Related papers: Classical and motivic Adams charts

We exhibit a relationship between motivic homotopy theory and spectral algebraic geometry, based on the motivic $\tau$-deformation picture of Gheorghe, Isaksen, Wang, Xu. More precisely, we identify cellular motivic spectra over $\mathbf C$…

For a variety with a Whitney stratification by affine spaces, we study categories of motivic sheaves which are constant mixed Tate along the strata. We are particularly interested in those cases where the category of mixed Tate motives over…

We construct well-behaved extensions of the motivic spectra representing generalized motivic cohomology and connective Balmer--Witt K-theory (among others) to mixed characteristic Dedekind schemes on which 2 is invertible. As a consequence…

This article has two purposes. The first is to give an expository account of the integrable systems approach to harmonic maps from surfaces to Lie groups and symmetric spaces, focusing on spectral curves for harmonic 2-tori. The most…

The bienergy of smooth maps between Riemannian manifolds, when restricted to unit vector fields, yields two different variational problems depending on whether one takes the full functional or just the vertical contribution. Their critical…

The symmetries of complex molecular structures can be modeled by the {\em topological symmetry group} of the underlying embedded graph. It is therefore important to understand which topological symmetry groups can be realized by particular…

Let $\mathfrak{A}$ be a finite abelian group. In this article, we classify harmonic $\mathfrak{A}$-covers of a tropical curve $\Gamma$ (which allow dilation along edges and at vertices) in terms of the cohomology group of a suitably defined…

Numerical semigroups have been extensively studied throughout the literature, and many of their invariants have been characterized. In this work, we generalize some of the most important results about symmetry, pseudo-symmetry, or…

Let X and Y be CW-complexes, U be an abelian group, and f:[X,Y]->U be a map (a homotopy invariant). We say that f has order at most r if the characteristic function of the r'th Cartesian power of the graph of a continuous map a:X->Y…

The article [14] gives a list of 51 symplectic hypergeometric monodromy groups corresponding to primitive pairs of degree four polynomials, which are products of cyclotomic polynomials, and for which, the absolute value of the leading…

We determine the number of labelled chordal planar graphs with $n$ vertices, which is asymptotically $c_1\cdot n^{-5/2} \gamma^n n!$ for a constant $c_1>0$ and $\gamma \approx 11.89235$. We also determine the number of rooted simple chordal…

Let k be an infinite perfect field. We provide a general criterion for a spectrum in the stable homotopy category over k to be effective, i.e. to be in the localizing subcategory generated by the suspension spectra of smooth schemes. As a…

We prove that for any two closed Riemannian manifolds $M^{2m}$ ($m\geq 1$) and $N$, there exists a minimizing (extrinsic) $m$-polyharmonic map for every free homotopy class in $[M^{2m}, N]$, provided that the homotopy group $\pi_{2m}(N)$ is…

We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…

The notion of $\times$-homotopy from \cite{DocHom} is investigated in the context of the category of pointed graphs. The main result is a long exact sequence that relates the higher homotopy groups of the space $\Hom_*(G,H)$ with the…

We give an explicit construction of the p-adic de Rham comparison isomorphism for 1-motives. In particular, we prove that our construction recovers the classical de Rham comparison isomorphism and is functorial with respect to morphisms of…

Harmonic maps are nonlinear extensions of harmonic functions. They are critical points of natural energy functionals between Riemannian manifolds. Such type of problems appear in Physics, Geometry of Finance and the study of regularity and…

We prove a general homological stability theorem for certain families of groups equipped with product maps, followed by two theorems of a new kind that give information about the last two homology groups outside the stable range. (These…

We construct Toda brackets in unstable motivic homotopy theory and prove some fundamental properties of them. Furthermore we construct some examples of motivic Toda brackets.

We study algebras encoding stable range branching rules for the pairs of complex classical groups of the same type in the context of toric degenerations of spherical varieties. By lifting affine semigroup algebras constructed from…