Related papers: Heights and arithmetic dynamics over finitely gene…
Statistical properties of evolving random graphs are analyzed using kinetic theory. Treating the linking process dynamically, structural characteristics such as links, paths, cycles, and components are obtained analytically using the rate…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
A theory of higher colimits over categories of free presentations is developed. It is shown that different homology functors such as Hoshcshild and cyclic homology of algebras over a field of characteristic zero, simplicial derived…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
$V$ is a complete intersection scheme in a multiprojective space if it can be defined by an ideal $I$ with as many generators as $\textrm{codim}(V)$. We investigate the multigraded regularity of complete intersections scheme in…
The paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on categories with finite limits and colimits. As an…
We consider the problem of explicitly computing Beilinson--Bloch heights of homologically trivial cycles on varieties defined over number fields. Recent results have established a congruence, up to the rational span of logarithms of primes,…
Let F be a function field of one variable over an algebraically closed field of characteristic zero, X a geometrically irreducible smooth projective variety over F, and L a line bundle on X. In this note, we will prove that if the…
We study questions inspired by Erd\H os' celebrated distance problems with dot products in lieu of distances, and for more than a single pair of points. In particular, we study point configurations present in large finite point sets in the…
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
A periodic connection is constructed for a double well potential defined in the plane. This solution violates Modica's estimate as well as the corresponding Liouville Theorem for general phase transition potentials. Gradient estimates are…
We compute the behaviour of Hodge data under additive middle convolution for irreducible variations of polarized complex Hodge structures on punctured complex affine lines.
Equidistribution of the orbits of points, subvarieties or of periodic points in complex dynamics is a fundamental problem. It is often related to strong ergodic properties of the dynamical system and to a deep understanding of analytic…
We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…
In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the…
Height-offset variables (HOVs) provide a mechanism, known as "pinning at infinity", to lift gradient Gibbs measures (GGMs) - describing interface increments - to proper Gibbs measures that describe absolute heights. Starting from…
We exhibit invariants of smooth projective algebraic varieties with integer values, whose nonvanishing modulo p prevents the existence of an action without fixed points of certain finite p-groups. The case of base fields of characteristic p…
For a representation of a finite group $G$ on a complex vector space $V$ we determine when a holomorphic $\binom{p}{q}$-tensor field on the principle stratum of the orbit space $V/G$ can be lifted to a holomorphic $G$-invariant tensor field…
We discuss and prove a number of results for calculating characteristic cycles, or graded, enriched characteristic cycles. We concentrate particularly on results related to hypersurfaces.
The Collatz Conjecture's connection to dynamical systems opens it to a variety of techniques aimed at recurrence and density results. First, we turn to density results and strengthen the result of Terras through finding a strict rate of…