Pillowcases and quasimodular forms.- Cluster ?-varieties, amalgamation, and Poisson-Lie groups.- Local geometric Langlands correspondence and affine Kac-Moody algebras.- Integration in valued fields.- On the Euler-Kronecker constants of global fields and primes with small norms.- Asymptotic behaviour of the Euler-Kronecker constant.- Crystalline representations and F-crystals.- Integrable linear equations and the Riemann-Schottky problem.- Fibres de Springer et jacobiennes compactifiées.- Iterated integrals of modular forms and noncommutative modular symbols.- Structures membranaires.