Colloquium: Torsion, zeta functions and symmetries

Abstract: In the 1930s, Reidemeister and Franz developed an invariant for compact spaces that we now call Reidemeister-Franz torsion. This invariant detects subtle differences between different spaces, and was used for example to classify lens spaces. In the 1970s, Ray and Singer used analysis to construct an analogue of Reidemeister-Franz torsion: analytic torsion.
For a continuous-time dynamical system on a compact space, one can define the Ruelle dynamical zeta function, encoding information on the periodic orbits of the system. Fried showed in the 1980s that for certain systems, the absolute value of the Ruelle zeta function at zero equals analytic torsion of the space on which the system is defined. The problem to generalise this equality to other cases has become known as the Fried conjecture, and is still an active area of research.
With Hemanth Saratchandran, we developed versions of analytic torsion and the Ruelle zeta function that take symmetries into account. This leads to a symmetric version of Fried’s conjecture. With Chris Pirie, we have obtained some first positive results on this problem.

Host: Yanli Song

Reception: There will be light refreshments served in Cupples I Hall, Room 200 (Lounge) following the talk.