Related papers: Representation Stability for Marked Graph Complexe…

We prove a general representation stability result for polynomial coefficient systems which lets us prove representation stability and secondary homological stability for many families of groups with polynomial coefficients. This gives two…

Using the language of twisted skew-commutative algebras, we define \emph{secondary representation stability}, a stability pattern in the {\it unstable} homology of spaces that are representation stable in the sense of Church, Ellenberg, and…

The rational homology groups of the packing complexes are important in algebraic geometry since they control the syzygies of line bundles on projective embeddings of products of projective spaces (Segre--Veronese varieties). These complexes…

We establish a strong, geometric lower bound on the (sequential) topological complexity of the unordered configuration spaces of a general graph. As an application, we show that, for most graphs, the topological complexity eventually…

In this paper we prove homological stability for certain subgroups of surface braid groups. Alternatively, this is equivalent to proving homological stability for configurations of subsets of exactly $\xi$ points in a surface as we increase…

It is proved that vertical graphs and radial graphs are strongly stable for a certain type of densities in Euclidean space ${\mathbb R}^{n+1}$. Particular cases of these densities include translators, expanders and singular minimal…

For a fixed algebraic variety $X$, curve class $\alpha \in N_1(X)$, and genus $g \in \mathbb N$, we consider the sequence of $S_n$ representations obtained from the homology of the Kontsevich space of stable maps to $X$, $\bar…

For fixed j and w, we study the j-th homology of the configuration space of n labeled disks of width 1 in an infinite strip of width w. As n grows, the homology groups grow exponentially in rank, suggesting a generalized representation…

This paper analyzes the representation theoretic stability, in the sense of Thomas Church and Benson Farb, of the rank-selected homology of the Boolean lattice and the partition lattice, proving sharp uniform representation stability bounds…

We consider for two based graphs $G$ and $H$ the sequence of graphs $G_k$ given by the wedge sum of $G$ and $k$ copies of $H$. These graphs have an action of the symmetric group $\Sigma_k$ by permuting the $H$-summands. We show that the…

We study representation stability in the sense of Church and Farb of sequences of cohomology groups of complements of arrangements of linear subspaces in real and complex space as $S_n$-modules. We consider arrangement of linear subspaces…

We prove Farber's conjecture on the stable topological complexity of configuration spaces of graphs. The conjecture follows from a general lower bound derived from recent insights into the topological complexity of aspherical spaces. Our…

We prove geometric and cohomological stabilization results for the universal smooth degree $d$ hypersurface section of a fixed smooth projective variety as $d$ goes to infinity. We show that relative configuration spaces of the universal…

We study graph complexes related to configuration spaces and diffeomorphism groups of highly connected manifolds of odd dimension. In particular we compute the cohomology in the "high genus" limit. This paper is a continuation of previous…

We prove a slope 1 stability range for the homology of the symplectic, orthogonal and unitary groups with respect to the hyperbolic form, over any fields other than $F_2$, improving the known range by a factor 2 in the case of finite…

Graph neural networks are experiencing a surge of popularity within the machine learning community due to their ability to adapt to non-Euclidean domains and instil inductive biases. Despite this, their stability, i.e., their robustness to…

In this paper we introduce the notion of the stability of a sequence of modules over Hecke algebras. We prove that a finitely generated consistent sequence associated with Hecke algebras is representation stable.

In this paper, we study the topology of ordered Hurwitz space. These are moduli spaces of branched covers with a choice of ordering on the branched points. Answering a question of Ellenberg, we prove that the homology of ordered Hurwitz…

We prove a homological stability theorem for families of discrete groups (e.g. mapping class groups, automorphism groups of free groups, braid groups) with coefficients in a sequence of irreducible algebraic representations of arithmetic…

We study stability patterns in the high dimensional rational homology of unordered configuration spaces of manifolds. Our results follow from a general approach to stability phenomena in the homology of Lie algebras, which may be of…