Related papers: On a class of inhomogeneous extensions for integra…

In this paper we introduce the notion of evolution rank and give a decomposition of an evolution algebra into its annihilator plus extending evolution subspaces having evolution rank one. This decomposition can be used to prove that in…

While persistent homology has taken strides towards becoming a wide-spread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is the serious drawback of no longer having a concise and…

We consider the class of non-negative rank-one convex isotropic integrands on $\mathbb{R}^{n\times n}$ which are also positively $p$-homogeneous. If $p \leq n = 2$ we prove, conditional on the quasiconvexity of the Burkholder integrand,…

We give strengthened versions of the Herwig-Lascar and Hodkinson-Otto extension theorems for partial automorphisms of finite structures. Such strengthenings yield several combinatorial and group-theoretic consequences for homogeneous…

In this paper we introduce the galaxy of Coxeter groups -- an infinite dimensional, locally finite, ranked simplicial complex which captures isomorphisms between Coxeter systems. In doing so, we would like to suggest a new framework to…

In this paper we prove that a morphism between schemes or stacks naturally corresponds to a symmetric monoidal functor between stable infinity-categories of quasi-coherent complexes. It can be viewed as a derived analogue of Tannaka…

We show that the Yang-Baxter equations for two dimensional models admit as a group of symmetry the infinite discrete group $A_2^{(1)}$. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the…

We prove that the classical integrability condition for almost complex structures on finite-dimensional smooth manifolds also works in infinite dimensions in the case of almost complex structures that are real analytic on real analytic…

We develop a theory of levels for irreducible representations of symmetric groups of degree $n$ analogous to the theory of levels for finite classical groups. A key property of level is that the level of a character, provided it is not too…

We prove homological stability for both general linear groups of modules over a ring with finite stable rank and unitary groups of quadratic modules over a ring with finite unitary stable rank. In particular, we do not assume the modules…

In this paper, a new class of $\Z$-graded Lie conformal algebras $\CW(a,c)$ of infinite rank is constructed. The conformal derivations and one-dimensional central extensions of $\CW(a,c)$ are completely determined. And all conformal modules…

For a finite field k and a triple of integers g \ge r \ge s \ge 0, we count the number of semilinear endomorphisms of a g-dimensional k-vector space which have rank r and stable rank s. Such endomorphisms show up naturally in the…

We prove that some skew group algebras have Noetherian cohomology rings, a property inherited from their component parts. The proof is an adaptation of Evens' proof of finite generation of group cohomology. We apply the result to a series…

For each integer n\ge 2, we construct an irreducible, smooth, complex projective variety M of dimension n, whose fundamental group has infinitely generated homology in degree n+1 and whose universal cover is a Stein manifold, homotopy…

We prove that any group acting essentially without a fixed point at infinity on an irreducible finite-dimensional CAT(0) cube complex contains a rank one isometry. This implies that the Rank Rigidity Conjecture holds for CAT(0) cube…

We propose a new method for solution of the integrability problem for evolutionary differential-difference equations of arbitrary order. It enables us to produce necessary integrability conditions, to determine whether a given equation is…

Suppose a finite group acts on a scheme $X$ and a finite-dimensional Lie algebra $\mathfrak{g}$. The associated equivariant map algebra is the Lie algebra of equivariant regular maps from $X$ to $\mathfrak{g}$. The irreducible…

The extension space conjecture of oriented matroid theory states that the space of all one-element, non-loop, non-coloop extensions of a realizable oriented matroid of rank $d$ has the homotopy type of a sphere of dimension $d-1$. We…

We develop a notion of rank one properly convex domains (or Hilbert geometries) in the real projective space. This is in the spirit of rank one non-positively curved Riemannian manifolds and CAT(0) spaces. We define rank one isometries for…

We offer a criterion for showing that the automorphism group of an ultrahomogeneous structure is topologically 2-generated and even has a cyclically dense conjugacy class. We then show how finite topological rank of the automorphism group…