Related papers: The Symplectic Penrose Kite
Motivated by relations with a symplectic invariant known as the "cylindrical symplectic capacity", in this note we study the expectation of the area of a minimal projection to a complex line for a randomly rotated cube.
A list of open problems on holomorphic symplectic, contact and Poisson manifolds.
In this paper we survey some recent works that take the first steps toward establishing bilateral connections between symplectic geometry and several other fields, namely, asymptotic geometric analysis, classical convex geometry, and the…
We compute the symplectic structure of the spin Calogero model in terms of algebro-geometric data on the associated spectral curve.
A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism, facts and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the…
A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short…
In this paper, a geometric interpretation is provided of a new rational Landen transformation. The convergence of its iterates is also established.
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
In this article we consider a version of the geography question for simply-connected symplectic 4-manifolds that takes into account the divisibility of the canonical class as an additional parameter. We also find new examples of 4-manifolds…
This is the preliminary manuscript of a book on symplectic field theory based on a lecture course for PhD students given in 2015-16. It covers the essentials of the analytical theory of punctured pseudoholomorphic curves, taking the…
The purpose of this paper is to present some results on the existence of homologous, nonisotopic symplectic or lagrangian surfaces embedded in a simply connected symplectic 4-dimensional manifold.
I give an overview of the motivations for and theory/phenomenology of supersymmetry.
This text is a short but comprehensive introduction to the basics of supergeometry and includes some of the recent advances in colored supergeometry. We do not aim for a standard text that states results and proves them more or less…
We introduce the notion of the symplectic characteristic polynomial of an endomorphism of a symplectic vector space. This is a polynomial in two variables and can be considered as a generalization of the characteristic polynomial of the…
We give a detailed study of the symplectic geometry of a family of integrable systems obtained by coupling two angular momenta in a non trivial way. These systems depend on a parameter t $\in$ [0, 1] and exhibit different behaviors…
By investigating the symplectic geometry and geometric quantization on a class of supermanifolds, we exhibit BRST structures for a certain kind of algebras. We discuss the undeformed and q-deformed cases in the classical as well as in the…
Outer billiards is a basic dynamical system, defined relative to a planar convex shape. This system was introduced in the 1950's by B.H. Neumann and later popularized in the 1970's by J. Moser. All along, one of the central questions has…
This paper is intended to provide an introduction to the theory of substitution tilings. For our purposes, tiling substitution rules are divided into two broad classes: geometric and combinatorial. Geometric substitution tilings include…
In the article "Construction of the discrete hull for the combinatorics of a regular pentagonal tiling of the plane" we gave the construction of a discrete hull for a combinatorial pentagonal tiling of the plane. In this paper, we give the…
This paper will appear in the Proceedings of the 1995 Santa Cruz Summer Institute. The paper is a survey of recent developments in the theory of toric varieties, including new constructions of toric varieties and relations to symplectic…