Department of Mathematics at Columbia University - From the Desk Of: Mohammed Abouzaid

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

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Sep. 26: Ailana Fraser (UBC)

Added on September 17, 2018 by Mohammed Abouzaid

Title: The geometry of extremal eigenvalue problems
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Sep. 12: Bernard Julia (ENS, Paris)

Added on September 07, 2018 by Mohammed Abouzaid