Speaker
Description
A flat connection on a compact, oriented manifold defines cohomology groups, which equal the kernels of the corresponding Laplacians by the Hodge theorem. If these cohomology groups vanish, then Ray-Singer analytic torsion is an invariant of such a manifold, defined in terms of the spectra of these Laplacians. For a flow on a compact manifold satisfying a nondegeneracy condition, the Ruelle dynamical zeta function is a quantity defined in terms of the lengths of closed flow curves.
The Fried conjecture states that for a large class of flows, the absolute value at zero of the Ruelle dynamical zeta function is well-defined and equals analytic torsion. With Hemanth Saratchandran, we define an equivariant version of analytic torsion for proper, cocompact group actions. We also define an equivariant Ruelle dynamical zeta function, and investigate when an equality like the Fried conjecture holds.
