課程題目：An introduction to Poisson geometry : a minicourse
授 課 人：Camilo Andres Angulo Santacruz 博士後
所在單位：巴西弗魯米嫩塞聯邦大學
課程地點：ZOOM ID：862 062 0549，密碼：2022
Zoom會議鍊接：https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
校内聯系人：生雲鶴 shengyh@jlu.edu.cn
課程介紹：Poisson geometry is a lively area of research that lies at the crossroads of several fields in mathematics. On the one hand, it lies at the intersection of symplectic geometry, Lie theory, and foliation theory; and on the other, it serves as the background for several theories in mathematical physics. Though Poisson brackets can be traced back to the XIXth century, its current incarnation started in the late 1970s with the work of Lichnerowicz and rapidly developed as a field in its own right as well as through connections with other areas of mathematics. In this mini-course, we aim at introducing Poisson manifolds and offer a panoramic view of some classical and modern developments of the theory. We will start with basic definitions and properties of Poisson manifolds, some foundational results, and a wealth of examples. We will then discuss the connection to Lie theory exploring the larger world of Lie algebroids and Lie groupoids and their geometry. We will recognize that the algebroids naturally associated with Poisson manifolds come with additional geometric structures and discuss when these can be integrated to multiplicative structures on their Lie groupoids. Lastly, we will gloss over a collection of related structures and close with a particular class of examples: Poisson-Lie groups.
報告人簡介：Camilo Andres Angulo Santacruz，巴西弗魯米嫩塞聯邦大學博士後，從事泊松幾何，高階李理論的Van Est定理研究。 在Commun. Contemp. Math.，J. Math. Phys.等雜志上發表多篇高水平論文。
