Random Functions, Random Surfaces and Interfaces


January 4 - 9, 2009


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.

The meeting will take place at Hotel Mont-Gabriel, Sainte-Adèle, Québec, Canada (Laurentian region, north of Montréal), from January 4 (arrival day) to January 9, 2009 in the afternoon (departure day).

A shuttle will travel from Montreal to the hotel on Sunday, January 4 and back to Montreal on Friday, January 9, 2009.

The shuttle is scheduled to leave the campus of the UniversitÈ de Montréal (Pavillon André-Aisenstadt, see Campus map) on Sunday, January 4 at 5:30 pm. On January 9, the shuttle will leave Sainte-Adele at 2:30 pm, will first stop at the Montréal-Trudeau airport and then go to the campus.

Scientific Organizers