Palestrante: Prof. Pedro Lauridsen Ribeiro

Título: Hyperbolic Differential Complexes

Resumo:
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)