My research is in Probability and Statistical Mechanics. More specifically, I have acquired some experience with:
The course studies recurrence properties of random walks on general graphs. The analysis is carried on by introducing potential theory and the mathematical formalism of electric networks.
Literature: Probability on Trees and Networks, by Lyons and Peres. Intesection of Random Walks, by G. F. Lawler.
The course explores the properties of spin systems with discrete and continuous symmetries. The program includes existence of the thermodynamic limit, high and low temperature representation for the Ising model, correlation inequalities, Lee and Yang cirle theorem, Mermin-Wagner theorem and connections to random walks.
Literature: Statistical Mechanics of Lattice Systems a Concrete Mathematical Introduction, of S. Friedly and Y. Velenik
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