Analytic torsion for twisted de Rham complexes

I will define and discuss the properties of the analytic torsion of

twisted cohomology and briefly of Z_2-graded elliptic complexes

in general, as an element in the graded determinant line of the

cohomology of the complex, generalizing most of the variants of Ray-

Singer analytic torsion in the literature. IThe definition uses pseudo-

differential operators and residue traces. Time permitting, I will

also give a couple of applications of this generalized torsion to

mathematical physics. This is joint work with Siye Wu.