### Recent Submissions

• #### Universality of Euler flows and flexibility of Reeb embeddings ﻿

(2019-11-05)
External research report
Open Access
The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao launched a programme to address the global existence problem for the Euler and Navier ...
• #### A Poincaré lemma in geometric quantisation ﻿

(2013)
External research report
Open Access
This paper presents a Poincaré lemma for the Kostant comple x, used to compute geometric quantisation, when the polarisat ion is given by a Lagrangian foliation defined by an integrable system wit h non-degenerate singularities.
• #### Convexity for Hamiltonian torus actions on b-symplectic manifolds ﻿

(2014-12)
External research report
Open Access
In [GMPS] we proved that the moment map image of a b-symplectic toric manifold is a convex b-polytope. In this paper we obtain convexity results for the more general case of non-toric hamiltonian torus actions on b-symplectic ...
• #### Desingularizing b^m-symplectic structures ﻿

(2015-12)
External research report
Open Access
A 2n-dimensional Poisson manifold (M,¿) is said to be bm-symplectic if it is symplectic on the complement of a hypersurface Z and has a simple Darboux canonical form at points of Z which we will describe below. In this ...
• #### Cotangent models for integrable systems on $b$-symplectic manifolds ﻿

(2016-01)
External research report
Open Access
• #### Equivariant classification of bm-symplectic surfaces and Nambu structures ﻿

(2016)
External research report
Open Access
In this paper we extend the classification scheme in [S] for bm-symplectic surfaces, and more generally, bm-Nambu structures to the equivariant setting. When the compact group is the group of deck-transformations of an ...
• #### From action-angle coordinates to geometric quantization ﻿

(2011-03-01)
External research report
Open Access
The 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 Access
We 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 Access
We 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 Access
The 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 Access
Motivated 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 Access
Kostant 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 ...