We prove a homological stabilization theorem for Hurwitz spaces: moduli spaces of
branched covers of the complex projective line. This has the following arithmetic …

Given a family of groups admitting a braided monoidal structure (satisfying mild
assumptions) we construct a family of spaces on which the groups act and whose …

We study analogues of FI-modules where the role of the symmetric group is played by the
general linear groups and the symplectic groups over finite rings, and we prove basic …

We prove a homological stability theorem for moduli spaces of simply connected manifolds
of dimension $2 n> 4$, with respect to forming connected sum with $ S^ n\times S^ n $. This …

We prove a homological stability theorem for families of discrete groups (eg mapping class
groups, automorphism groups of free groups, braid groups) with coefficients in a sequence …

We extend the definition of Khovanov–Lee homology to links in connected sums of S 1× S
2's and construct a Rasmussen-type invariant for null-homologous links in these manifolds …

We give a complete and detailed proof of Harer's stability theorem for the homology of
mapping class groups of surfaces, with the best stability range presently known. This …

We show that a certain locus inside the moduli space $ M_g $ of hyperbolic surfaces, given
by surfaces with" sufficiently many" short geodesics, is a classifying space of the handlebody …

In this paper we develop machinery for studying sequences of representations of any of the
three families of classical Weyl groups, extending work of Church, Ellenberg, Farb, and …

The main result of this article is that pure orbifold braid groups fit into an exact sequence
$1\rightarrow K\rightarrow\pi_1^{orb}(\Sigma_\Gamma (n-1+ L))\xrightarrow {\iota_ {\textrm …