It follows a list of available proposals for "reading course"; students can contact the indicated instructor for each single course:

1. Optimal control of stochastic processes (Cecchin Alekos)

Possible topics: value function, dynamic programming equation, backward stochastic differential equations, stochastic maximum principle, second order viscosity

solutions.

2. Statistical physics, information theory and optimization (Marco Formentin)

Statistical mechanics uses the language of probability to study the collective behavior of systems composed of a huge number of particles. The introduction of

disordered systems has opened up the road to interesting applications beyond physics, in particular to information theory and combinatorial optimization.

Bibliography: M. Mezard, A. Montanari, “Information, physics and computation”, Oxford, 2008

3. Quantization of random variables (Giorgia Callegaro)

Quantization is a versatile and robust technique used in many applied sciences (including mathematical finance) for discretize random variables and stochastic

processes and quickly compute expectations and conditional expectations.

4. Large deviation theory: the art of estimating the probability of rare events (Alberto Chiarini)

5. Random Graphs and Networks (Alessandra Bianchi)

Random graphs are probabilistic models for real-world networks, roughly defined as a probability measure on a

given set of graphs. They allow to analyze the large-scale features appearing in complex networks, including "small world" and "scale-free" phenomena.

6. Topics in Algebra (Jorge Vitoria)

Proposed topics are available at this page: https://sites.google.com/view/jorgevitoria/#h.pzks8h9p20b2