String Theory Seminar


Thursday, September 11, 2003, 4:00 pm, 332 Phillips Hall, Mathematics Colloquium at UNC
    Katrin Wendland (University of Warwick),
    Decoding the Geometry of Conformal Field Theories
    

        Geometric structures can be encoded by several competing means
        in mathematics. In differential geometry, for instance, and very loosely speaking,
        the Riemannian metric tensor of a manifold is  the most fundamental object to
        study, whereas in algebraic geometry the commutative algebra of specific functions
        on a variety gives the basic structure. In Connes' noncommutative geometry, these
        ideas are combined. Here, geometry is encoded in terms of spectral triples, that is
        function spaces together with the action of specific multiplicative and differential
        operators on them.
               Since a similar structure arises from conformal field theory, Connes'
        noncommutative geometry   provides a useful tool and guideline in order to extract
        geometric data from conformal field theories.   This deciphering of geometry from
        conformal field theory is the topic of our talk. However, we  do not presume knowledge
        of conformal field theory or noncommutative geometry. We argu  that degeneration
        phenomena in geometry and thereby also in conformal field theory play an
        important role for the deciphering, and we present a non-standard degenerating
        example along  with its geometric interpretation.