Buser: https://files.eric.ed.gov/fulltext/EJ1149196.pdf (education and Riem surfaces) Veech: https://link.springer.com/article/10.1007%2FBF01896876 billiard in a reg polygon McMullen https://www.ams.org/journals/jams/2003-16-04/S0894-0347-03-00432-6/ billiards and teich curves on hilb mod surfaces ******* from Yuliy Baryshnikov Glad you asked (-; there is this old paper of mine ; the polyhedra introduced there were then studied a lot by the French (under the names like Serpent Nests and Accordion Complexes ), and nowadays they appear in JHEP in papers like this . Sure! ping me when you're back... Best, Y On 10/5/21 8:48 AM, Richard Montgomery wrote: > ! > wow. Thanks. > > Where could I read about these polytopes encoding these bifurcations? > Do you want to explain to me in a Zoom in the next week or or so? *********** Ercolani. finite gap https://doi.org/10.1016/j.anihpc.2019.04.002 *********** Romik Taylor coeffs of a theta fn and number theory. The theta fn is the sum of exp(- \pi n^2 x) over all n's pretty wild result .. dfafafafsf ****** https://algant.eu/documents/theses/destefano.pdf fermat curves, modular curves, 2,3 7; X(7), ... ; a master's thesis out of bordeaux seems nice ! ***** completions of X(N)'s and general finite vol quotients by way of a projective embedding defined by modular forms: https://www.esi.ac.at/preprints/esi2400.pdf ***** Shimura: intro to arithmetic of ... https://wstein.org/edu/Fall2003/252/references/Shimura-Intro/Shimura-Introduction_to_the_arithmetic_theory_of_automorphic_functions.pdf