WEEKLY SEMINAR

ABSTRACT OF THE TALK
In this talk we review a number of old results concerning certain statistical mechanics models and their possible connections to the Riemann Hypothesis. A standard reformulation of the Riemann Hypothesis (RH) is: The (two-sided) Laplace transform of a certain specific function on the real line is automatically an entire function on the complex plane; the RH is equivalent to this transform having only pure imaginary zeros. Also is a positive integrable function, so (modulo a multiplicative constant ) is a probability density function. A (finite) Ising model is a specific type of probability measure on the points with each . The Lee-Yang theorem implies that that for non-negative , the Laplace transform of the induced probability distribution of has only pure imaginary zeros. The big question here is whether it's possible to find a sequence of Ising models so that the limit as tends to of such distributions has density exactly . We'll discuss some hints as to how one might try to do this.
BIOGRAPHY
Chuck Newman is a mathematician at the Courant Institute of Mathematical Sciences of New York University. He works in the fields of mathematical physics, statistical mechanics, and probability theory. He is a member of the National Academy of Sciences since 2004, and of the American Academy of Arts and Sciences since 2006. In 2012 he became a fellow of the American Mathematical Society. Newman graduated from MIT in 1966 with degrees in both mathematics and physics. He completed his PhD at Princeton University in 1971 with advisor Arthur Wightman.