Joint Colloquium: Segal -- Geometric aspects of the positivity of energy in quantum field theory

The Riemannian metrics on a manifold are the real points of a complex domain of
complex-valued metrics which has the Lorentzian metrics on its boundary.  In quantum
field theory the positivity of energy is encoded in the assertion that the theory
extends holomorphically from Lorentzian manifolds to this complex domain.  (The
expresssion ``Wick rotation" is often used for this extension.)  The domain has
interseting geometric properties, suggestive for both mathematics and physics, which are
especially vivid in the two-dimwnsional case.  I shall discuss some of these properties
in the talk, which is based on work in progress with Maxim Kontsevich.  

G.Segal, 

All Souls College, Oxford.