Related papers: Numerical functors on Voevodsky's motives
A systematic study of the relations between fluctuations of the extensive multiparticle variables and integrals of the inclusive multipaticle densities is analysed. The generalized factorial moments are introduced and their physical meaning…
We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
We discuss several conjectures about the real-rootedness of polynomials whose coefficients are determinants of coefficients of a real-rooted polynomial. We also consider some questions about matrices generalizing totally positive matrices,…
In this article we further the study of the relationship between pure motives and noncommutative motives. Making use of Hochschild homology, we introduce the category NNum(k)_F of noncommutative numerical motives (over a base ring k and…
We develop a "motivic integration" version of the Poisson summation formula for function fields, with values in the Grothendieck ring of definable exponential sums. We also study division algebras over the function field, and obtain…
We describe simple criteria under which a given functor is naturally equivalent to an enriched one. We do this for several bases of enrichment, namely (pointed) simplicial sets, (pointed) topological spaces and orthogonal spectra. We also…
This article shows that under general conditions, p-adic orbital integrals of definable functions are represented by virtual Chow motives. This gives an explicit example of the philosophy of Denef and Loeser, which predicts that all…
The zeta function of a motive over a finite field is multiplicative with respect to the direct sum of motives. It has beautiful analytic properties, as were predicted by the Weil conjectures. There is also a multiplicative zeta function,…
In this paper we study Chow motives whose identity map is killed by a natural number. Examples of such objects were constructed by Gorchinskiy-Orlov. We introduce various invariants of torsion motives, in particular, the $p$-level. We show…
Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…
Algorithms and underlying mathematics are presented for numerical computation with periodic functions via approximations to machine precision by trigonometric polynomials, including the solution of linear and nonlinear periodic ordinary…
We introduce a $q$-analog of the higher continued fractions introduced by the last three authors in a previous work (together with Gregg Musiker), which are simultaneously a generalization of the $q$-rational numbers of Morier-Genoud and…
Based on a new coinductive characterization of continuous functions we extract certified programs for exact real number computation from constructive proofs. The extracted programs construct and combine exact real number algorithms with…
The aim of this work is to develop a theory parallel to that of motivic complexes based on cycles and correspondences with coefficients in quadratic forms. This framework is closer to the point of view of $\mathbb{A}^1$-homotopy than the…
Taking a quotient roughly means changing the notion of equality on a given object, set or type. In a quantitative setting, equality naturally generalises to a distance, measuring how much elements are similar instead of just stating their…
We define notions of regularity and (Barr-)exactness for 2-categories. In fact, we define three notions of regularity and exactness, each based on one of the three canonical ways of factorising a functor in Cat: as (surjective on objects,…
Building on work by Dan-Cohen--Wewers, Dan-Cohen [DC], and Brown, we push the computational boundary of our explicit motivic version of Kim's method in the case of the thrice punctured line over an open subscheme of Spec ZZ. To do so, we…
We explore computational tools that allow to compute the class on the Grothendieck ring of varieties of finite cyclic quotients in some interesting examples. As an main application, we determine the motive of low rank representation…
We study the conjecture claiming that, over a flexible field, isotropic Chow groups coincide with numerical Chow groups (with ${\Bbb{F}}_p$-coefficients). This conjecture is essential for understanding the structure of the isotropic motivic…