We compute the groups H*(Aut(F$_{n}$);M) and H*(Out(F$_{n}$);M) in a stable range, where M is obtained by applying a Schur functor to H$_{Q}$ or H$_{Q}$, respectively the first rational homology and cohomology of F$_{n}$. ...

Human microbiome studies use sequencing technologies to measure the abundance of bacterial species or Operational Taxonomic Units (OTUs) in samples of biological material. Typically the data are organized in contingency ...

We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there are no harmonic spinors on a manifold with positive scalar curvature ...

We prove a homological stability theorem for moduli spaces of manifolds of dimension 2$\textit{n}$, for attaching handles of index at least $\textit{n}$, after these manifolds have been stabilised by countably many copies ...

A $\textit{permutoid}$ is a set of partial permutations that contains the identity and is such that partial compositions, when defined, have at most one extension in the set. In 2004 Peter Cameron conjectured that there ...

We consider the critical behaviour of the continuous-time weakly self-avoiding walk with contact self-attraction on $\mathbb{Z}$$^{4}$, for sufficiently small attraction. We prove that the susceptibility and correlation ...

We introduce a very general method for high-dimensional classification, based on careful combination of the results of applying an arbitrary base classifier to random projections of the feature vectors into a lower-dimensional ...

We show that if $\textit{p}$ is a prime, then all elliptic curves de ned over the cyclotomic $\mathbb{Z}$$_{p}$-extension of Q are modular.

The connective constant $μ$($G$) of an infinite transitive graph $G$ is the exponential growth rate of the number of self-avoiding walks from a given origin. In earlier work of Grimmett and Li, a locality theorem was proved ...

We formulate a notion of K-stability for Kähler manifolds, and prove one direction of the Yau–Tian–Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi functional being bounded below (resp. ...

Let π be a cuspidal, cohomological automorphic representation of GL$_{n}$(A). Venkatesh has suggested that there should exist a natural action of the exterior algebra of a certain motivic cohomology group on the π-part of ...

We construct almost toric fibrations (ATFs) on all del Pezzo surfaces, endowed with a monotone symplectic form. Except for CP$^{2}$#CP$^{2}$, CP$^{2}$#2CP$^{2}$, we are able to get almost toric base diagrams (ATBDs) of ...

A matrix is called totally positive (resp. totally nonnegative) if all its minors are positive (resp. nonnegative). Consider the Ising model with free boundary conditions and no external field on a planar graph G. Let ...

In this paper we construct a two variables p-adic L-function for the standard representation associated with a Hida family of parallel weight genus g Siegel forms, using a method previously developed by B\"ocherer--Schmidt ...

We consider several natural sets of curves associated to a given Teichmüller disc, such as the systole set or cylinder set, and study their coarse geometry inside the curve graph. We prove that these sets are quasiconvex ...

We prove that the pseudoisotopy stable range for manifolds of dimension 2n can be no better than (2n - 2). In order to do so, we define new characteristic classes for block bundles, extending our earlier work with Ebert, ...

This paper shows that, in dimensions two or more, there are no holomorphic isometries between Teichüller spaces and bounded symmetric domains in their intrinsic Kobayashi metric.

We study tautological rings for high-dimensional manifolds, that is, for each smooth manifold $M$ the ring $R^*$($M$) of those characteristic classes of smooth fibre bundles with fibre $M$ which is generated by generalised ...

With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ...

Let $\textit{A}$ be a quasi-hereditary algebra. We prove that in many cases, a tilting module is rigid (i.e. has identical radical and socle series) if it does not have certain subquotients whose composition factors extend ...