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