Martedì 29 maggio 2018 alle ore 14:30 Giambattista Giacomin (Université Paris Diderot) terrà un seminario dal titolo "On phase transitions in disordered systems and singular behavior of Lyapunov exponents" Aula 3014, Dipartimento di Matematica e Applicazioni (edificio U5, terzo piano, via Cozzi 55, Milano) Università di Milano-Bicocca Trovate il sommario di seguito. Tutti gli interessati sono invitati a partecipare. Francesco Caravenna %%%%%%%%%%%%%%%%%%%%%%%%%% Abstract: Understanding the effect of disorder on phase transitions and crtical phenomena is a challenging problem that has been repeatedly considered in the phyisics literature. In this domain there is a highly non trivial model that takes the center stage because it is considered to be «exactly solvable». It is the two dimensional Ising model with a special type of disorder («columnar disorder»). I will provide an introduction to this model and to what has been conjectured about it. I will also explain why the exact solvability claim is an overstatement. The solvability aspect in fact is limited to the reduction of the problem to another one - the computation of the Lyapunov exponent of a certain product of two by two random matrices - that seems (and probably is) much easier. In collaboration with Francis Comets and Rafael Greenblatt, we have made some progress toward understanding this product of random matrices. The main aim of the talk is explaining these results and what they imply on the two dimensional Ising model with columnar disorder. %%%%%%%%%%%%%%%%%%%%%%%%%% _________________________________________ Francesco Caravenna Dipartimento di Matematica e Applicazioni Università degli Studi di Milano-Bicocca Via Cozzi 55, 20125 Milano, Italy http://www.matapp.unimib.it/~fcaraven/ _________________________________________