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After the Nobel prize in Physics to Giorgio Parisi this series of lessons regards some of the arguments mostly touched by the prize motivations, namely disordered systems and complexity.

These lessons will have a theoretical nature, but I will also mention some experimental results the theory has to account for. Lessons are thought as being self-contained, therefore there is no need of any previous knowledge of the matter, besides a sufficient mathematical background; everything needed will be developed during the course. For this reason, the lessons are addressed to Mathematics and Physics students (but also students coming from different scientific disciplines) as well as to researchers of various areas which are interested in such themes. In these lessons I will recall some basic concepts of Thermodynamics and Statistical Mechanics, such as the statistical ensembles, the phenomenon of phase transitions, sp ontaneous symmetry breaking, broken ergodicity, pure states, mean-field theories and universality. These concepts will be generalized to the realm of disordered systems, particularly the frustrated ones, namely the class of spin-glass systems, particularly the p-spin model. This model will be solved in mean-field using the replica method. The replica symmetric solution will be worked out and the solutions with different replica symmetry breakings, up to the Parisi solution. I will also discuss some other models close to spin-glasses, like the random energy model (REM) and some complex optimization problems.

Calendario

25/2/2025, 09:00 - 11:00 Room: Lab. di Ottica e Termologia - III P. Ed. F
28/2/2025, 09:00 - 11:00 Room: P16-IV P. Ed. F3
4/3/2025, 15:00 - 17:00 Room: S4-I piano St.9
7/3/2025, 09:00 - 11:00 Room: P16-IV P. Ed. F3
11/3/2025, 15:00 - 17:00 Room: S4-I piano St.9