Abstract

The speaker recently designed a new variant of Newton's method, named Backtracking New Q-Newton's method (BNQN). This method has strong global convergence guarantees, in particularly in finding roots of meromorphic functions in 1 complex variable, and has strong connections to topics as Newton's flow, Voronoi's diagrams, Poincare-Bendixon theorem. This talk presents a new equivalence to the Riemann hypothesis via the dynamics of BNQN, and experiments exploring using the method to find roots of the Riemann xi function. The insights from the experiments suggests a new approach towards the Riemann hypothesis. The method BNQN can in general be applicable to higher dimensions and to optimization. This includes joint work with John Erik Fornæss, Mi Hu, Thuan Quang Tran and Takayuki Watanabe.

 

Organizer: Chun-Yen Shen (NTU)