Distributing points on spheres and other manifolds


During the week of 27 February–3 March we will have Juan González Criado del Rey from the University of Cantabria visiting RMIT. Juan will give a talk on Monday 27 February on Distributing points on spheres and other manifolds and another talk on 1 March on Condition metrics and curvature.

Speaker: Mr Juan González Criado del Rey
University of Cantabria, Santander (Spain)

Title: Distributing points on spheres and other manifolds

Date and time: Monday, 27 February 2017, 11:00am-12:00pm
Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus

Abstract: Distributing points on spheres or other sets is a very classical problem. Its modern formulation in terms of energy-minimising configurations is due to the discoverer of the electron J. J. Thomson who in 1904 posed the question in which position—within some set such as a ball or a sphere—would N electrons lie in order to minimise their electrostatic potential? There are many different approaches to the definition of what a sensibly distributed collection of spherical points is. Apart from the aforementioned minimization of energy, other definitions include minimising the separation distance, having a small discrepancy, providing exact integral formulas for low degree polynomials, etc. In this talk we will review some of these problems and address the problem of defining minimal-energy points in an arbitrary compact manifold from an intrinsic viewpoint.

Bio: Juan G. Criado del Rey is a PhD student at the University of Cantabria, Spain. He has been working on some geometric aspects of problems in Numerical Analysis such as S. Smale's problems 7 (elliptic Fekete points) and 17 (solving systems of polynomial equations). His main interests are Differential Geometry and Analysis, and their interplay with Computational Mathematics. Juan received his degree in Mathematics from the Complutense University of Madrid and his master's degree from the University of Cantabria. He currently lives in Santander, Spain.

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