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.
Speaker: Mr Juan González Criado del Rey (University of Cantabria, Santander, Spain)
Event website: www.rmitopt.org
About the speaker:
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.
How to participate in this seminar:
1. Book your nearest ACE facility;
2. Notify Vera Roshchina at RMIT (rmitopt@rmit.edu.au) to notify you will be participating.
No access to an ACE facility? Contact Maaike Wienk to arrange a temporary Visimeet licence for remote access (limited number of licences available – first come first serve)