Using quantum statistical mechanical systems to study real quadratic fields (Jane Panangaden, Pitzer College)

The original Bost-Connes system was constructed in 1990 and is a QSM system with deep connections to the field of rationals. In particular, its partition function is the Riemann-zeta function and its ground states evaluated on certain arithmetic objects yield generators of the maximal Abelian extension of the rationals. In this talk we describe the construction of a related QSM system adapted to the study of real quadratic fields, called the Boundary GL2 System. We describe its thermal properties and show how these relate to class field theory of real quadratic fields. These results are joint work with Matilde Marcolli.