Thomson's 5 Point Problem and Power-Law Potentials - Rothschild Lecture

Explore Thomson's 5 point problem in this Rothschild Lecture delivered by Professor Richard Evan Schwartz from Brown University. Delve into the fascinating world of electrostatic potential minimization as points arrange themselves on spheres or other spaces. Discover the historical context of this problem, dating back to J.J. Thomson's 1904 paper, and learn about its applications in mathematics and physics. Examine special cases where potential minimizers form highly symmetric objects like the regular icosahedron or the E8 cell. Focus on the intriguing case of 5 points on a 2-sphere, where little has been proven until now. Witness Professor Schwartz's computer-assisted yet rigorous proof of a phase transition constant S=15.048..., which determines when the triangular bi-pyramid is the minimizer for power-law potentials. Engage with colorful computer demos that illustrate these complex mathematical concepts and gain insights into a problem that has puzzled researchers since 1977.