09:30 to 10:10 M Sodin (Tel Aviv University)New results on Rademacher Fourier and Taylor series This is a report on a joint work in progress with Fedor Nazarov and Alon Nishry. We prove that any power of the logarithm of Rademacher Fourier series (i.e. a square summable Fourier series with random independent signs) is integrable. This result has several applications to zeroes and value-distribution of random Talor series. One of this applications gives asymptotics for the counting function of zeroes of arbitrary Taylor series with random independent signs, and proves their angular equidistribution. Another application answers an old question by J.-P.Kahane. INI 1 10:10 to 10:50 P Le Doussal (École Normale Supérieure)Universal statistics for directed polymers and the KPZ equation from the replica Bethe Ansatz INI 1 10:50 to 11:10 Morning Coffee 11:10 to 11:50 T Shcherbina (Institute for Advanced Study, Princeton)Universality of the second mixed moment of the characteristic polynomials of the 1D Gaussian band matrices We consider the asymptotic behavior of the second mixed moment of the characteristic polynomials of the 1D Gaussian band matrices, i.e. of the hermitian matrices $H_n$ with independent Gaussian entries such that $\langle H_{ij}H_{lk}\rangle=\delta_{ik}\delta_{jl}J_{ij}$, where $J=(-W^2\triangle+1)^{-1}$. Assuming that $W^2=n^{1+\theta}$, \$0 INI 1 11:50 to 12:30 P Ostrovsky (Max Planck Institut für Festkörperforschung)Anderson localization, topology, and interaction Field-theoretical approach to Anderson localization in 2D disordered fermionic systems of chiral symmetry classes (BDI, AIII, CII) is developed. Important representatives of these symmetry classes are random hopping models on bipartite lattices at the band center. As was found by Gade and Wegner two decades ago within the sigma-model formalism, quantum interference effects in these classes are absent to all orders of perturbation theory. We demonstrate that the quantum localization effects emerge when the theory is treated nonperturbatively. Specifically, they are controlled by topological vortexlike excitations of the sigma models by a mechanism similar to the Berezinskii-Kosterlitz-Thouless transition. We derive renormalization-group equations including these nonperturbative contributions. Analyzing them, we find that the 2D disordered systems of chiral classes undergo a metal-insulator transition driven by topologically induced Anderson localization. We also show that the topological terms on surfaces of 3D topological insulators of chiral symmetry (in classes AIII and CII) overpower the vortex-induced localization. Similar vortex excitations also emerge in systems with strong spin-orbit interaction (symplectic symmetry class AII). Such systems may exhibit topological insulator state both in three and two dimensions. Interplay of nontrivial topology and Coulomb repulsion induces a novel critical state on the surface of a 3D topological insulator. Remarkably, this interaction-induced criticality, characterized by a universal value of conductivity, emerges without any adjustable parameters. Interaction also leads to a direct transition between trivial insulator and topological insulator in 2D (quantum-spin-Hall transition) via a similar critical state. The nature of this latter critical state is closely related to the effects of vortices within the Finkelstein sigma model. INI 1 12:30 to 13:30 Lunch at Wolfson Court 13:30 to 17:30 Discussion Time INI 1 18:45 to 19:30 Dinner at Wolfson Court