Related papers: On genericity of pseudo-Anosovs in the Torelli gro…

We prove that the Lyapunov exponents of random products in a (real or complex) matrix group depends continuously on the matrix coefficients and probability weights. More generally, the Lyapunov exponents of the random product defined by any…

We prove that two Enriques surfaces defined over an algebraically closed field of characteristic different from $2$ are isomorphic if their Kuznetsov components are equivalent. This improves and completes our previous result joint with Nuer…

We prove that any finite abelian group $G$ contains a collection of not too many subsets with a special structure, so that for every subset $A$ of $G$ with a small doubling, there is a member $F$ of the collection that is fully contained in…

We prove that second rational homology of the Torelli group of an orientable closed surface of genus g is finite dimensional for g at least 51. This rules out the simplest obstruction to the Torelli group being finitely presented and…

The Andrews-Curtis conjecture claims that every normally generating $n$-tuple of a free group $F_n$ of rank $n \ge 2$ can be reduced to a basis by means of Nielsen transformations and arbitrary conjugations. Replacing $F_n$ by an arbitrary…

In this article we formulate a version of the analytic Novikov conjecture for semigroups rather than groups, and show that the descent argument from coarse geometry generalises effectively to this new situation.

Let $G$ be a random group in Gromov's density model $G(m,d,L)$ with $d<\tfrac12$. We prove a sharp quantitative constraint on products of conjugates equal to the identity: for every $n\ge1$ and $\varepsilon>0$, with overwhelming probability…

We prove a non-generosity theorem for proper cosets in groups of finite Morley rank and elaborate on the theory of Weyl groups in this context.

We consider random walks on the mapping class group whose support generates a non-elementary subgroup and contains a pseudo-Anosov map whose invariant Teichm\"uller geodesic is in the principal stratum. For such random walks, we show that…

We show that for any Cayley graph, the probability (at any $p$) that the cluster of the origin has size n decays at a well-defined exponential rate (possibly 0). For general graphs, we relate this rate being positive in the supercritical…

We provide new vanishing and glueing results for relative simplicial volume, following up on two current themes in bounded cohomology: The passage from amenable groups to boundedly acyclic groups and the use of equivariant topology. More…

In this note we prove the following results: $\bullet$ If a finitely presented group $G$ admits a strongly aperiodic SFT, then $G$ has decidable word problem. More generally, for f.g. groups that are not recursively presented, there exists…

We show that a finitely generated soluble group is virtually nilpotent if and only if the diameter of its finite coset spaces admits a uniform polynomial lower bound in terms of their size. We obtain the same conclusion for certain finitely…

We study random nilpotent groups in the well-established style of random groups, by choosing relators uniformly among freely reduced words of (nearly) equal length and letting the length tend to infinity. Whereas random groups are quotients…

We show that generically a pseudogroup generated by holomorphic diffeomorphisms defined about $0 \in \mathbb{C}$ is free in the sense of pseudogroups even if the class of conjugacy of the generators is fixed. This result has a number of…

We compute the growth series and the growth functions of reducible and pseudo-Anosov elements of the pure mapping class group of the sphere with four holes with respect to a certain generating set. We prove that the ratio of the number of…

For a smooth expanding circle map, we show that the empirical distribution of Lyapunov exponents of periodic points of any fixed period is close to normal, with an error that decreases as the period grows. This establishes a version of the…

We propose an algorithm for deciding whether a given braid is pseudo-Anosov, reducible, or periodic. The algorithm is based on Garside's weighted decomposition and is polynomial-time in the word-length of an input braid. Moreover, a…

Suppose that A_1,\dots, A_N are independent random matrices whose atoms are iid copies of a random variable \xi of mean zero and variance one. It is known from the works of Newman et. al. in the late 80s that when \xi is gaussian then…

We associate to any irreducible germ S of complex quasi-ordinary hypersurface an analytically invariant semigroup. We deduce a direct proof (without passing through their embedded topological invariance) of the analytical invariance of the…