Andrea Cavagna, Istituto dei Sistemi Complessi, CNR, Italy

Collective Behaviour in Biological Systems (12h)

1. The Hallmarks of Collective Behaviour:

Degrees of freedom, structure, order parameters, correlation functions, susceptibility, scaling.

2. How not to panic when you lack an Ensemble:

Phase averages vs space averages, what scale-free correlations look like in real life, data from flocks and swarms, orientation vs speed correlations.

3. What you really need to know about Continuous Symmetry Breaking:

Goldstone mechanism, massless modes, transverse vs longitudinal susceptibility, the problem of the modulus, what is due to math and what is due to biology?

4. Static Correlation vs Information Propagation:

The paradox of sound, are scale-free correlations necessary for information propagation? How to escape the falcon, necessary vs sufficient conditions for information transfer.

5. Models of Active Systems:

Ferromagnets on the move, Vicsek model, first or second order differential equation? Toner-Tu field theory, first sound propagation.

6. Inertial Dynamics:

The trap of the over-damped limit, finite-size transients matter, symmetries and their generators, second sound propagation, dispersion relations in models and experiments, finite-size inertial crossover.

7. Renormalization Group in Finite-Size Biological Systems:

Mode-coupling models at equilibrium, why are we talking about liquid Helium? The dynamical critical exponent, finite-size RG crossover and the relevance of unstable fixed points, going off-equilibrium.

8. Perspectives:

A light yet exhilarating lecture about everything else.