Tropical Geometry and Moduli Spaces: Satellite Conference of the 2018 International Congress of Mathematicians (ICM)

热带几何与模空间：2018年国际数学家大会（ICM）卫星会议

• 批准号: 1760342
• 负责人: Sam Payne
• 金额: $ 1.08万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-04-01 至 2019-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1760342&HistoricalAwards=false
• 关键词: Tropical; Geometry; Moduli; Spaces; Satellite

This award will support US based participants and speakers at Tropical Geometry and Moduli Spaces, a satellite conference of the 2018 International Congress of Mathematicians (ICM), to be held August 13-17 in Cabo Frio, Brazil. This event will leverage the assembly of a vast number of mathematicians at the ICM in Rio de Janeiro as an opportunity to bring together a global community of leading experts and early career researchers in an especially active and rapidly developing field. This conference will be the largest ever in tropical geometry with over 80 participants anticipated.The scientific focus of the conference will be broadly centered on connections to moduli spaces, including interactions logarithmic structures, Berkovich spaces, and enumerative geometry. In just the past few years, there have been a number of significant advances in building explicit links among these different geometric theories, especially for curves and abelian varieties, using skeletons of nonarchimedean analytic spaces as a shared common tool. These links explain many older correspondence theorems, from the beginnings of tropical enumerative geometry, and are being used to establish new correspondences and to prove new enumerative results of classical flavor, e.g. for counting curves with fixed invariants, and to prove degeneration formulas for logarithmic Gromov-Witten invariants as part of a broader program linking tropical geometry to mirror symmetry. At the same time, new algebraic foundations are emerging for scheme-theoretic tropical geometry, built out of idempotent semirings, which will also be featured at the 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.

该奖项将支持美国的参与者和演讲者在热带几何和模数空间，2018年国际数学家大会（ICM）的卫星会议，将于8月13日至17日在巴西的卡波弗里奥举行。 本次活动将利用里约热内卢ICM众多数学家的集会，将全球领先的专家和早期职业研究人员聚集在一个特别活跃和快速发展的领域。这次会议将是有史以来最大的热带几何与超过80与会者预期.会议的科学重点将广泛集中在连接到模空间，包括相互作用对数结构，布科维奇空间，和枚举几何. 在过去的几年里，在这些不同的几何理论之间建立明确的联系方面取得了许多重大进展，特别是对于曲线和阿贝尔变种，使用非阿基米德解析空间的骨架作为共享的公共工具。这些链接解释了许多旧的对应定理，从热带枚举几何的开始，并被用来建立新的对应和证明新的枚举结果的经典风味，例如计数曲线与固定不变量，并证明退化公式对数格罗莫夫-威滕不变量的一部分，更广泛的计划连接热带几何镜像对称。与此同时，新的代数基础正在出现的图式理论的热带几何，建立了幂等半环，这也将在会议上的特色。这个奖项反映了NSF的法定使命，并已被认为是值得的支持，通过评估使用基金会的智力价值和更广泛的影响审查标准。