Related papers: Polyfold and SFT Notes I: A Primer on Polyfolds an…

In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the…

These notes are an introduction to symplectic groupoids and the double structures associated with them. The treatment is intended to lie about midway between the original account of Coste, Dazord and Weinstein, which relied on effective use…

The aim of this note is to present a construction of symplectic structures on orientable globally hyperbolic 4-dimensional lorentzian manifolds. Said structures are defined on the manifold itself, not on its cotangent bundle. It also…

A book, concerning the classical restricted three body problem, and the approach to this old conundrum coming from the modern methods of symplectic and contact geometry. It is split into Part I (theoretical aspects), and Part II (practical…

This note is the sequel of "Geometric structures as variational objects, I." It generalizes the main result and perspectives of that work to a class of geometric structures that includes integrable almost-complex structures.

These are the notes from my courses on the arithmetic of quadratic forms.

This text is a set of lecture notes for a series of four talks given at I.P.A.M., Los Angeles, on March 18-20, 2003. The first lecture provides a quick overview of symplectic topology and its main tools: symplectic manifolds, almost-complex…

A method of constructing a class of bihamiltonian structures is presented. Elements of this class are generalizations of the so-called bihamiltonian structures of general position on odd-dimensional manifolds. The method consists in a…

This volume contains the proceedings of the Ninth Workshop on Mathematically Structured Functional Programming (MSFP 2022). The meeting took place on the 2nd of April as a satellite of European Joint Conferences on Theory & Practice of…

This note is an invitation to the theory of geometric functions. The foundation techniques and some of the developments in the field are explained with the mindset that the audience is principally young researchers wishing to understand…

This is the revised version of the second paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. The theory will be illustrated in upcoming papers by applications to Floer Theory,…

This survey paper addresses uniqueness questions for symplectic forms on closed manifolds, explains what is known in several examples, and reviews some open problems.

This note introduces the construction of relational symplectic groupoids as a way to integrate every Poisson manifold. Examples are provided and the equivalence, in the integrable case, with the usual notion of symplectic groupoid is…

Examples of nonformal simply connected symplectic manifolds are constructed.

This work presents the tessellations and polytopes from the perspective of both n-dimensional geometry and abstract symmetry groups. It starts with a brief introduction to the terminology and a short motivation. In the first part, it…

These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A…

We give an overview over several constructions of TQFT's over finite fields and cyclotomic integers and their applications to characterizing 3-manifolds and their fundamental groups.

This is a survey of known algorithms in algebraic topology with a focus on finite simplicial complexes and, in particular, simplicial manifolds. Wherever possible an elementary approach is chosen. This way the text may also serve as a…

We give a non-technical summary of the classification program, very dear to the hearts of both authors, of four dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) based on the study of their Coulomb branch geometries. We…

This survey wants to give a short introduction to the transversality problem in symplectic field theory and motivate to approach it using the new Fredholm theory by Hofer, Wysocki and Zehnder. With this it should serve as a lead-in for the…