# Colloquium

November 30, 2007 from 16:00 to 18:00 (Montreal/EST time) On location

### Exact Solution of the Six-Vertex Model of Statistical Physics

We prove the conjecture of Zinn-Justin that the partition function of the six-vertex model on the $N\times N$ lattice with domain wall boundary conditions has the asymptotics, $Z_N\sim  CN^\kappa e^{N^2}f$ as $N\to \infty$, and we find the exact value of the exponent $\kappa$. The solution is based on the Riemann-Hilbert approach and the Deift-Zhou nonlinear steepest descent method.