### Recent Submissions

• #### On the singular Weinstein conjecture and the existence of escape orbits for b-Beltrami fields ﻿

(2021-10-07)
Research report
Open Access
Motivated 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 Access
In 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 Access
In 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 Access
In 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 Access
In 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 Access
The 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 ...
• #### Enquesta sobre la situació del col·lectiu del professorat associat a la Universitat Politècnica de Catalunya ﻿

(2021-03-15)
Research report
Open Access
La utilització de la figura del professorat associat per part de les universitats públiques a Catalunya en molts casos està lluny de l’esperit d’aquesta figura en la legislació (especialista de reconeguda competència i amb ...
• #### The singular Weinstein conjecture ﻿

(2020-06-04)
Research report
Open Access
In 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 Access
In 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
• #### The geometry and topology of contact structures with singularities ﻿

(2020-05-20)
Research report
Open Access
In this article we introduce and analyze in detail singular contact structures, with an emphasis on $b^m$-contact structures, which are tangent to a given smooth hypersurface $Z$ and satisfy certain transversality conditions. ...
• #### D.01. GPS-DF FE characterisation report ﻿

(2018-01-14)
Research report
Restricted access - confidentiality agreement
• #### Bernstein's inequality and holonomicity for certain singular rings ﻿

(2021)
Research report
Open Access
In this manuscript we prove the Bernstein inequality and develop the theory of holonomic D-modules for rings of invariants of finite groups in characteristic zero, and for strongly F-regular finitely generated graded ...