Collaborative Research: Deformations of Geometric Structures in Current Mathematics

该项目将于2022年5月3日至6日在哥伦比亚大学和2022年5月9日至12日在哈佛大学数学科学与应用中心（CMSA）举办为期两周的会议，主题为“当前数学中的几何结构变形”。本次活动将汇集来自不同领域的早期职业研究人员和世界知名数学家，包括复分析，辛几何，微分几何和偏微分方程。本次活动将为年轻数学家和来自代表性不足群体的数学家提供一个很好的机会来参加会议，并与各种数学领域的领导者建立关系和合作。几何结构的变形一直是当前数学发展中一个非常活跃的主题，来自许多独立来源的思想涌入，包括代数几何、辛几何、偏微分方程和弦理论。这些思想导致了计数几何、格罗莫夫-维滕理论、辛几何、模问题和新的几何和拓扑不变量的发现的重大进展。会议将举办一系列广泛的讲座，来自这些思想具有影响力的各个领域的专家。几何结构的变形是由哥伦比亚大学的已故教授Masatake Kuranishi开创的，他在局部完全变形方面的里程碑式的作品和他引入的许多新技术。会议网站可在https://cmsa.fas.harvard.edu/kuranish-conference/This上找到奖项反映了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 project will conduct a two week long conference on the topic of "Deformations of Geometric Structures in Current Mathematics", to be hosted at Columbia University from May 3-6, 2022 and the Center of Mathematical Sciences and Applications (CMSA) at Harvard University from May 9-12, 2022. This event will bring together early career researchers and world renowned mathematicians from a variety of fields, including complex analysis, symplectic geometry, differential geometry and partial differential equations. This event will provide a great opportunity for young mathematicians, and mathematicians from under-represented groups to attend the conference and build relationships and collaborations with leaders in a variety of mathematical fields.Deformations of geometric structures has been an exceptionally active theme in current developments in mathematics, with an infux of ideas from many independent sources, including algebraic geometry, symplectic geometry, partial differential equations, and string theory. The ideas have lead to significant advances in enumerative geometry, Gromov-Witten Theory, symplectic geometry, as well as moduli problems and the discovery of new geometric and topological invariants. The conference will host a wide array of talks from experts in a variety of fields where these ideas have been infuential. Deformations of geometric structures were pioneered by the late Professor Masatake Kuranishi of Columbia University, with his landmark works on locally complete deformations and the many novel techniques which he introduced. The conference website can be found at https://cmsa.fas.harvard.edu/kuranish-conference/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.