Modern Mathematics Lecture Series | Percolation Theory: Some Open Problems

Speaker 

Charles M. Newman

Silver Professor of Mathematics,

New York University

Born in Chicago in 1946, Professor Charles M. Newman received two B.S. (1966) degrees (Mathematics and Physics) from MIT, and M.A. (1966) and Ph.D. (1971) degrees in Physics from Princeton. His specialties are probability theory and statistical physics, with over 200 published papers in those and related areas. Beginning his academic career at NYU's University Heights campus in 1971, he went on to the mathematics departments of Indiana University and the University of Arizona, and returned to NYU as Prof. of Math. in 1989.

At the Courant Institute of Math. Sciences, Newman has been Director (2002-06), Silver Prof. (2011-), Global Network Prof. (2016-) and Emeritus (2022-). At NYU-Shanghai, he has been Affiliated Prof. (2013-) and Director of the Inst. of Math. Sciences (2016-19).

Newman has been a Sloan Fellow (1978-81) and a Guggenheim Fellow (1984-85), was elected to membership in the U.S. National Academy of Sciences in 2004, the American Academy of Arts and Sciences in 2006 and the Brazilian Academy of Sciences in 2008. He has been married to Arlene Newman since 1970 and they have two daughters, Jennifer and Serena.

Abstract

We introduce two simple percolation models--Invasion Percolation and Bernoulli Percolation. Then we discuss a easily stated open problem common to both of them, which sounds like it should be straightforward to solve (and maybe it will turn out so). We then go on to present some open problems that occur when one has two copies of percolation and why they are of interest. This is because of their relation to spin glasses (such as occur in the work of Physics Nobelist Giorgio Parisi).