Ford, G. AustinHassell, AndrewHillairet, Luc2021-08-232021-08-231664-039Xhttp://hdl.handle.net/1885/244983We study wave diffraction on Euclidean surfaces with conic singularities (X, g)(X,g). We determine, for the first time, the precise microlocal structure of the wave at the intersection of the direct (or geometric) and diffracted fronts. Namely, we show that the wave kernel is a singular Fourier integral operator in a calculus associated to two intersecting Lagrangian submanifolds (corresponding to the two fronts), introduced originally by Melrose and Uhlmann [23]. We investigate the singularities of the trace of the half-wave group, Tre^{-it\sqrt\Delta}e−it Δ, on (X, g)(X,g). We compute the leading-order singularity associated to periodic orbits with successive degenerate diffractions. This result extends the previous work of the third author [12] and the two-dimensional case of the work of the first author and Wunsch [10] as well as the seminal result of Duistermaat and Guillemin [7] in the smooth setting. In future work, we shall use these results to obtain inverse spectral results on Euclidean surfaces with conic singularities.This research was supported by National Science Foundation Postdoctoral Fellowship DMS1204304 (GAF); Australian Research Council Discovery grants FT0990895, DP1095448 and DP120102019 (AH); and L’Agence Nationale de la Recherche program ANR-13-BS01-0007-01 GERASIC (LH). GAF also thanks the Mathematical Sciences Institute of the Australian National University for its hospitality during part of this work.2018-06-0310.4171/JST/209