Related papers: Classification of stacked central configurations i…

We show that the category of mixed Hodge complexes admits a Cartan-Eilenberg structure, a notion introduced in [GNPR10] leading to a good calculation of the homotopy category in terms of (co)fibrant objects. This result provides a…

We expose the relation between the properties of the three-body continuum states and their two-body subsystems. These properties refer to their bound and virtual states and resonances, all defined as poles of the $S$-matrix. For one…

Central configurations are fundamental equilibrium solutions of the Newtonian $n$-body problem and play a key role in understanding the structure and dynamics of gravitational systems. However, the classification and enumeration of such…

Let $G$ be a discrete group. We prove that the category of $G$-posets admits a model structure that is Quillen equivalent to the standard model structure on $G$-spaces. As is already true nonequivariantly, the three classes of maps defining…

I introduce an extended configuration space for classical mechanical systems, called pair-space, which is spanned by the relative positions of all the pairs of bodies. To overcome the non-independence of this basis, one adds to the…

In this article we introduce a general definition of the concept of center of an $n$-gon, for $n\geq 3$, generalizing the idea of C. Kimberling for triangle. We define centers associated to functions instead of to geometrical properties. We…

We discuss geometric aspects of orbifold conformal field theories in the moduli space of N=(4,4) superconformal field theories with central charge c=6. Part of this note consists of a summary of our earlier results on the location of these…

Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This last one classifies the case of $a^3b$-quadrilaterals with some irrational angle: there are a sequence of…

We give a normal form for families of 3-dimensional Poisson structures. This allows us to classify singularities with nonzero 1-jet and typical bifurcations. The Appendix contains corollaries on classification of families of integrable…

We survey and expand on the work of Segal, Milgram and the author on the topology of spaces of maps of positive genus curves into $n$-th complex projective space, $n\geq 1$ (in both the holomorphic and continuous categories). Both based and…

We study systems of orientations on triples that satisfy the following so-called interiority condition: $\circlearrowleft(ABD)=~\circlearrowleft(BCD)=~\circlearrowleft(CAD)=1$ implies $\circlearrowleft(ABC)=1$ for any $A,B,C,D$. We call…

A symmetric planar central configuration of the Newtonian six-body problem $x$ is called cross central configuration if there are precisely four bodies on a symmetry line of $x$. We use complex algebraic geometry and Groebner basis theory…

Consider the focusing cubic semilinear Schroedinger equation in R^3 i \partial_t \psi + \Delta \psi + | \psi |^2 \psi = 0. It admits an eight-dimensional manifold of special solutions called ground state solitons. We exhibit a…

New expansionary and rotational quadratic forms are constructed for $E^n$-endomorphisms. Relations amongst the various eigenvalues, eigendirections and matrix invariants are established, including propositions on complexity and geometric…

We give a classification theorem for a relevant class of $t$-structures in triangulated categories, which includes in the case of the derived category of a Grothendieck category, the $t$-structures whose hearts have at most $n$ fixed…

In the theory of configuration spaces, "splitting" usually refers to the phenomenon that the configuration spaces on a manifold and those on its punctured version are closely related cohomologically. We prove a splitting theorem that is…

In the first work of this series [physics/0204035] it was shown that the conformational space of a molecule could be described to a fair degree of accuracy by means of a central hyperplane arrangement. The hyperplanes divide the espace into…

In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal masses. This is accomplished by using the polyhedral homotopy method to approximate all the isolated solutions of…

We introduce the cotangent universal hierarchy that extends the so-called universal hierarchy (as for the latter, see e.g. arXiv:nlin/0202008, arXiv:nlin/0312043 and arXiv:nlin/0310036). Then we construct a (2+1)-dimensional double central…

A new class of non-linear O(3) models is introduced. It is shown that these systems lead to integrable submodels if an additional integrability condition (so called the generalized eikonal equation) is imposed. In the case of particular…