19 citations · 98 across the 26 of their papers we have counts for
28 papers
Minimal 3-regular Penny Graph
Alexander Karabegov, Tanya Khovanova
We prove that a 3-regular penny graph has at least 16 vertices and show that such a graph with 16 vertices exists.
Lagrangian fields, Calabi functions, and local symplectic groupoids
Alexander Karabegov
A Lagrangian field on a symplectic manifold is a family of pointed Lagrangian submanifolds of . This notion is a generalization of a real Lagrangian pola…
Formal oscillatory distributions
Alexander Karabegov
We introduce the notion of an oscillatory formal distribution supported at a point. We prove that a formal distribution is given by a formal oscillatory integral if and only if it…
An algebra of distributions related to a star product with separation of variables
Alexander Karabegov
Given a star product with separation of variables on a pseudo-Kähler manifold and a point , we construct an associative algebra of formal distributions suppo…
Formal oscillatory integrals and deformation quantization
Alexander Karabegov
Following [14] and [12], we formalize the notion of an oscillatory integral interpreted as a functional on the amplitudes supported near a fixed critical point of the phase f…
A heat kernel proof of the index theorem for deformation quantization
Alexander Karabegov
We give a heat kernel proof of the algebraic index theorem for deformation quantization with separation of variables on a pseudo-Kahler manifold. We use normalizations of the canon…