Related papers: Shifted Symplectic Geometry by Examples
These lecture notes are based on an introductory course given by the author at the summer school "Noncommutative Algebraic Geometry" at MSRI in June 2012. The emphasis throughout is on examples to illustrate the many different facets of…
Symplectic and Poisson geometry emerged as a tool to understand the mathematical structure behind classical mechanics. However, due to its huge development over the past century, it has become an independent field of research in…
These notes are based on an introductory minicourse on Poisson geometry given at CRM, Barcelona, in July 2022. They mostly contain foundational material, including motivating questions and key examples of Poisson structures, and highlight…
In this work, we study symplectic structures on graded manifolds and their global counterparts, higher Lie groupoids. We begin by introducing the concept of graded manifold, starting with the degree 1 case, and translating key geometric…
These are lecture notes for the course "Poisson geometry and deformation quantization" given by the author during the fall semester 2020 at the University of Zurich. The first chapter is an introduction to differential geometry, where we…
These are expanded notes from lectures given at the \'{E}tats de la Recherche workshop on "Derived algebraic geometry and interactions". These notes serve as an introduction to the emerging theory of Poisson structures on derived stacks.
We review recent results and ongoing investigations of the symplectic and Poisson geometry of derived moduli spaces, and describe applications to deformation quantization of such spaces.
We examine shifted symplectic and Poisson structures on spaces of framed maps. We prove some results about shifted Poisson structures analogous to those in existing ones about symplectic structures. Then, we consider the space Map(X,D,Y) of…
These are the notes of rather informal lectures given by the first co-author in UPMC, Paris, in January 2017. Practical goal is to explain how to compute or estimate the Morse index of the second variation. Symplectic geometry allows to…
This manuscript is essentially a collection of lecture notes which were given by the first author at the Summer School Wisl-2019, Poland and written down by the second author. As the title suggests, the material covered here includes the…
This is an overview article on selected topics in symplectic geometry written for the Handbook of Differential Geometry (volume 2, edited by F.J.E. Dillen and L.C.A. Verstraelen).
This paper develops new aspects of the interplay between shifted symplectic geometry and classical Poisson geometry, focusing on lagrangian morphisms into 2-shifted symplectic groups. We establish a Lie-type correspondence between such…
The mathematical theory underlying Hamiltonian mechanics is called symplectic geometry. So symplectic geometry arose from the roots of mechanics and is seen as one of the most valuable links between physics and mathematics today. Symplectic…
Generalized complex geometry was classically formulated by the language of differential geometry. In this paper, we reformulated a generalized complex manifold as a holomorphic symplectic differentiable formal stack in a homotopical sense.…
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…
Our aim is to give a friendly introduction for students to systolic inequalities. We will stress the relationships between the classical formulation for Riemannian metrics and more recent developments related to symplectic measurements and…
These are expanded lecture notes from the author's minicourse at the 2022 Poisson Geometry Summer School, which took place at the Centre de Recerca Matematica in Barcelona, Spain. After giving a general introduction to wonderful varieties,…
In this paper we study the symplectic and Poisson geometry of moduli spaces of flat connections over quilted surfaces. These are surfaces where the structure group varies from region to region in the surface, and where a reduction (or…
We introduce scattering-symplectic manifolds, manifolds with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be…
Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly…