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Random Functions, Random Surfaces and Interfaces

(Web site soon online)

January 4 - 9, 2009
Organizers: R. Bond (Toronto), M. Douglas (Rutgers), S. Shlosman (CNRS), S. Sheffield (New York), S. Zelditch (Johns Hopkins)

This workshop is devoted to random fields such as Gaussian random fields f ~ ∑1≤i≤∞ ai(w) ji(x) where {ji} is an orthonormal basis for a Hilbert space H and where the coefficients ai(w) are independent (real or complex) Gaussian random variables of mean zero and variance one. Motivated by such physical models as (i) the large scale matter distribution in the universe or (ii) landscape statistics in string theory or (iii) the random wave model in quantum chaos or (iv) limit shapes of phase interfaces in statistical mechanics, the workshop will largely focus on the zeros or critical points of random fields.

Specific topics include: the Nazarov-Sodin theorem that the average number of nodal domains of random spherical harmonics of degree N has an asymptotic formula of a kind predicted by Bogomolny-Schmidt, Smilanksy and others; the Sheffield-Schramm results on the zero sets of the two-dimensional Gaussian free field and their relation to SLE6 curves; work of Douglas and collaborators Ashkok, Denef, Shiffman, Zelditch and others on the applications  of random complex geometry to counting vacua in string-M models; results of Shlosman, Schonmann and others on properties of  phase interfaces such as flatness of crystal facets.