Reports de recerca
Recent Submissions
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From action-angle coordinates to geometric quantization
(2011-03-01)
External research report
Open AccessThe philosophy of geometric quantization is to ¯nd and understand a \(one-way) dictionary" that \translates" classical systems into quantum systems . In this way, a quantum system is associated to a classical system in ... -
Up-to-homotopy algebras with strict units
(2018-12-20)
External research report
Open AccessWe prove the existence of minimal models à la Sullivan for operads with non trivial arity zero. So up-to-homotopy algebras with strict units are just operad algebras over these minimal models. As an application we give ... -
Contact structures with singularities
(2018-06-15)
External research report
Open AccessWe study singular contact structures, which are tangent to a given smooth hypersurface Z and satisfy certain transversality conditions. These singular contact structures are determined by the kernel of non-smooth differential ... -
Open problems, questions, and challenges in finite-dimensional integrable systems
(2018-04-11)
External research report
Open AccessThe paper surveys open problems and questions related to different aspects of integrable systems with finitely many degrees of freedom. Many of the open problems were suggested by the participants of the conference ... -
The geometry of E-manifolds
(2018-02-09)
External research report
Open AccessMotivated by the study of symplectic Lie algebroids, we study a describe a type of algebroid (called an E-tangent bundle) which is particularly well-suited to study of singular differential forms and their cohomology. ... -
Geometric quantization of semitoric systems and almost toric manifolds
(2017)
External research report
Open AccessKostant gave a model for the real geometric quantization associated to polarizations via the cohomology associated to the sheaf of flat sections of a pre-quantum line bundle. This model is well-adapted for real polarizations ... -
An invitation to singular symplectic geometry
(2017)
External research report
Open AccessIn this paper we analyze in detail a collection of motivating examples to consider bm- symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every bm-symplectic ... -
Decomposition spaces in combinatorics
(2016-12)
External research report
Open AccessA decomposition space (also called unital 2-Segal space) is a simplicial object satisfying an exactness condition weaker than the Segal condition: just as the Segal condition expresses (up to homotopy) composition, the new ... -
Three Hopf algebras and their common simplicial and categorical background
(2016-07)
External research report
Open AccessWe consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebras of Goncharov for multiple zeta values, that of Connes--Kreimer ... -
Sullivan minimal models of operad algebras
(2016-12-12)
External research report
Open AccessWe prove the existence of Sullivan minimal models of operad algebras, for a quite wide family of operads in the category of complexes of vector spaces over a field of characteristic zero. Our construction is an adaptation ... -
Non-commutative integrable systems on b-symplectic manifolds
(2016)
External research report
Open AccessIn this paper we study non-commutative integrable systems on b-Poisson manifolds. One important source of examples (and motiva- tion) of such systems comes from considering non-commutative systems on manifolds with ... -
Examples of integrable and non-integrable systems on singular symplectic manifolds
(2016-12)
External research report
Open AccessWe present a collection of examples borrowed from celes- tial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization trans- formations, Appell's ...
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