Related papers: Semiholonomic jets and induced modules in Cartan g…
In the 1990s, P. Vanhecke described a Hamiltonian system with two degrees of freedom and a polynomial Hamiltonian integrable in Abelian functions of two variables. This system provides a convenient example of an integrable system in which…
In the framework of sub-Riemannian Manifolds, a relevant question is: what are the \enquote{metric lines} (i.e., the isometric embedding of the real line)? This article presents a conjecture classifying the metric lines in Carnot groups and…
There is a mysterious connection between the multiple polylogarithms at N-th roots of unity and modular varieties. In this paper we "explain" it in the simplest case of the double logarithm. We introduce an Euler complex data on modular…
We consider the germ of a reduced curve, possibly reducible. F.Delgado de la Mata proved that such a curve is Gorenstein if and only if its semigroup of values is symmetrical. We extend here this symmetry property to any fractional ideal of…
Fargues-Scholze developed a framework for the geometric Langlands program on the Fargues-Fontaine curve. In particular, they proved the geometric Satake equivalence on the moduli space of closed Cartier divisors on the curve. We prove the…
We describe noncommutative geometric aspects of twisted deformations, in particular of the spheres in Connes and Landi [8] and in Connes and Dubois Violette [7], by using the differential and integral calculus on these spaces that is…
In the late nineteenth century, Felix Klein revived the problem of solving the quintic equation from the moribund state into which Galois had placed it. Klein's approach was a mix of algebra and geometry built on the structure of the…
On a $3$D manifold, a Weyl geometry consists of pairs $(g, A) =$ (metric, $1$-form) modulo gauge $\widehat{g} = {\rm e}^{2\varphi} g$, $\widehat{A} = A + {\rm d}\varphi$. In 1943, Cartan showed that every solution to the Einstein-Weyl…
We show that for every complex simple Lie algebra, the equations of Schubert divisors on the flag variety give a complete integrable system of the minimal nilpotent orbit. The approach is motivated by the integrable system on Coulomb…
In principle, the local classification of spacetimes is always possible using the Cartan-Karlhede algorithm. However, in practice, the process of determining equivalence of two spacetimes is potentially computationally difficult or not at…
Mechanical systems naturally evolve on principal bundles describing their inherent symmetries. The ensuing factorization of the configuration manifold into a symmetry group and an internal shape space has provided deep insights into the…
We discuss the projectivity of the moduli space of semistable vector bundles on a curve of genus $g\geq 2$. This is a classical result from the 1960s, obtained using geometric invariant theory. We outline a modern approach that combines the…
The f-invariant is a higher version of the e-invariant that takes values in the divided congruences between modular forms; it can be formulated as an elliptic genus of manifolds with corners of codimension two. In this thesis, we develop a…
Lund diagrams, a theoretical representation of the phase space within jets, have long been used in discussing parton showers and resummations. We point out that they can be created for individual jets through repeated Cambridge/Aachen…
We give the explicit algorithm computing the motivic generalization of the Poincare series of the plane curve singularity introduced by A. Campillo, F. Delgado and S. Gusein-Zade. It is done in terms of the embedded resolution of the curve.…
During the last months or so we had the opportunity to read two papers trying to relate the study of Macaulay (1916) inverse systems with the so-called Riquier (1910)-Janet (1920) initial conditions for the integration of linear analytic…
This paper is to serve as a key to the projective (homogeneous) model developed by Charles Gunn (arXiv:1101.4542 [math.MG]). The goal is to explain the underlying concepts in a simple language and give plenty of examples. It is targeted to…
We extend to general Cartesian categories the idea of Coherent Differentiation recently introduced by Ehrhard in the setting of categorical models of Linear Logic. The first ingredient is a summability structure which induces a partial…
The cohomology of the Hilbert schemes of points on smooth projective surfaces can be approached both with vertex algebra tools and equivariant tools. Using the first tool, we study the existence and the structure of universal formulas for…
The role of linear and projective groups of transformations in line geometry and electromagnetism is examined in accordance with Klein's Erlanger Programm for geometries. The group of collineations of real projective space is chosen as the…