Programme

Minicourses

Andrés Navas: TBA

Victor Kleptsyn: Properties of (smoooth) group actions on the circle

My mini-course will be devoted to the characterisation of properties of actions of finitely generated groups on the circle. We will see the properties (for non-measure preserving actions) in three different regimes: the dynamics with a Cantor minimal set, "rich" dynamics admitting local flows in the local closure, and the (most difficult) part for what lies in between. This mini-course will group many works of many different authors, and will address full or partial answers to several questions in the domain

Research Talks

Joaquin Brum: TBA

Francesco Fournier-Facio: Second bounded cohomology of PL groups and applications

Bounded cohomology is a functional analytic analogue of ordinary group cohomology, which in degree 2 is especially rich because of its relation with stable commutator length, simplicial volume and actions on the circle. I will talk about joint work with Yash Lodha about the second bounded cohomology of PL groups of the interval and circle, and its applications (time permitting, also one in joint work with Yash and Matt Zaremsky).

Sang-hyun Kim: Remark on the nonamenbability of F

Recently, OpenAI announced a proof that the Thompson's group F is nonamenable. We give a streamlined account of the details. Joint work with Yash Lodha.

Shuhei Maruyama: On cohomology classes related to Mather's homomorphism

For the group G of compactly-supported $C^{1+bv}$-diffeomorphisms of the real line, Mather defined a surjective homomorphism from G to the real line. In this talk, I will introduce two kinds of cohomology classes related to Mather's homomorphism, and explain their properties.

Sam Mellick: TBA

Juan Paucar: On the growth of cocycles of isometric representations on $L^p$-spaces. 

By the Delorme–Guichardet theorem, for σ-compact locally compact groups, property (T) coincides with property FH, that is, the property that every continuous isometric action on a Hilbert space has a fixed point. Equivalently, every 1-cocycle of every unitary representation is bounded. Inspired by the work of V. Lafforgue, we study, for compactly generated locally compact groups without property $FL^p$ (an $L^p$-analogue of property FH), how fast unbounded 1-cocycles can grow. This is joint work with Antonio López Neumann.

Xiaolei Wu: On the Boone–Higman Conjecture for groups acting on locally finite trees

Simple groups have played an important role in the studying of groups. The Boone–Higman Conjecture (1974) says a finitely generated group can be embedded into a finitely presented simple group if and only if  it has solvable word problem. The conjecture has now been proved for many classes of groups, including hyperbolic groups, RAAGs and linear groups over the rationals. In this talk, we will first give an overview of the conjecture. Then we discuss a strategy that can be used to embed many groups acting faithfully on locally finite trees to finitely presented simple groups. In particular we verify the conjecture for the Baumslag-Solitar groups, free-by-cyclic groups and all fundamental groups of virtually fibered 3-manifolds. The talk is based on a joint work with Kai-Uwe Bux and Claudio Llosa Isenrich.