Come join us on **Wednesday, October 31, 2018**** between 4:30 – 5:30pm in Rm 520 and Thursday, November 1, 2018 between 5:30 – 6:30pm in Rm 417**, Professor **Eugenia Malinnikova** (Norwegian University of Science and Technology) will be giving a special lecture titled ** An improvement of Liouville’s theorem for discrete harmonic functions**.

**ABSTRACT**

“The classical Liouville theorem says that if a harmonic function on the plane is bounded then it is a constant. At the same time for any angle on the plane, there exist non-constant harmonic functions that are bounded everywhere outside the angle. The situation is different for discrete harmonic functions on the standard square lattices. The following strong version of the Liouville theorem holds on the two-dimensional lattice. If a discrete harmonic function is bounded on 99% of the lattice then it is constant. Simple counter-example shows that in higher dimensions such improvement is no longer true.

We will present some discrete methods, compare the behavior of continuous and discrete harmonic functions and discuss some related questions and motivation.

The lectures are based on a joint work with L. Buhovsky, A. Logunov and M. Sodin.”

Tea will be served at 4 pm in 508 Mathematics.

*Joseph Fels Ritt Lecture Flyer*

**Time & Location**

**Wednesday, October 31, 2018**** between 4:30 – 5:30 pm in Rm 520**

**&**

**Thursday, November 1, 2018 between 5:30 – 6:30 pm in Rm 417**