Related papers: What is a period ?
We present a general conjecture on the divisibility of a certain expression in terms of Kostka numbers and their close variants. This conjecture is closely related to a variant of the period-index problem of noncommutative algebra, with…
We show that coefficients in the Laurent series of Igusa Zeta functions are periods. This will be used in a subsequent paper (by P. Brosnan) to show that certain numbers occurring in study of Feynman amplitudes (upto gamma factors) are…
We define a 1-cocycle in the space of long knots that is a natural generalization of the Kontsevich integral seen as a 0-cocycle. It involves a 2-form that generalizes the Knizhnik--Zamolodchikov connection. We show that the well-known…
Nekrashevych conjectured that the iterated monodromy groups of quadratic polynomials with preperiodic critical orbit have intermediate growth. We illustrate some of the difficulties that arise in attacking this conjecture and prove…
We study conjectures of Ben-Zvi--Sakellaridis--Venkatesh that categorify the relationship between automorphic periods and $L$-functions in the context of the Geometric Langlands equivalence. We provide evidence for these conjectures in some…
We study the periods mapping from the moduli space of real hyperelliptic curves with marked point on an oriented oval to the euclidean space. The mapping arises in the analysis of Chebyshev construction used in the constrained optimization…
It is proved that a certain type of monotone flow has a global period provided periodic points are dense.
The examples of rhythmical signals with variable period are considered. The definition of periodic function with the variable period is given as a model of such signals. The examples of such functions are given and their variable periods…
The second part of a set of notes based on lectures given at the IHES in 2015 on Feynman amplitudes and motivic periods.
We present period domains of complex Hodge structures and some of their basic properties from representation theory point of view. Specifically we introduce the automorphic cohomology of period domains and the complex structure on symmetric…
Multiple zeta values (MZVs for short) can be represented as iterated integrals of $\mathbb{Q}$-rational algebraic differential forms on $\mathbb{P}^1(\mathbb{C})\setminus\{0, 1, \infty\}$. This interpretation allows us to consider MZVs…
We consider multiple zeta values, which are periods of mixed Tate motives over $\mathbb Z$. For a given multiple zeta value $\zeta$, there exists a unique minimal motive $M(\zeta)$ such that $\zeta$ is a period of $M(\zeta)$. In general,…
The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical…
We study algebraic aspects of Kontsevich integrals as generating functions for intersection theory over moduli space and review the derivation of Virasoro and KdV constraints. 1. Intersection numbers 2. The Kontsevich integral 2.1. The main…
Euler sums (also called Zagier sums) occur within the context of knot theory and quantum field theory. There are various conjectures related to these sums whose incompletion is a sign that both the mathematics and physics communities do not…
In April, 2006, Kontsevich asked me whether the category of motives over F_p (p prime) has a fibre functor over a number field of finite degree since he had a conjecture that more-or-less implied this. This article is my response.…
This is an English translation of the paper in which N. I. Akhiezer discovered his famous orthogonal polynomials on two intervals in a connection with a generalization of the Korkin-Zolotarev (Korkine-Zolotaref) problem (see the small…
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…
The equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and…
Personal recollections about Alexandre Grothendieck and early days of his theory of motives