國立清華大學 數學系

In his book of `A Treatise on Electricity and Magnetism', J.C. Maxwell made a claim on the number of non-degenerate equilibrium points of the electrostatic field created by stationary point charges. Later, J.J. Thomson in 1891 while proof-reading the third edition of Maxwell’s book commented on this claim as `I have not been able to find any place where this result is proved.' In 2007, a paper by A. Gabrielov, D. Novikov and B. Shapiro revisited this problem and call his unproved claim the Maxwell’s conjecture. In this talk, I will introduce this conjecture, present current progress, and talk about some tools from real and computational algebraic geometry in dealing with this conjecture.