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Summer School and Conference: Poisson 2022

Summer School and Conference: Poisson 2022
暑期学校和会议:泊松 2022
批准号:
2210602
负责人:
Rui Loja Fernandes
金额:
$3.2万
依托单位国家:
美国
项目类别:
Standard Grant
财政年份:
2022
资助国家:
美国
项目状态:
已结题
起止时间:
2022-07-01 至 2023-06-30

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中文摘要
翻译
泊松2022是一系列两年一次的国际会议和学校中的第12届,这些会议和学校被称为泊松几何的数学子领域。2022年的活动包括2022年7月18日至22日在西班牙巴塞罗那的Recerca Matematica中心举办高级学校,以及2022年7月25日至29日在西班牙马德里的西班牙国家研究委员会(CSIC)总部举行的会议。泊松几何是一个最初受到物理学启发的领域,它在数学和其他科学领域都有大量的应用。这项活动将汇集不同的数学家群体,探索泊松几何及其在不同领域的许多应用之间的现代相互作用。这所学校将由四门由顶尖的初级和高级数学家讲授的迷你课程组成。它将向参与者(主要是早期职业数学家)介绍泊松几何现代研究前沿的广泛思想。会议计划将有21个主要专家的演讲,涵盖了泊松几何及其应用中最活跃的话题。这些活动的目标是使所有参与者都能接触到该领域的最新发展,拓宽他们对当前主要研究领域的看法,并创造一个令人兴奋的环境,使他们能够分享想法并开始持久的跨学科合作。该奖项的目的是支持美国的研究人员参与这一活动。本次会议旨在促进数学家、物理学家和从不同角度从事相关领域工作的团体之间的互动。会议是宣布和讨论该领域最近最重要的进展,并讨论该主题未来可能的方向的论坛。主题涵盖了由泊松括号及其应用引起的广泛领域,包括辛,狄拉克,广义复结构和相关结构,李代数和李群,几何力学,泊松代数和泊松变异,聚类代数,可积系统,量子化和高级结构,非交换几何,量子群和表示理论。学院拥有强大的培训组成部分,包括泊松几何和叶理理论两门入门课程,以及几何量化和奇妙紧化两门更高级的课程。在会议开幕期间,安德烈·利赫内罗维茨泊松几何奖的获奖者将被宣布。该奖项颁发给在泊松几何及其应用方面做出杰出贡献的研究人员,这些研究人员在大会召开前最多八年完成了博士学位。有关该学院的更多信息请访问https://www.crm.cat/2022-advanced-school-poisson/,会议信息请访问https://www.icmat.es/congresos/2022/poisson/index.php.This。奖项反映了NSF的法定使命,并通过使用基金会的知识价值和更广泛的影响审查标准进行评估,认为值得支持。
英文摘要
Poisson 2022 is the 12th in a series of biennial international conferences and schools in a subfield of mathematics known as Poisson geometry. The 2022 event includes an Advanced School at the Centre de Recerca Matematica, Barcelona, Spain, July 18-22, 2022 and a Conference at the headquarters of the Spanish National Research Council (CSIC), Madrid, Spain, July 25-29, 2022. Poisson geometry is an area originally inspired by physics, which has found a huge number of applications both in mathematics and other areas of science. This activity will bring together a diverse group of mathematicians to explore the modern interplay between Poisson geometry and its many applications in different fields. The school will consist of four mini-courses given by leading junior and senior mathematicians. It will introduce the participants, mostly early-career mathematicians, to a broad spectrum of ideas on the forefront of modern research in Poisson geometry. The conference program will feature 21 talks given by leading experts, covering the most active topics in Poisson geometry and its applications. The goal of these activities is to make recent developments in the field accessible to all participants, to broaden their perspective on major areas of current research, and to create a stimulating environment in which they can share ideas and begin lasting interdisciplinary collaborations. The purpose of the award is to support the participation of US-based researchers in this event.This meeting aims to promote interaction between mathematicians, physicists, and groups working on related areas from different points of view. The Conference is the forum where the most significant recent advances in the area are announced and discussed, and the potential future directions of the subject are addressed. Topics cover a wide range of areas arising from Poisson brackets and its applications, including symplectic, Dirac, generalized complex and related structures, Lie algebroids and Lie groupoids, geometric mechanics, Poisson algebras and Poisson varieties, cluster algebras, integrable systems, quantization and higher structures, non-commutative geometry, quantum groups and representation theory. The School has a strong training component, including two introductory courses in Poisson Geometry and Foliation Theory, and two more advanced level courses in Geometric Quantization and Wonderful Compactifications. During the opening of the conference, the winner(s) of the Andre Lichnerowicz Prize in Poisson geometry will be announced. The prize is awarded for notable contributions to Poisson geometry and its applications, to researchers who completed their doctorates at most eight years before the year of the Conference. More information about the school is at https://www.crm.cat/2022-advanced-school-poisson/ and conference information is at https://www.icmat.es/congresos/2022/poisson/index.php.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
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会议论文
Symplectic groupoids and quantization of Poisson manifolds
Geometric Structures on Lie Groupoids and their Applications
Poisson Manifolds of Compact Types and Geometric Structures on Stacks
Deformations and Rigidity in Poisson Geometry
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