Geometry and Physics--Higher structures: derived geometry and quantization

该奖项为两个几何和物理暑期学校（GAP）的美国参与者提供部分支持：GAP XIII（2015）将于2015年7月6日至10日在韩国浦项工业大学IBS几何和物理中心举行，GAP XIV（2016）将于2016年夏季在宾夕法尼亚州立大学举行。这些活动的主要目的是：(1)聚集研究快速发展学科的顶尖专家和年轻研究人员；(2)促进研究相关问题不同方面的数学家和物理学家团体之间的互动，以促进不同领域之间的交流，并传播当前研究的最新成果。有许多有才华的年轻人在这个地区工作。第十三和第十四届GAP将为他们提供极好的机会来传播他们的想法和扩大他们的视野。组织者希望邀请许多博士后和研究生水平的数学家（来自亚洲、欧洲和美国）参加这些暑期学校。两所暑期学校都将包括一个海报环节，让年轻的研究人员有机会展示他们最近的工作。每个暑期学校也将为年轻的美国科学家提供与外国同行交流思想和开展合作的绝佳机会。GAP XIII的网站是http://cgp.ibs.re.kr/conferences/gapxiii/The，学校的主题是“高级结构：衍生几何和量化”。GAP XIII（2015）将致力于推导几何，GAP XIV（2016）将致力于量化。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。由于与代数拓扑、李论、同伦代数、镜像对称、弦论、量子场论和非交换几何等数学和数学物理领域的密切联系，这门学科最近经历了巨大的探索。该项目将致力于汇集高等结构的不同方面，特别是衍生几何和量化，以及确定新的研究方向，随着该领域的进展，这将变得越来越紧迫。衍生几何发展了一种强大的机制，用于研究在数学和数学物理的不同领域中表现不良的交叉点和商空间的剩余几何，而量子化则在经典物理和量子物理之间建立了桥梁。粗略地说，量子化是对量子现象的研究和预测，量子现象通常由非交换关联代数描述，基于底层经典对象的几何。

This award provides partial support for U.S.-based participants in two summer schools in Geometry and Physics (GAP): GAP XIII (2015) to be held at the IBS Center for Geometry and Physics at POSTECH, Republic of Korea, July 6--10, 2015, and GAP XIV (2016) to be held at Penn State University in summer 2016. The main purposes of the proposed activities are: (1) gathering leading experts and young researchers working in rapidly developing subjects and (2) fostering interaction between groups of mathematicians and physicists working on different aspects of related problems to facilitate cross-fertilization between different fields and dissemination of the most recent results of current research. There are many talented young people working in this area. GAP XIII and GAP XIV will provide them with excellent opportunities to disseminate their ideas and to broaden their perspective. The organizers anticipate inviting many mathematicians at the postdoctoral and graduate student level (from Asia, Europe, and the United States) to these summer schools. Both summer schools will include a poster session so as to give young researchers a chance to present their recent work. Each summer school will also constitute an excellent opportunity for young American scientists to exchange ideas with their foreign peers and launch collaborations. The website for GAP XIII is http://cgp.ibs.re.kr/conferences/gapxiii/The theme of the schools is "Higher Structures: Derived Geometry and Quantization." GAP XIII (2015) will be devoted to derived geometry and GAP XIV (2016) to quantization. Higher structures has emerged as a new field in mathematics, as well as in mathematical and theoretical physics. The subject has undergone tremendous exploration recently due to its close connection to a number of areas of mathematics and mathematical physics, including algebraic topology, Lie theory, homotopy algebras, mirror symmetry, string theory, quantum field theory and noncommutative geometry. The project will be devoted to bringing together different aspects of higher structures, in particular derived geometry and quantization, as well as identifying new emerging directions of investigation, which is becoming more and more urgent as the field progresses. Derived geometry develops a powerful machinery for studying the residual geometry of badly behaved intersections and quotient spaces of high current interest in different areas of mathematics and mathematical physics while quantization establishes bridges between classical and quantum physics. Roughly speaking, quantization is the study and prediction of quantum phenomena, which are normally described by noncommutative associative algebras, based on the geometry of the underlying classical objects.