Related papers: Regulators

We obtain results describing the behavior of the action of rotation generators on polynomials over a commutative ring. We also explore harmonic polynomials in a purely algebraic setting.

Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…

We use the theory of motivic integration in order to give a geometric explanation of the behavior of some p-adic integrals.

We discuss some examples of geometrically meaningful rational self-maps of moduli space of curves of low genus and homogeneous forms.

Over a field of characteristic zero, we construct a De Rham motivic complex and generalize the De Rham cohomology of a smooth variety to any Voevodsky motive.

We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the…

We consider equations arising from rational Lax representations. A general method to construct recursion operators for such equations is given. Several examples are given, including a degenerate bi-Hamiltonian system with a recursion…

The modeling framework of port-Hamiltonian systems is systematically extended to constrained dynamical systems (descriptor systems, differential-algebraic equations). A new algebraically and geometrically defined system structure is…

We describe derived moduli functors for a range of problems involving schemes and quasi-coherent sheaves, and give cohomological conditions for them to be representable by derived geometric n-stacks. Examples of problems represented by…

We study the dynamical properties of small regulatory networks treated as non autonomous dynamical systems called modules when working inside larger networks or, equivalently when subject to external signal inputs. Particular emphasis is…

We construct the motivic t-structure on 1-motives with integral coefficients over a scheme of characteristic zero or a Dedekind scheme. When we invert the residue characteristic exponents of the base, this t-structure induces a t-structure…

A mechanism deriving new well-posed evolutionary equations from given ones is inspected. It turns out that there is one particular spatial operator from which many of the standard evolutionary problems of mathematical physics can be…

We present a list of algebraic, combinatorial, and analytic mechanisms that give rise to determinantal point processes.

We present an introduction to the derived and relative resolutions of the moduli of stable maps. We discuss one application and mention a few problems.

This paper is an introduction to classical polylogarithms and is an expanded version of a talk given by the author at the Motives conference. Topics covered include, monodromy; the polylogarithm local systems; Bloch's constructions of…

Dirac structures and Morse families are used to obtain a geometric formalism that unifies most of the scenarios in mechanics (constrained calculus, nonholonomic systems, optimal control theory, higher-order mechanics, etc.), as the examples…

For a finite dimensional vector space equipped with a $\mathbb C$-algebra structure, one can define rational maps using the algebraic structure. In this paper, we describe the growth of the degree sequences for this type of rational maps.

A new class of structured matrices is presented and a closed form formula for their determinant is established. This formula has strong connections with the one for Vandermonde matrices.

We construct a version of Beilinson's regulator as a map of sheaves of commutative ring spectra and use it to define a multiplicative variant of differential algebraic K-theory. We use this theory to give an interpretation of Bloch's…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…