Related papers: Heights and arithmetic dynamics over finitely gene…

Period domains, the classifying spaces for (pure, polarized) Hodge structures, and more generally Mumford-Tate domains, arise as open $G_{\mathbb{R}}$--orbits in flag varieties $G/P$. We investigate Hodge--theoretic aspects of the geometry…

Let K be a function field, let f be a rational function of degree d at least 2 defined over K, and suppose that f is not isotrivial. In this paper, we show that a point P in P^1(Kbar) has f-canonical height zero if and only if P is…

We prove upper bounds on the face numbers of simplicial complexes in terms on their girths, in analogy with the Moore bound from graph theory. Our definition of girth generalizes the usual definition for graphs.

In this article we study homotopes of finite-dimensional algebras (not necessarily, associative). In the case of associative algebras we study homotopes by methods of Category theory and give description of so-called well-tempered elements…

Let R be a locally finitely generated algebra over a discrete valuation ring V of mixed characteristic. For any of the homological properties, the Direct Summand Theorem, the Monomial Theorem, the Improved New Intersection Theorem, the…

A polarizable endomorphism on a projective variety enables us to consider given morphism as constant multiplication in the height function. In this paper, we will generalize it for arbitrary dominant endomorphism by defining the height…

We give a formula with explicit error term for the number of $K$-rational points $P$ satisfying $H(f(P)) \le X$ as $X \to \infty$, where $f$ is a nonconstant morphism between projective spaces defined over a number field $K$ and $H$ is the…

We show that a finite collection of stable subgroups of a finitely generated group has finite height, finite width and bounded packing. We then use knowledge about intersections of conjugates to characterize finite families of…

Various extensions of standard inflationary models have been proposed recently by adding vector fields. Because they are generally motivated by large-scale anomalies, and the possibility of statistical anisotropy of primordial fluctuations,…

In this paper we consider the complex vector spaces of holomorphic cross-sections of homogeneous holomorphic vector bundles over elliptic adjoint orbits, and provide a sufficient condition for the vector spaces to be finite dimensional in…

We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…

In this paper, we study multiplicative dependence of values of polynomials or rational functions over a number field. As an application, we obtain new results on multiplicative dependence in the orbits of a univariate polynomial dynamical…

Let K be a p-adic field and let F and G be two formal groups over O_K. We prove that if F and G have infinitely many torsion points in common, then F=G. This follows from a rigidity result: any bounded power series that sends infinitely…

We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in…

We provide a construction of the fixed points of functors which may not be inital algebras or final coalgebras. For an endofunctor F, this fixed point construction may be expressed as a pair of adjoint functors between F-coalgebras and…

A momentum dependent projection of the Wegner-Hougton equation is derived for a scalar theory coupled to an external field. This formalism is useful to discuss the phase diagram of the theory. In particular we study some properties of the…

One-dimensional interacting particle systems, 1+1 random growth models, and two-dimensional directed polymers define 2d height fields. The KPZ universality conjecture posits that an appropriately scaled height function converges to a…

We give necessary and sufficient conditions for a family of inner products in a finite-dimensional vector space $V$ over an arbitrary field $\mathbb{K}$ to have an orthogonal basis relative to all the inner products. Some applications to…

Let $S$ be a set of dominant rational self-maps on $\mathbb{P}^N$. We study the arithmetic and dynamical degrees of infinite sequences of $S$ obtained by sequentially composing elements of $S$ on the right and left. We then apply this…

We prove the first inverse theorem for point--sphere incidence bounds over finite fields in dimensions $d \ge 3$, showing that near-extremality forces algebraic rigidity. While sharp upper bounds have been known for over a decade, the…