Speaker: Mark Shusterman (Tel-Aviv University): Title: Howson's Theorem for (pro-p) Surface groups Abstract: A classical result of Howson says that the intersection of two finitely generated subgroups of a free group is finitely generated. This result has been generalized to surface groups by Greenberg, to limit groups by Dahmani, and established in many other cases as well. Furthermore, the problem of bounding the number of generators of the intersection received much attention, culminating in the groundbreaking works of Friedman, Mineyev, and Jaikin-Zapirain. I will prove Howson's theorem for various pro-p groups: pro-p completions of surface groups, maximal pro-p extensions of p-adic fields, maximal pro-p quotients of etale fundamental groups, Sylow subgroups of the absolute Galois group of a global field, and other pro-p groups of arithmetic origin. We will then see that the proof gives bounds on the number of generators of the intersection in discrete groups such as Fuchsian groups, thus improving upon the bounds of Soma in certain cases. This is a joint work with Pavel Zalesskii.