded Hankel operators on the Bergman space of a strongly pseudoconvex domain and show that it is equivalent to BMO plus analytic. (Here we mean the Bergman metric BMO of Berger, Coburn and Zhu.) In the course of the proof we obtain new d -estimates that may be of independent interest. Some applications include a decomposition of BMO si...

For α > −1, let Aα denote the corresponding weighted Bergman space of the unit ball. For any self-adjoint subset G ⊂ L∞, let T(G) denote the C∗−subalgebra of B(Aα) generated by {Tf : f ∈ G}. Let CT(G) denote the commutator ideal of T(G). It was showed by D. Suárez (in 2004 for n = 1) and by the author (in 2006 for all n ≥ 1) that CT(L∞) = T(L∞) in the case α = 0. In this paper we show that in t...

The recent theorem by D.Luecking about finite rank Bergman-Toeplitz operators is extended to weights being distributions with compact support and to the spaces of harmonic functions.

The boundedness of the difference of two weighted composition operators from weighted Bergman spaces to weighted-type spaces in the unit ball are investigated in this paper.

Tetradentate metalloenediynes with strong imine and weaker thioether coordination serve as a geometrically non-rigid switch to drive thermal Bergman cyclization.

We exhibit a class of bounded, strongly convex Hartogs domains with realanalytic boundary which are not Lu Qi-Keng, i.e. whose Bergman kernel function has a zero.