Related papers: Periods of Limit Mixed Hodge Structures
Classical polylogarithms give rise to a variation of mixed Hodge-Tate structures on the punctured projective line $S=\mathbb{P}^1\setminus \{0, 1, \infty\}$, which is an extension of the symmetric power of the Kummer variation by a trivial…
We extend the relative theory of admissible pairs and $p$-adic Hodge structures introduced in Part II to allow variation in the underlying local systems of $\mathbb{Q}_p$-vector spaces and isocrystals. This extension accommodates, in…
These are the notes for the talk "Hodge numbers of a hypothetical complex structure on $S^6$" given by the author at the MAM1 "(Non)-existence of complex structures on $S^6$" held in Marburg in March 2017. They are based on [A. Gray, A…
In a recent work, the author has constructed two families of algebraic cycles in Bloch cycle algebra over the prjective line minus 3 points that are expected to correspond to multiple polylogarithms in one variable and have a good…
We study a period map for triple coverings of $\mathbf P^2$branching along special configurations of $6$ lines. Though the moduli space of special configurations isa two dimensional variety,the minimal models of the coverings form a…
We investigate a relationship between a particular class of two-dimensional integrable non-linear $\sigma$-models and variations of Hodge structures. Concretely, our aim is to study the classical dynamics of the $\lambda$-deformed $G/G$…
We express total set of rational Gromov-Witten invariants of projective spaces via periods of variations of semi-infinite Hodge structure associated with their mirror partners.
The present note is devoted to an amendment to a recent paper of Ellenberg, Lawrence and Venkatesh. Roughly speaking, the main result here states the subpolynomial growth of the number of integral points with bounded height of a variety…
This text is the write-up of a series of lectures on the asymptotic mixed Hodge theory of isolated hypersurface singularities, held at the Third Latin American school on Algebraic Geometry and its applications (ELGA 3) in Guanajuato,…
In this note, we study a certain class of trigonometric series which is important in many problems. An unproved statement in Zygmund's book [5] will be proved and generalized. Further discussions based on this problem will also be made…
We define and construct mixed Hodge structures on real schematic homotopy types of complex projective varieties, giving mixed Hodge structures on their homotopy groups and pro-algebraic fundamental groups. We also show that these split on…
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,…
Information Theoretic analysis of the periods of a hyperelliptic curve provides more information about the well--known but abstract relationship between the branch points and the periods. Here one constructs a canonical homology basis for a…
Over the past fifteen years or so, Minhyong Kim has developed a framework for making effective use of the fundamental group to bound (or even compute) integral points on hyperbolic curves. This is the third installment in a series whose…
This is primarily an expository piece and the first sentence of the introduction pretty much sums it up: This article is aimed at people who already know what mixed Hodge structures are and what they are good for, but who are not sure how…
We give a way of constructing real variations of mixed Hodge structures over compact K\"ahler manifolds by using mixed Hodge structures on Sullivan's $1$-minimal models of certain differential graded algebras associated with real variations…
We exhibit a precise connection between N\'eron--Tate heights on smooth curves and biextension heights of limit mixed Hodge structures associated to smoothing deformations of singular quotient curves. Our approach suggests a new way to…
We discuss the variations of mixed Hodge structure for cohomology with compact support of quasi-projective simple normal crossing pairs. We show that they are graded polarizable admissible variations of mixed Hodge structure. Then we prove…
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…
Recently, the author defined multiple Dedekind zeta values [5] associated to a number K field and a cone C. These objects are number theoretic analogues of multiple zeta values. In this paper we prove that every multiple Dedekind zeta value…