June 5 - 14, Wednesday and Friday, 2:00-4:00
Additive invariants on morphisms in the cobordism category may be viewed as being positioned between classical cobordism invariants (genera) and quantum cobordism invariants (TQFTs). The purpose of these lectures will be to use logarithmic-functors to put in place a categorical framework for this class of semi-classical invariants and to use these structures to construct and compute exotic Milnor and Reidemeister torsions as characters of logarithmic representations. This may be viewed as a categorification of the theory of trace invariants associated to spectral zeta functions of pseudodifferential operators, and of their pasting formula with respect to a partition of the manifold over which they are defined.
J. Lurie: On the classification of topological field theories (2010).
N. Berline, E. Getzler and M. Vergne: Heat kernels and Dirac operators, Springer, Berlin-Heidelberg-New York (1992).
M. A. Shubin: Pseudo-differential operators and spectral theory, Springer (1987).