Dr Petridis works on analytic aspects of automorphic forms and their relation to the spectral theory of the Laplace operator on hyperbolic Riemann surfaces. He has applied perturbation methods to understand the location of scattering poles, which in arithmetic examples relate to the nontrivial zeros of the Riemann zeta function and other L-series. Currently he works on the distribution of modular symbols and distributional questions of closed geodesics and groups elements with restrictions of (co)homological type. Problems in quantum chaos for hyperbolic manifolds are investigated in relation to the behavior of (more complicated) L-series.

Another line of investigation is the distribution of the eigenvalues of the Laplace operator, in particular Weyl's law. He has applied techniques from analytic number theory (exponential sums)to this problem for specific manifolds e.g. Heisenberg manifolds.