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.

该奖项为美国早期职业数学家参加在奈梅亨举行的会议“枚举几何的动机和非交换方面”和“同伦理论、K 理论和迹方法”的旅行和当地费用提供支持。荷兰，于 2023 年 7 月 3 日至 7 日举行。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。这些活动旨在将美国数学家与欧洲研究人员联系起来，并提供建立新合作的机会。除了与该领域更知名的研究人员互动之外，简短的演讲环节还旨在让研究生、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 理论记录了环或环的重要而微妙的不变量。方案。不幸的是，在少数示例之外计算这些 K 群是非常困难的。为了解决这个问题，出现了两种主要方法：动机同伦，它在代数几何中根据稳定同伦理论构建了许多经典构造；以及迹方法，它通过经典和等变稳定同伦的构造来逼近代数 K 群。这些会议将汇集代表所有这些领域和数学中几个相关领域的专家，以令人兴奋的最新发展为基础，并提供一个论坛，让早期职业数学家在代数几何和同伦理论中接触到这些领域。该奖项反映了 NSF 的法定使命和通过使用基金会的智力价值和更广泛的影响审查标准进行评估，该项目被认为值得支持。