# Problem list

Inhyeok Choi: Let G be a discret group acting on a metric space X. Given a nontrivial measure on G, what does the ratio between the asymptotic entropy and asymptotic first moment (=drift) tells us about the action?

Wonyong Jang: Suppose that a group G acts on a hyperbolic space X. If the kernel of the natural action of G on its Gromov boundary X is finite, then can we obtain a dynamical property of the action of X, or an algebraic property of G? For instance, the kernel finiteness implies conboundedness or the SQ-universality of G, etc.

KyeongRo Kim: What is the Mather invariant of elements in Diff_0^(1+a)(S^1) for the C^a-flowability when 0<a<1?

Shuhei Maruyama: Let G be the fundamental group of the sphere minus a Cantor set. Can we show some rigidity of G-actions on the circle? Can we use it to prove Calegari--Chen's rigidity theorem of the mapping class group of the plane minus a Cantor set?

Brendan Murran: When is a group hyperbolic?

Andres Navas: Let G be a finitely-generated group of C1 circle diffeomorphisms. Suppose that G has no resilient pairs. Given ε > 0, can G be conjugated (by a homeomorphism) into a group of Lipschitz homeomorphisms for which the Lipschitz constants of the generators are all ≤ eε ?

(See also this file)

Christobal Rivas: Let H be Higman's group. Does H admit a free action on the sphere S^2? Does H admit an action without global fixed point on S^2?