09:00 to 10:00 Hendrik Weber (University of Bath)Space-time localisation for the dynamic $\Phi^4_3$ model We prove an a priori bound for solutions of the dynamic $\Phi^4_3$ equation. This bound provides a control on solutions on a compact space-time set only in terms of the realisation of the noise on an enlargement of this set, and it does not depend on any choice of space-time boundary conditions.   We treat the  large and small scale behaviour of solutions with completely different arguments. For small scales we use bounds akin to those presented in Hairer's theory of regularity structures. For large scales we use a PDE argument based on the maximum principle. Both regimes are connected by a solution-dependent regularisation procedure.   The fact that our bounds do not depend on space-time boundary conditions makes them useful for the analysis of large scale properties of solutions. They can for example be used  in a compactness argument to construct solutions on the full space and their invariant measures.   Joint work with A. Moinat. INI 1 10:00 to 11:00 Cedric Bernardin (Université de Nice Sophia Antipolis); (NICE)Hydrodynamic limit for a disordered harmonic chain We consider a one-dimensional unpinned chain of harmonic oscillators with random masses. We prove that after hyperbolic scaling of space and time the distributions of the elongation, momentum and energy converge to the solution of the Euler equations. Anderson localization decouples the mechanical modes from the thermal modes, allowing the closure of the energy conservation equation even out of thermal equilibrium. This example shows that the derivation of Euler equations rests primarily on scales separation and not on ergodicity. Joint with F. Huveneers and S. Olla INI 1 11:00 to 11:30 Morning Coffee 11:30 to 12:30 Weijun Xu (University of Warwick)On mass-critical stochastic nonlinear Schrodinger equation We report some recent joint works with Chenjie Fan on construction of global solutions to defocusing mass-critical stochastic nonlinear Schrodinger equation. INI 1 12:30 to 13:30 Lunch buffet at the INI 13:30 to 14:30 Franco Flandoli (Scuola Normale Superiore di Pisa)Remarks on 2D inverse cascade turbulence Recently the interest in certain invariant measures of 2D Euler equations was renewed, motivated for instance by questions of existence for almost every initial condition, similarly to the case of dispersive equations where probability on initial conditions allowed very succesful progresses. Obviusly invariant measures of 2D Euler equations are primarily of interest for turbulence but those known are not realistic from several viewpoints, beside some element of great interest. We discuss this issue and show modifications, unfortunately mostly heuristic, that would give much better results for turbulence. INI 1 14:30 to 15:30 Hao Shen (University of Wisconsin-Madison)SPDE limits of six-vertex model The theme of the talk is deriving stochastic PDE limits as description of large-scale fluctuations of the six-vertex (6V) model in various regimes. We will consider two types of 6V model: stochastic 6V and symmetric 6V. For stochastic 6V in a weakly asymmetric regime, under parabolic scaling the height function fluctuation converges to solution of KPZ equation after suitable re-centering and tilting. For symmetric 6V, in a regime where parameters are tuned into the ferroelectric/disordered phase critical point, under parabolic scaling the line density fluctuations in a one-parameter family of Gibbs states converge to solution of stationary stochastic Burgers. Again for stochastic 6V, in a regime where the corner-shape vertex weights are tuned to zero, under hyperbolic scaling, the height fluctuation converges to the solution of stochastic telegraph equation. We will discuss challenges and new techniques in the proofs. Based on a joint work with Ivan Corwin, Promit Ghosal and Li-Cheng Tsai, and a joint work with Li-Cheng Tsai. INI 1 15:30 to 16:00 Afternoon Tea