Open Problems from workshop "Differential Geometry, Billiards, and Geometric Optics", CIRM, October 4–8, 2021

The uploaded CIRM open‑problems note (dated Oct 22, 2021) formulates the projective billiards questions explicitly, states known examples for k=3 and for every even k ≥ 4 (polygonal), and, crucially, records that no examples are known for odd k ≥ 5, asking “Can one find examples of k‑reflective projective billiards with k ≥ 5 odd?” This matches the model’s assessment that the odd‑k ≥ 5 case was open as of the cutoff, and it aligns with the paper’s own background and figures that include the right‑spherical (3‑reflective) and even‑k polygonal examples. Hence the correct joint assessment is that the problem was open at that time. See the definitions, figures, and questions in the note’s projective billiards section and the two questions it poses (existence for odd k ≥ 5 and a projective Ivrii‑type classification) .