This paper is a brief account of the moduli of complex curves from the perspective of noncommutative geometry. We focus on problems of Riemann surface theory, which can be settled using K-groups of a noncommutative C∗-algebra. On this way, we prove “generic” arithmeticity of the mapping class group and study correspondences between complex and noncommutative tori.

We develop an information-theoretic perspective on some questions in convex geometry, providing for instance a new equipartition property for log-concave probability measures, some Gaussian comparison results for log-concave measures, an entropic formulation of the hyperplane conjecture, and a new reverse entropy power inequality for log-concave measures analogous to V. Milman’s reverse Brunn-M...

We propose a notion of competitive equilibrium in an abstract setting called a Convex Economy using a concept of convexity borrowed from Convex Geometry. The "magic” of linear equilibrium prices is put into perspective in this abstract setting. The abstract notion of competitive equilibrium is applied to a variety of convex economies and versions of the first and second fundamental welfare theo...

The General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) provides structure of mesoscopic multiscale dynamics that guarantees emergence equilibrium states. Similarly, a lift the GENERIC to iterated cotangent bundles, called rate GENERIC, vector fields generate approach equilibrium. Moreover, also extends Onsager's variational principle. MaxEnt (Maximum Entropy) princi...

In the robotics, omnidirectional vision is favored because it increases the field of sensor's view allowing for better navigation and localization of robots. The Catadioptric sensors (combination of mirror (s) + camera (s)) are a quick and easy solution to reach a large view satisfactory. However, because of the geometry of the mirrors used, these sensors provide images with a nonuniform resolu...