|
ESI Senior Research Fellow Programme, spring term 2013
Logarithmic TQFT, torsion, and trace invariants
Course of advanced graduate lectures by
Professor Simon Scott
(King's College, London)
Mini-Lecture course
June 5 - 14, Wednesday and Friday, 2:00-4:00
ESI, Erwin Schrödinger Lecture Hall
Abstract:
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.
Bibliography:
J. Lurie: On the classification of topological field theories,
available at http://www.math.harvard.edu/ lurie/papers/cobordism.pdf
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).
ESI Senior Research Fellow Programme coordinated by Prof. Piotr
T. Chrusciel, Gravitational Physics , Faculty of Physics, University
of Vienna, Währinger Straße 17, A-1090 Wien
(piotr.chrusciel@univie.ac.at)
and Prof. Adrian Constantin, Institute of Mathematics, University of
Vienna, Nordbergstraße 15 (UZA +IV), A-1090 Wien,
(adrian.constantin@univie.ac.at).
|
