Speaker
Prof.
Pedro Lauridsen Ribeiro
(University of Sao Paolo)
Description
Complexes of differential operators are a concept of great importance in several areas of mathematics. Particularly, elliptic differential complexes play a fundamental role in the theory of the index of elliptic operators put forward by Atiyah, Singer and others in the sixties, whose relevance in analysis, geometry and topology is well known. Much less developed is a similar theory for complexes of hyperbolic partial differential operators, which are of utmost importance for formulating the dynamics of relativistic field theories with constraints and/or gauge symmetries. In this talk, we shall present a few steps towards such a theory, partly based on a former proposal by MacKichan (1975). Our main focus will be how to properly formulate and prove well-posedness of the Cauchy problem for such complexes, and how this theory elegantly encodes both constraints and gauge symmetries. Connections to the BV-BRST formalism for gauge- theoretic field models and possible extensions to nonlinear systems will also be discussed, if time allows. (joint work with Michael Forger)
