Related papers: Strong Orbit Equivalence and Superlinear Complexit…

We derive the subleading soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. Our results are…

We investigate the $p$-essential normality of Hilbert quotient submodules on a relatively compact smooth strongly pseudoconvex domain in a complex manifold satisfying Property (S). For analytic subvarieties that have compact singularities…

We investigate compactifications with duality twists and their relation to orbifolds and compactifications with fluxes. Inequivalent compactifications are classified by conjugacy classes of the U-duality group and result in gauged…

Through highly non-constructive methods, works by Bestvina, Culler, Feighn, Morgan, Paulin, Rips, Shalen, and Thurston show that if a finitely presented group does not split over a virtually solvable subgroup, then the space of its discrete…

Let S=Sym(\Omega) be the group of all permutations of a countably infinite set \Omega, and for subgroups G_1, G_2\leq S let us write G_1\approx G_2 if there exists a finite set U\subseteq S such that < G_1\cup U > = < G_2\cup U >. It is…

Extending prior investigations, we study three of the the four distinct minimal (4,0) scalar multiplets coupled to (4,0) supergravity. It is found that the scalar multiplets manifest their differences at the component level by possessing…

Let X and Y be bounded multiply connected Lipschitz domains in \R^2. We consider the class H_p (X, Y) of homeomorphisms h : X -> Y in the Sobolev space W^{1,p} (X, \R^2). We prove that the weak and strong closures of H_p (X, Y), 2 \le p<…

Let F : P^n --> P^n be a morphism of degree d > 1 defined over C. The dynamical Mordell--Lang conjecture says that the intersection of an orbit O_F(P) and a subvariety X of P^n is usually finite. We consider the number of linear…

Let $X$ be an inner product space, let $G$ be a group of orthogonal transformations of $X$, and let $R$ be a bounded $G$-stable subset of $X$. We define very weak and very strong regularity for such pairs $(R,G)$ (in the sense of…

In this note, we prove that if G is a countable group that contains a nonabelian free subgroup then every pair of nontrivial Bernoulli shifts over G are weakly isomorphic.

It is shown that the set of orbits of the action of the elementary symplectic transvection group on all unimodular elements of a symplectic module over a commutative ring of characteristic not 2 is identical with the set of orbits of the…

We consider aspects of the relationship between nilpotent orbits in a semisimple real Lie algebra $\mathfrak{g}$ and those in its complexification $\mathfrak{g}_{\mathbb{C}}$. In particular, we prove that two distinct real nilpotent orbits…

We show that any clone over a finite domain that has a quasi Maltsev operation and fully symmetric operations of all arities has an incoming minion homomorphism from I, the clone of all idempotent operations on a two element set. We use…

For an affine spherical homogeneous space G/H of a connected semisimple algebraic group G, we consider the factorization morphism by the action on G/H of a maximal unipotent subgroup of G. We prove that this morphism is equidimensional if…

We determine upper bounds for the maximum order of an element of a finite almost simple group with socle T in terms of the minimum index m(T) of a maximal subgroup of T: for T not an alternating group we prove that, with finitely many…

An action of a group $G$ on a compact space $X$ is called weakly almost periodic if the orbit of every continuous function on $X$ is weakly relatively compact in $C(X)$. We observe that for a topological group $G$ the following are…

The relational complexity of a subgroup $G$ of $\mathrm{Sym}(\Omega)$ is a measure of the way in which the orbits of $G$ on $\Omega^k$ for various $k$ determine the original action of $G$. Very few precise values of relational complexity…

The universal enveloping algebra of any simple Lie algebra g contains a family of commutative subalgebras, called the quantum shift of argument subalgebras math.RT/0606380, math.QA/0612798. We prove that generically their action on…

Motivated by relating the representation theory of the split real and $p$-adic forms of a connected reductive algebraic group $G$, we describe a subset of $2^r$ orbits on the complex flag variety for a certain symmetric subgroup. (Here $r$…

We prove that, under suitable assumptions on a category C, the existence of supercompact cardinals implies that every absolute epireflective class of objects of C is a small-orthogonality class. More precisely, if L is a localization…