Abstracts of the invited speakers
László Erdös:
Derivation of nonlinear evolution equations
from the dynamics of interacting quantum particles We study the evolution of $N$ quantum particles interacting via weak pair interactions. In a certain scaling limit, the evolution of the marginal density of the system can be described by an effective nonlinear onebody equation. For bosonic particles, this equation is the nonlinear Hartree equation with a selfconsistent effective potential, for fermions it is the corresponding semiclassical limiting equation, the Vlasov equation. For very singular potentials, we derive the GrossPitaevskii equation that is especially important for describing the dynamics of the BoseEinstein condensate. Most of this work is joint with H.T. Yau and B. Schlein. Fabio Martinelli: Kinetically constrained spin models Kinetically constrained spin models (KSCM) are interacting particle systems with Glauberlike dynamics, no static interactions beyond hard core and reversible w.r.t. simple i.i.d product measure. The essential feature is that the creation/destruction of a particle on $x$ can occur only if the configuration around $x$ satisfies certain constraints (which completely define each specific model). KCSM have been introduced and studied in physical literature as examples of models showing a slow relaxation and in the attempt to model liquid/glass transition. Because of the constraints KCSM may show ergodicity breakdown (dynamical phase transition) without any equilibrium counterpart and it is this phenomenon that has been the main object of investigation in the physical community. In these lectures, starting from the basics of reversible continuous time Markov chains, we will develop rigorous tools to analyze the density and volume dependence of the relaxation time for a fairly general class of KCSM. 
Abstracts of the talks
Nicoletta Cancrini:
Kinetically constrained spin models: the east model
Kinetically constrained spin models have been introduced in physics literature as models which can have some properties of glass transition. They are lattice particle systems with Glauber like dynamics reversible with respect to the product Bernoulli measure. Creation/annihilation of one particle on a site can happen iff the configuration around the site satisfies a particular constraint which completely defines the model. I will discuss one of the models studied with F. Martinelli, C. Roberto, C. Toninelli: the east model (one dimensional). Each site changes its occupation iff its right neighbor is empty. In particular I will show the results we obtained on the dependence of the relaxation time to equilibrium on the system size and on the particle density.
Anna Maria Cherubini: Asymptotic Behaviour for a collision model
Michele Correggi: Rapidly Rotating Bose Gases in Anharmonic Traps
Domenico Finco:
Two scale approximation for a class of Many Body
Schrödinger equation
Alessandro Michelangeli:TBA
Daniela Morale:
Stochastic many particle systems in biology and medicin
Laura Morato:
Stochastic quantization for a system of N interacting Bose particles
Benjamin Schlein: Rate of convergence towards Hartree dynamics
Petra Scudo:
Entanglement in the quantum Ising model
Fabio Zucca: Ecological Equilibrium
for
Restrained Branching Random Walks

Posters
Lucie Fajfrová:
Zero range process on a binary tree
Equilibrium behaviour of Zero rage processes is studied in the case
when the set of sites, on which the particles move,
has a structure different from the usually considered set $\mathbb{Z}^d$.
We have chosen the tree structure, since the zero range process corresponds to
an infinite system of queues and the arrangement of servers in the
tree structure is natural in a number of situations.
