Related papers: A note on formal periods
In this paper, we give a natural construction of mixed Tate motives whose periods are a class of iterated integrals which include the multiple polylogarithm functions. Given such an iterated integral, we construct two divisors $A$ and $B$…
We define and study the space of mixed modular symbols for a given finite index subgroup $\Gamma$ of $SL_2(\mathbf{Z})$. This is an extension of the usual space of modular symbols, which in some cases carries more information about…
This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…
We first give a geometric construction of a 2-dimensional mixed motive over $\mathbb{Q}$ with the Catalan constant $\mathbf{G}=1-1/3^2+1/5^2-1/7^2+\cdots$ as a period. We then use this motive to obtain a supply of linear forms in 1 and…
We formulate the problem of renormalization of Feynman integrals and its relation to periods of motives in configuration space instead of momentum space. The algebro-geometric setting is provided by the wonderful compactifications of…
The purpose of this paper is to show that, under certain combinatorial conditions on the graph, parametric Feynman integrals can be realized as periods on the complement of the determinant hypersurface in an affine space depending on the…
Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce…
We establish a correspondence between (fragments of) $\mathcal{TEL}^\bigcirc$, a temporal extension of the $\mathcal{EL}$ description logic with the LTL operator $\bigcirc^k$, and some specific kinds of formal grammars, in particular,…
We define various formal moduli spaces of p-divisible groups which are regular, and morphisms between them. We formulate arithmetic transfer conjectures, which are variants of the arithmetic fundamental lemma conjecture of the third author…
Every system in physics is described in terms of interacting elementary particles characterized by modulated spacetime recurrences. These intrinsic periodicities, implicit in undulatory mechanics, imply that every free particle is a…
This is my habilitation thesis. As the tradition wants, I tried to give an introduction of my field of research. I post it on the ArXiv with the hope it can be useful to young researchers looking for a short and friendly text on…
Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have…
We show that, for an arrangement of subspaces in a complex vector space with geometric intersection lattice, the complement of the arrangement is formal. We prove that the Morgan rational model for such an arrangement complement is formal…
We answer some enumerative questions about irreducible rational curves on Hirzebruch surfaces, by combining an idea of Kontsevich with the study of the geometry of certain natural parameter spaces. Our formulas generalize Kontsevich's…
We define motivic multiple polylogarithms and prove the double shuffle relations for them. We use this to study the motivic fundamental group of the multiplicative group - {N-th roots of unity} and relate it to geometry of modular…
The time ordering of two spacelike separated events is arbitrary, when all inertial frames are taken into account, but for three or more events it is not generally so. We determine the structure of possible time orderings, or chronologies,…
Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit…
Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…
We define a category of motives for semi-algebraic spaces and show that it is trivial. This implies that there is no good extension of algebraic de Rham cohomology to semi-algebraic spaces compatible with the period isomorphism.
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…