Related papers: Graded geometry and Poisson reduction

We establish primitive recursive versions of some known facts about computable ordered fields of reals and computable reals, and then apply them to proving primitive recursiveness of some natural problems in linear algebra and analysis. In…

We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear differential forms on Lie algebroids and encompasses many known…

We introduce an additive basis of the integral cohomology ring of the Peterson variety which reflects the geometry of certain subvarieties of the Peterson variety. We explain the positivity of the structure constants from a geometric…

We propose an iterated version of the Gilbert model, which results in a sequence of random mosaics of the plane. We prove that under appropriate scaling, this sequence of mosaics converges to that obtained by a classical Poisson line…

The generalized projection-tensor geometry introduced in an earlier paper is extended. A compact notation for families of projected objects is introduced and used to summarize the results of the previous paper and obtain fully projected…

This manuscript is intended as an accompaniment to Guth's "A restriction estimate using polynomial partitioning". We begin by summarizing the core ideas of the proof, elaborating the history and development of the techniques therein. From…

The Marden theorem of geometry of polynomials and the great Poncelet theorem from projective geometry of conics by their classical beauty occupy very special places. Our main aim is to present a strong and unexpected relationship between…

It is a basic introduction to differential graded Lie algebras, Maurer-Cartan equation and associated deformation functors.

This paper is the sequel to [PTVV] (IHES Vol. 117, 2013). We develop a general and flexible context for differential calculus in derived geometry, including the de Rham algebra and polyvector fields. We then introduce the formalism of…

We recall the space of seminorms discussed by Payne in \cite{P} and define a slight modification, the space of graded valuations. After explaining how these spaces relate to tropical geometry, we describe examples of graded valuations which…

We introduce the first geometric construction of codes in the sum-rank metric, which we called linearized Algebraic Geometry codes, using quotients of the ring of Ore polynomials with coefficients in the function field of an algebraic…

We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics,…

We give a Poisson-geometric proof of the Kashiwara-Vergne conjecture for quadratic Lie algebras, based on the equivariant Moser trick.

This article describes recent applications of algebraic geometry to noncommutative algebra. These techniques have been particularly successful in describing graded algebras of small dimension.

We give a natural definition of a Poisson Differential Algebra. Consistence conditions are formulated in geometrical terms. It is found that one can often locally put the Poisson structure on differential calculus in a simple canonical form…

Using a Lax pair based on twisted affine $sl(2,R)$ Kac-Moody and Virasoro algebras, we deduce a r-matrix formulation of two dimensional reduced vacuum Einstein's equations. Whereas the fundamental Poisson brackets are non-ultralocal, they…

These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…

We study the graded derivation-based noncommutative differential geometry of the $Z_2$-graded algebra ${\bf M}(n| m)$ of complex $(n+m)\times(n+m)$-matrices with the ``usual block matrix grading'' (for $n\neq m$). Beside the…

We give an alternative proof of Madsen-Weiss' generalized Mumford conjecture. Our proof is based on ideas similar to Madsen-Weiss' original proof, but it is more geometrical and less homotopy theoretical in nature. At the heart of the…

This article addresses the problem of developing an extension of the Marsden- Weinstein reduction process to symplectic Lie algebroids, and in particular to the case of the symplectic cover of a fiberwise linear Poisson structure, whose…