Proposte di argomenti da parte dei docenti

Optimal control of stochastic processes (prof. Cecchin Alekos)

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

Statistical physics, information theory and optimization (prof. 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

Quantization of random variables (prof. 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.

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

Random Graphs and Networks (prof. 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.

Topics in Algebra (prof. Jorge Vitoria) 

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

"Nichols algebras for beginners" (prof. Giovanna Carnovale)

Nichols algebras are a family of rings that can be constructed starting from a vector space and and an operator. Examples include the polynomial rings on any number of variables, the exterior algebra, but in general they are much more complicated. The seminar would serve as an introduction to this subject. 

"An introduction to hyperplane arrangements" (prof. Giovanna Carnovale)

An hyperplane arrangement is a collection of affine or vector subspaces of codimension 1 in an affine or vector space. They can be studied by analyzing the combonatorics of their mutual intersection, as well as analyzing the geometry of their complement. The seminar would give an overview of the interplay of these two points of view, focusing on key examples.