Newton-Cartan trace anomalies

In this talk I will review some basic facts about Newton-Cartan geometry, which is the natural background to which non-relativistic field theories couple.
Then I will describe how to classify the general structure of the trace anomaly for Schroedinger-invariant theories in 2+1 dimensions using a technique based on a null reduction of an higher-dimensional conformal-invariant theory.
Finally, I will show explicit examples of the trace anomaly for a free scalar and a free fermion derived with the heat kernel method, and I will propose a non-relativistic version of the a-theorem.
Various applications of the study of Newton-Cartan anomalies will be emphasized.