## Mathematical Physics

## Integrable and Quasi-Integrable Systems

Analysis of algebraic and geometric structures underlying classical and quantum integrable systems. Hamiltonian formalism for partial derivative equations. Geometry of Dubrovin-Frobenius varieties (and generalizations) and associated integrable hierarchies. Study of integrable and quasi-integrable deformations of hyperbolic systems of conservation laws. Stability of dynamics for quasi-integrable systems: study of the existence of adiabatic invariants in the thermodynamic limit and connection with thermodynamic properties. Study of the onset of weak turbulence for partial derivative weakly nonlinear equations, deduction of the related kinetic equation.

**Participants:**

## Fluid Dynamics

Hamiltonian structures for stratified Euler fluids; analysis of integrability and Hamiltonian properties of models for motions between fluid interfaces; description of the interaction between fluid-fluid interfaces and rigid borders of the fluid domain. Vorticity dynamics in classical systems and quantum hydrodynamics.

**Participants:**

## Non Linear Dispersive Equations

Study of the properties of standing wave propagation on graphs and networks, particularly for dynamics described by the nonlinear Schroedinger equation and for equations of fluid-dynamic origin.

**Participants:**

## Stochastic Properties of Dynamic Systems

Stochastic properties of dynamical systems: limit theorems and anomalous diffusion. Similarity measures and information theory: applications to the human sciences and biology.

**Participants:**

## Topological Field Theory

Potential theory in topologically complex domains, kinetic and magnetic helicity, energy relaxation, physical nodes theory, defects in condensates, topological cascade processes, energy-complexity relations.

**Participants:**

## Field and String Theories

Geometry of string compactifications; AdS/CFT correspondence; supersymmetric field theories.

**Participants:**

## Mathematical Aspects of Quantum Mechanics

Schrödinger and Dirac operators and applications. In particular: Schrödinger operators with point interactions and on metric graphs, Dirac operators with singular interactions, few-body systems.

**Participants:**