Conference: Motivic and non-commutative aspects of enumerative geometry, Homotopy theory, K-theory, and trace methods

会议：计数几何的本构和非交换方面、同伦理论、K 理论和迹方法

• 批准号: 2328867
• 负责人: Michael Hill
• 金额: $ 3万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2328867&HistoricalAwards=false
• 关键词: Conference; Motivic; non; commutative; aspects

This award provides support for the travel and local expenses of early-career U.S.-based mathematicians to attend the conferences "Motivic and non-commutative aspects of enumerative geometry" and "Homotopy theory, K-theory, and trace methods" in Nijmegen, the Netherlands, held from July 3-7th, 2023. The conferences focuses on exciting, interconnected areas of mathematics which broadly study foundational questions in algebraic K-theory. The events aim to connect U.S.-based mathematicians with European researchers and provide opportunities to build new collaborations. In addition to the interaction with more established researchers in the field, sessions of short presentations are designed to allow graduate students, postdoctoral researchers, and early career faculty to share their own work.Algebraic K-theory records important and subtle invariants of a ring or scheme. Unfortunately, computing these K-groups outside of a handful of examples is notoriously difficult. Two dominant approaches have arisen to tackle this problem: motivic homotopy, which builds in algebraic geometry many classical constructions from stable homotopy theory, and trace methods, which approximate the algebraic K-groups by constructions in classical and equivariant stable homotopy. These conferences will bring together experts representing all of these areas and several related fields in mathematics, building on exciting recent developments and providing a forum to expose early-career mathematicians in algebraic geometry and homotopy theory to these areas.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.

该奖项为职业生涯早期的美国人提供旅行和当地费用支持。2023年7月3日至7日，在荷兰奈梅亨举行的“枚举几何的动机和非交换方面”和“同伦理论，K理论和跟踪方法”会议上，数学家们参加了会议。会议重点关注令人兴奋的，相互关联的数学领域，广泛研究代数K理论中的基础问题。这些活动旨在连接美国-数学家与欧洲的研究人员，并提供机会，建立新的合作。除了与该领域更成熟的研究人员进行互动外，简短的演讲会议旨在让研究生，博士后研究人员和早期职业教师分享他们自己的工作。代数K理论记录了环或方案的重要和微妙的不变量。不幸的是，在少数例子之外计算这些K-群是非常困难的。两种主要的方法已经出现来解决这个问题：motivic同伦，它建立在代数几何中的许多经典结构从稳定的同伦理论，和跟踪方法，近似的代数K-群的结构在经典和等变稳定的同伦。这些会议将汇集代表所有这些领域和几个相关领域的数学专家，建立在令人兴奋的最新发展，并提供一个论坛，以暴露早期职业数学家在代数几何和同伦理论这些领域。这个奖项反映了NSF的法定使命，并已被认为是值得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的支持。