Colloquium: Alexander Logunov (Tel Aviv), "0,01% Improvement of the Liouville property for discrete harmonic functions on Z^2"

Thu, 15/06/201714:30-15:30
Manchester Building (Hall 2), Hebrew University Jerusalem
Let u be a harmonic function on the plane.
The Liouville theorem claims that if |u| is bounded on the whole plane, then u is identically constant.
It appears that if u is a harmonic function on a lattice Z^2, and |u| < 1 on 99,99% of Z^2,
then u is a constant function.
Based on a joint work(in progress) with L.Buhovsky, Eu.Malinnikova and M.Sodin.