相关论文: Multizeta values: Lie algebras and periods on $\ma…

This report outlines a combinatorial recipe for computing the bases, whose elements are oriented polygons, of two cohomology spaces associated to multizeta values: the top dimensional de Rham cohomology of moduli spaces of genus 0 complex…

In this paper, we introduce cell-forms on $\mathcal{M}_{0,n}$, which are top-dimensional differential forms diverging along the boundary of exactly one cell (connected component) of the real moduli space $\mathcal{M}_{0,n}(\mathbb{R})$. We…

Multiple zeta values have been studied by a wide variety of methods. In this article we summarize some of the results about them that can be obtained by an algebraic approach. This involves "coding" the multiple zeta values by monomials in…

In this paper we prove a conjecture due to Goncharov and Manin which states that the periods of the moduli spaces $\mathfrak{M}_{0,n}$ of Riemann spheres with $n$ marked points are multiple zeta values. In order to do this, we introduce a…

The values at 1 of single-valued multiple polylogarithms span a certain subalgebra of multiple zeta values. In this paper, the properties of this algebra are studied from the point of view of motivic periods.

We study the depth filtration on multiple zeta values, the motivic Galois group of mixed Tate motives over $\mathbb{Z}$ and the Grothendieck-Teichm\"uller group, and its relation to modular forms. Using period polynomials for cusp forms for…

The algebra of big zeta values we introduce in this paper is an intermediate object between multiple zeta values and periods of the multiple zeta motive. It consists of number series generalizing multiple zeta values, the simplest examples,…

In this paper, we consider the versal deformations of three dimensional Lie algebras. We classify Lie algebras and study their deformations by using linear algebra techniques to study the cohomology. We will focus on how the deformations…

Polyzetas, indexed by words, satisfy shuffle and quasi-shuffle identities. In this respect, one can explore the multiplicative and algorithmic (locally finite) properties of their generating series. In this paper, we construct pairs of…

We give a natural construction of unramified over Z framed mixed Tate motives, whose periods are the multiple zeta values. Namely, for each convergent multiple zeta-value we define two boundary divisors A and B in the moduli space M_{0,n+3}…

This paper is a review of concepts from graded commutative algebra with specific attention given to length and multiplicity. The author's motivation for this paper comes from the study of equivariant cohomology in algebraic topology where…

Some combinatorial aspects of relations between multiple zeta values of depths 2 and 3 and period polynomials are discussed.

In previous work, we established a duality between the algebraic de Rham cohomology of a flat algebraic connection on a smooth quasi-projective surface over the complex numbers and the rapid decay homology of the dual connection relying on…

Interpolated multiple zeta values can be regarded as interpolation polynomials of multiple zeta values and multiple zeta-star values. In this paper, we give some algebraic relations of interpolated multiple zeta values, such as the…

The linearized double shuffle Lie algebra $\mathfrak{ls}$ is a well-studied Lie algebra, which reflects the depth-graded structure of multiple zeta values. We introduce a generalization $\mathfrak{lq}$, which is motivated from the…

The linearized double shuffle Lie algebra introduced by Brown reflects the depth-graded structure of multiple zeta values. In a previous paper, the first author introduced an extension of this Lie algebra that accommodates multiple q-zeta…

In this paper, we study the multiple $L$-values and the multiple zeta values of level $N$. We set up the algebraic framework for the double shuffle relations of the multiple zeta values of level $N$. Using the regularized double shuffle…

We introduce an algebra which describes the multiplication structure of a family of q-series containing a q-analogue of multiple zeta values. The double shuffle relations are formulated in our framework. They contain a q-analogue of…

We study sheaves on holomorphic spaces of loops and apply this to the study of the complex, defined in \cite{BdSHK}, governing deformations of the \emph{Poisson vertex algebra} structure on the space of holomorphic loops into a Poisson…

In this dissertation, we investigate the cohomology theory of restricted Lie algebras. The representation theory of restricted Lie algebras is reviewed including a description of the restricted universal enveloping algebra. In the case of…