Related papers: On nice $\mathbb{G}_m$-actions arising from locall…

We study the core of a proper action by a Lie group $G$ on a smooth manifold $M$, extending the construction for $G$ compact by Skjelbred and Straume. Moreover, we show that many properties of a proper $G$-action on $M$ are determined by…

Following a suggestion of Peter Scholze, we construct an action of $\hat{\mathbb{G}}_m$ on the Katz moduli problem, a profinite-\'{e}tale cover of the ordinary locus of the $p$-adic modular curve whose ring of functions is Serre's space of…

Consider the action of $SL(n+1,\mathbb{R})$ on $\mathbb{S}^n$ arising as the quotient of the linear action on $\mathbb{R}^{n+1}\setminus\{0\}$. We show that for a semigroup $\mathfrak{S}$ of $SL(n+1,\mathbb{R})$, the following are…

We consider possible discretizations for a gauge-fixed Green-Schwarz action of Type IIB superstring. We use them for measuring the action, from which we extract the cusp anomalous dimension of planar $\mathcal{N}=4$ SYM as derived from…

Let $M$ be a finite volume analytic pseudo-Riemannian manifold that admits an isometric $G$-action with a dense orbit, where $G$ is a connected non-compact simple Lie group. For low-dimensional $M$, i.e. $\dim(M) < 2\dim(G)$, when the…

We investigate Gaussian actions through the study of their crossed-product von Neumann algebra. The motivational result is Chifan and Ioana's ergodic decomposition theorem for Bernoulli actions (Ergodic subequivalence relations induced by a…

Let $X$ be a smooth scheme with an action of a reductive algebraic group $G$ over an algebraically closed field $k$ of characteristic zero. We construct an action of the extended affine Braid group on the $G$-equivariant absolute derived…

We prove Freudenburg's Freeness Conjecture: Let B be the polynomial ring in three variables over a field of characteristic zero, let D : B --> B be a nonzero locally nilpotent derivation, and let A = ker(D). Then B is a free A-module, and…

We derive a path-integral expression for the effective action in the continuum limit of an AFM Heisenberg spin ladder with an arbitrary number of legs. The map is onto an $O(3)$ nonlinear $\sigma$-model (NL$\sigma$M) with the addition of a…

Let $\ell$ be a prime, $k$ a finitely generated field of characteristic different from $\ell$, and $X$ a smooth geometrically connected curve over $k$. Say a semisimple representation of $\pi_1^{\mathrm{et}}(X_{\bar k})$ is arithmetic if it…

A closed subgroup $H$ of a locally compact group $G$ is confined if the closure of the conjugacy class of $H$ in the Chabauty space of $G$ does not contain the trivial subgroup. We establish a dynamical criterion on the action of a totally…

We show that the connection between partial breaking of supersymmetry and nonlinear actions is not accidental and has to do with constraints that lead directly to nonlinear actions of the Born-Infeld type. We develop a constrained…

We generalize a construction of Freudenburg and Moser-Jauslin in order to obtain an example of a non-linearizable action of a commutative reductive algebraic group on the affine space for every field of characteristic zero which admits a…

Let $M$ be a finite dimensional topological aspherical manifold whose universal cover is ${\bf R}^n$. In this paper, we study $Aff(M)$, the subgroup of the group of homeomorphisms of $M$, whose elements can be lifted to affine…

Let G be a finite group. We explore the model theoretic properties of the class of differential fields of characteristic zero in m commuting derivations equipped with a G-action by differential field automorphisms. In the language of…

Let k be a field, and A a finite-dimensional k-algebra. Let d be an integer. Denote by Gr(d,A) the Grassmannian of d-subspaces of A (viewed as a k-vector space), and by GL_1(A) the algebraic k-group whose points are invertible elements of…

Let A be an associative algebra of arbitrary dimension over a field F and G a finite soluble group of automorphisms of A oforder n, prime to the characteristic of F. We prove that if the fixed-point subalgebra of A under the action of G…

We give some natural conditions on actions of discrete countable groups on abelian locally compact groups of Lie type that imply factoriality of the group von Neumann algebras of their semidirect products. This allows us to give a fairly…

A theorem of Glasner from 1979 shows that if $A \subset \mathbb{T} = \mathbb{R}/\mathbb{Z}$ is infinite then for each $\epsilon > 0$ there exists an integer $n$ such that $nA$ is $\epsilon$-dense and Berend-Peres later showed that in fact…

In this work, we address ergodicity of smooth actions of finitely generated semi-groups on an m-dimensional closed manifold M. We provide sufficient conditions for such an action to be ergodic with respect to the Lebesgue measure. Our…