Reports de recerca
Enviaments recents
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Open problems, questions, and challenges in finite-dimensional integrable systems
(2018-04-11)
Report de recerca
Accés obertThe 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)
Report de recerca
Accés obertMotivated 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)
Report de recerca
Accés obertKostant 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)
Report de recerca
Accés obertIn 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)
Report de recerca
Accés obertA 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)
Report de recerca
Accés obertWe 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)
Report de recerca
Accés obertWe 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)
Report de recerca
Accés obertIn 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)
Report de recerca
Accés obertWe 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 ... -
Homotopy linear algebra
(2016-02)
Report de recerca
Accés obertBy homotopy linear algebra we mean the study of linear functors between slices of the 8-category of 8-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices ... -
Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
(2015-12)
Report de recerca
Accés obertDecomposition spaces are simplicial 8-groupoids subject to a certain exactness condition, needed to induce a coalgebra structure on the space of arrows. Conservative ULF functors between decomposition spaces induce coalgebra ... -
Decomposition spaces, incidence algebras and Möbius inversion II: completeness, length filtration, and finiteness
(2015-12)
Report de recerca
Accés obertThis is part 2 of a trilogy of papers introducing and studying the notion of decomposition space as a general framework for incidence algebras and Möbius inversion, with coefficients in 8-groupoids. A decomposition space ...
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