Conference: Geometry and Physics---Deformations, Homotopy Algebras, and Higher Structures

该奖项为两所国际几何和物理暑期学校（GAP）的美国参与者提供财政支持：GAP XVII（2022）将于2022年5月16日至20日在加拿大温哥华的太平洋数学科学研究所举行，GAP XVIII（2023）将于2023年5月22日至26日在法国巴黎的亨利庞加莱研究所举行。提议的活动的双重目的是聚集在快速发展的学科的领先专家和早期职业研究人员，并促进在相关问题的不同方面工作的数学家和物理学家团体之间的互动；这将促进不同领域之间的交叉施肥，并传播当前研究的最新成果。GAP XVII和GAP XVIII将允许早期职业数学家在数学和国际上传播他们的思想并拓宽他们的视野。这两所暑期学校将为研究人员提供与外国同行交流思想和开展合作的机会，并将包括一个海报会议，供个人展示他们最近的工作。两个学派的主题都是“高级结构：变形和同伦代数”。GAP XVII（2022）将致力于“变形”，GAP XVIII（2023）将致力于“同伦代数”。高等结构已经成为数学以及数学和理论物理的一个新领域。该领域涵盖了许多不同的主题，包括变形理论、量子化、同伦代数、衍生几何、枚举几何、表示理论、泊松几何、镜像对称、非交换代数几何、弦理论和量子场论。该活动将致力于汇集高等结构的不同方面，特别是变形和同伦代数，以及确定新的研究方向。变形理论已成为数学的一个重要领域。变形量子化存在于经典力学和量子力学的边界上。粗略地说，它是对量子现象的研究和预测，这些现象通常由非交换结合代数描述，来自它们潜在的经典对立物的几何。同伦代数为研究当代数学和数学物理不同领域的许多相互关联的问题提供了一个强大的机制。该奖项将允许美国学者到国外参加这些有影响力的活动。有关会议系列的更多信息，请参阅http://www.geometryandphysics.org/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，被认为值得支持。

This award provides financial support for U.S.-based participants in two international summer schools in Geometry and Physics (GAP): GAP XVII (2022) to be held at the Pacific Institute for Mathematical Science in Vancouver, Canada during the week May 16-20, 2022 and GAP XVIII (2023) to be held at the Institut Henri Poincaré, in Paris, France during the week May 22-26, 2023. The twofold purpose of the proposed activities are to gather leading experts and early-career researchers working in rapidly developing subjects, and to foster interaction between groups of mathematicians and physicists working on different aspects of related problems; this will facilitate cross-fertilization between different fields and disseminate the most recent results of current research. GAP XVII and GAP XVIII will allow earlier-career mathematicians to disseminate their ideas and to broaden their perspective, both mathematically and internationally. Both summer schools, which will provide the opportunity for researchers to exchange ideas with foreign peers and launch collaborations, will include a poster session for individuals to present their recent work. The theme of both schools is "Higher Structures: Deformations and Homotopy Algebras". GAP XVII (2022) will be devoted to "Deformations" and GAP XVIII (2023) to "Homotopy Algebras". Higher structures has emerged as a new field in mathematics, as well as in mathematical and theoretical physics. Covering many different topics, this field encompasses deformation theory, quantization, homotopy algebras, derived geometry, enumerative geometry, representation theory, Poisson geometry, mirror symmetry, noncommutative algebraic geometry, string theory, and quantum field theory. The event will be devoted to bringing together different aspects of higher structures, in particular deformations and homotopy algebras, as well as identifying new emerging directions of investigation. Deformation theory has become an important area of mathematics. Deformation quantization lies on the boundary between classical and quantum mechanics. Roughly speaking, it is the study and prediction of quantum phenomena, which are normally described by noncommutative associative algebras, from the geometry of their underlying classical counterparts. Homotopy algebras provide a powerful machinery for studying many interconnected questions in different areas of contemporary mathematics and mathematical physics. This award will allow US scholars to abroad to attend these impactful events. For more information on the conference series, see http://www.geometryandphysics.org/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.