Reports de recerca
Recent Submissions
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Hamiltonian facets of classical gauge theories on E-manifolds
(2022-09-21)
Research report
Open AccessManifolds with boundary, with corners, b-manifolds and foliations model configuration spaces for particles moving under constraints and can be described as E-manifolds. E-manifolds were introduced in [NT01] and investigated ... -
Reduction theory for singular symplectic manifolds and singular forms on moduli spaces
(2022-05-25)
Research report
Open AccessThe investigation of symmetries of b-symplectic manifolds and folded-symplectic manifolds is well-understood when the group under consideration is a torus (see, for instance, [GMPS, GLPR,GMW18a]forb-symplecticmanifoldsand ... -
Bohr-Sommerfeld quantization of b-symplectic toric manifolds
(2022-03-07)
Research report
Open AccessWe define the Bohr-Sommerfeld quantization via T-modules for a b-symplectic toric manifold and show that it coincides with the formal geometric quantization of [GMW18b]. In particular, we prove that its dimension is given ... -
Singular cotangent models and complexity in fluids with dissipation
(2022-06-17)
Research report
Open AccessIn this article we analyze several mathematical models with singularities where the classical cotangent model is replaced by a b-cotangent model. We provide physical interpretations of the singular symplectic geometry ... -
On the singular Weinstein conjecture and the existence of escape orbits for b-Beltrami fields
(2021-10-07)
Research report
Open AccessMotivated by Poincare’s orbits going to infinity in the (restricted) three-body problem ´ (see [29] and [7]), we investigate the generic existence of heteroclinic-like orbits in a neighbourhood of the critical set of a ... -
Integrable systems on singular symplectic manifolds: from local to global
(2021-02-03)
Research report
Open AccessIn this article, we consider integrable systems on manifolds endowed with symplectic structures with singularities of order one. These structures are symplectic away from a hypersurface where the symplectic volume goes ... -
Turing universality of the incompressible Euler equations and a conjecture of Moore
(2021-04-09)
Research report
Open AccessIn this article we construct a compact Riemannian manifold of high dimension on which the time dependent Euler equations are Turing complete. More precisely, the halting of any Turing machine with a given input is equivalent ... -
Geometric quantization via cotangent models
(2022-05-05)
Research report
Open AccessIn this article we give a universal model for geometric quantization associated to a real polarization given by an integrable system with non-degenerate singularities. This universal model goes one step further than the ... -
Computability and Beltrami fields in Euclidean space
(2022-11-15)
Research report
Open AccessIn this article, we pursue our investigation of the connections between the theory of computation and hydrodynamics. We prove the existence of stationary solutions of the Euler equations in Euclidean space, of Beltrami ... -
Looking at Euler flows through a contact mirror: universality and undecidability
(2022-07-08)
Research report
Open AccessThe dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. In recent papers [5, 6, 7, 8] several unknown facets of the Euler flows have been discovered, including ... -
The singular Weinstein conjecture
(2020-06-04)
Research report
Open AccessIn this article, we investigate Reeb dynamics on $b^m$-contact manifolds, previously introduced in \cite{MO}, which are contact away from a hypersurface $Z$ but satisfy certain transversality conditions on $Z$. The study ... -
A b-symplectic slice theorem
(2020-09)
Research report
Open AccessIn this article, motivated by the study of symplectic structures on manifolds with bound-ary and the systematic study ofb-symplectic manifolds started in [10], we prove a slice theorem forLie group actions onb-symplectic manifolds
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