Unfolding conformal geometry

Conformal Geometry

Arrows in this diagram indicate input from one topic to another. Closely related topics are joined by lines. Conformal geometry is highly analogous to CR geometry, so their boxes are close together and arrows run in both directions. The left hand side of the diagram is largely algebraic. At the top of the diagram, Q-curvature and ambient metrics are specific aspects of conformal geometry, which...

Conformal Random Geometry

The Conformal Geometry of Billiards

This article provides an introduction to some recent results in billiard dynamics. We present results that follow from a study of compact Riemann surfaces (equipped with a holomorphic 1-form) and an SL2R action on the moduli spaces of these surfaces. We concentrate on the progress toward classification of “optimal” billiard tables, those with the simplest trajectory structure.

Fractional Laplacian in conformal geometry

In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli and Silvestre and a class of conformally covariant operators in conformal geometry. © 2010 Elsevier Inc. All rights reserved.

Qubit Geometry and Conformal Mapping

In the past ten years, there has been a growing interest in the theory of quantum computation and quantum information.ð1Þ Due to the quantum parallelism, quantum computers have the potential to outperform the classical computers. The quantum computers are based on two-level quantum systems, which are called qubits.ð2Þ In this paper, we will investigate a representation of a single qubit operati...