### On a result by Dang and Rivière

Ergodic Theory and Dynamical Systems Seminar

9th February 2023, 2:00 pm – 3:00 pm

Fry Building, G07

I will present an analogue for discrete graphs of results by Dyatlov-Zworski and Dang-Rivière on surfaces of negative curvature.

These results concern the values at 0 dynamical zeta functions and Poincaré series, and relate these values to the fundamental topological invariant, i.e. the Euler characteristic. In an attempt to better understand their work, I did similar calculations on discrete graphs. All the difficulties of functional analysis disappear (we are in finite dimension) but we lose completely the use of differential geometry.

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