CRM CAMP in Nonlinear Analysis

Computer-Assisted Mathematical Proofs in Nonlinear Analysis

April 27, 2021 from 10:00 to 11:00 (Montreal/EST time) Zoom meeting

A computer assisted counterexample to Payne’s nodal line conjecture with few holes

Seminar presented by Joel Dahne (Uppsala University, Sweden)

Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the boundary of the domain. In their 1997 breakthrough paper, Hoffmann-Ostenhof, Hoffmann-Ostenhof and Nadirashvili proved this to be false by constructing a counterexample in the plane with an unspecified, but large, number of holes and raised the question of the minimum number of holes a counterexample can have. In this talk I will present a computer assisted counter example with 6 holes. This is joint work with Javier Gómez-Serrano and Kimberly Hou.