Blocking light in compact Riemannian manifolds

We study compact Riemannian manifolds for which the light between any pair of points is blocked by finitely many point shades. Compact flat Riemannian manifolds are known to have this finite blocking property. We conjecture that amongst compact Riemannian manifolds this finite blocking property characterizes the flat metrics. Using entropy considerations, we verify this conjecture amongst metrics with nonpositive sectional curvatures. Using the same approach, K. Burns and E. Gutkin have independently obtained this result. Additionally, we show that compact quotients of Euclidean buildings have the finite blocking property. On the positive curvature side, we conjecture that compact Riemannian manifolds with the same blocking properties as compact rank one symmetric spaces are necessarily isometric to a compact rank one symmetric space. We include some results providing evidence for this conjecture.Comment: 19 page

Quantifying the Artistic Experience with Perceptive Sketching Tools: Cognitive Technologies to Support Creativity Researchers

Creativity research has gradually moved away from controlled laboratory settings to more naturalistic and real world domains. As a result, new research methods are required to systematically analyze the artistic experience that includes the artist’s perception, behavior, and conception throughout the creative process. We use research findings from the Cognitive Science literature to create a framework called Perceptual Logic to categorize different types of artistic experience. This framework is applicable to open-ended artistic creativity. Empiri- cally validating such a framework requires new tools that provide insight into the naturalistic creative process. We describe the initial design of a set of digital sketching tools that enables creativity researchers to quantitatively analyze the artistic experience. These tools focus spe- cifically on understanding how visual digital artists perceive and interact with their drawings and paintings throughout their creative process