Related papers: Polylogarithms, regulators and Arakelov motivic co…

We introduce a family of matrix dilogarithms, which are automorphisms of C^N tensor C^N, N being any odd positive integer, associated to hyperbolic ideal tetrahedra equipped with an additional decoration. The matrix dilogarithms satisfy…

Polylogarithms are those multiple polylogarithms that factor through a certain quotient of the de Rham fundamental group of the thrice punctured line known as the polylogarithmic quotient. Building on work of Dan-Cohen, Wewers, and Brown,…

We introduce a new geometric object, the correlahedron, which we conjecture to be equivalent to stress-energy correlators in planar N=4 super Yang-Mills. Re-expressing the Grassmann dependence of correlation functions of n chiral…

We show how to make the additive Chow groups of Bloch-Esnault, Ruelling and Park into a graded module for Bloch's higher Chow groups, in the case of a smooth projective variety over a field. This yields a a projective bundle formula as well…

We define higher polyhedral K-groups for commutative rings, starting from the stable groups of elementary automorphisms of polyhedral algebras. Both Volodin's theory and Quillen's + construction are developed. In the special case of…

The goal of this paper is to define a certain Chow weight structure for the category of Voevodsky's motivic complexes with integral coefficients (as described by Cisinski and Deglise) over any excellent finite-dimensional separated scheme…

For a smooth manifold X of dimension <d we construct a homomorphism from the algebraic K-theory group in degree d of the algebra of smooth functions on X to the degree -d-1 topological K-theory of X with coefficients in C/Z. This map…

We use a theorem of Tolman and Weitsman to find explicit formul\ae for the rational cohomology rings of the symplectic reduction of flag varieties in C^n, or generic coadjoint orbits of SU(n), by (maximal) torus actions. We also calculate…

This paper is an introduction to classical polylogarithms and is an expanded version of a talk given by the author at the Motives conference. Topics covered include, monodromy; the polylogarithm local systems; Bloch's constructions of…

This paper is a sequel to our earlier paper "Wach modules and Iwasawa theory for modular forms" (arXiv: 0912.1263), where we defined a family of Coleman maps for a crystalline representation of the Galois group of Qp with nonnegative…

It was shown in \cite{FPV} that the classification of $n$-component systems of conservation laws possessing a third-order Hamiltonian structure reduces to the following algebraic problem: classify $n$-planes $H$ in $\wedge^2(V_{n+2})$ such…

The main goal of this paper is to define the so-called Chow weight structure for the category of Beilinson motives over any 'reasonable' base scheme $S$ (this is the version of Voevodsky's motives over $S$ defined by Cisinski and Deglise).…

We show that the knowledge of the Dirichlet-to-Neumann map on the boundary of a bounded open set in $\mathbb R^n$, $n\ge 3$, for the perturbed polyharmonic operator $(-\Delta)^m+A\cdot D+q$, $m\ge 2$, with $n>m$, $A\in…

The algebraic approach to the construction of the reflexive polyhedra that yield Calabi-Yau spaces in three or more complex dimensions with K3 fibres reveals graphs that include and generalize the Dynkin diagrams associated with gauge…

Associated to a convex integral polygon $N$ is a cluster integrable system $\mathcal X_N$ constructed from the dimer model. We compute the group $G_N$ of symmetries of $\mathcal X_N$, called the (2-2) cluster modular group, showing that it…

We use cluster structures and mirror symmetry to explicitly describe a natural class of Newton-Okounkov bodies for Grassmannians. We consider the Grassmannian $X=Gr_{n-k}(\mathbb C^n)$, as well as the mirror dual Landau-Ginzburg model…

The projective linear group $\text{PGL}(3)$ naturally acts on the Grassmannian $\text{Gr}(3, V_2)$ of $3$-dimensional subspaces of the vector space $V_2$ of homogeneous conics in 3 variables. It was proved by Abdallah, Emsalem and Iarrobino…

In this paper we study the group K_{2n}^{(n+1)}(F) where F is the function field of a complete, smooth, geometrically irreducible curve C over a number field, assuming the Beilinson--Soul\'e conjecture on weights. In particular, we compute…

We introduce a notion of lexicographic shellability for pure, balanced boolean cell complexes, modelled after the $CL$-shellability criterion of Bj\"orner and Wachs for posets and its generalization by Kozlov called $CC$-shellability. We…

In this paper we construct arbitrarily large families of smooth projective varieties and closed Riemannian manifolds that share many algebraic and analytic invariants. For instance, every non-arithmetic, closed hyperbolic $3$--manifold…