The seminar will be focused on the mathematical treatment of physical systems composed of a large number of particles.
Three major aspect will be discussed:
(a) The mathematical existence (non-existence) of ordinary matter (electrons and nuclei/fermions/bosons) which goes under the category of  "Stability of Matter", a theory whose foundations have been developed by Elliott Lieb and Walter Thirring.
(b) The existence of the thermodynamic limit for ordinary matter, that is the mathematical proof that indeed thermodynamics is rigorously founded.
This is based on the seminal work of Joel Lebowitz and Elliott Lieb.
(c) Additivity and thermodynamics (nanothermodynamics). That is the problem of partitioning a large systems in small subsysatems and find the corrections to thermodynamic quantities when the subsystems is too small. Based on the work of T.Hill this aspect is strictly related to (b) and it is becoming of great importance in modern applications.