Research report 2003 - Max Planck Institute for Mathematics
Noncommutative geometry and number theory
Authors
Marcolli, Prof. Matilde
Departments
Summary
We describe how noncommutative geometry, a mathematical formulation of geometry adapted to quantum phenomena, interacts with number theory through quantum statistical mechanical systems with phase transitions and spontaneous symmetry breaking. This provides a unified setting for many important arithmetic results including the spectral realization of zeros of the Riemann zeta function and the Galois theory of modular functions.