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.

该奖项为荷兰Nijmegen的荷兰Nijmegen在荷兰Nijmegen举行的“动机和非共同方面”和“同型几何学的动机和非指定方面”和“同型几何学，K理论和痕量方法”参加会议，为参加会议的旅行和本地支出提供了支持。代数K理论。这些活动旨在将美国的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。除了与该领域中更知名的研究人员的互动外，简短演讲的会议旨在允许研究生，博士后研究人员和早期职业教师分享自己的工作。代数K理论记录的重要和微妙的不变性的戒指或计划。不幸的是，众所周知，在少数几个示例之外计算这些K组。已经出现了两种主要方法来解决这个问题：动机同喻，它以代数几何形状构建了许多经典构造，从稳定的同型理论和痕量方法中，它通过古典和等价稳定同型的构造近似于代数k组。这些会议将汇集代表所有这些领域以及数学领域的几个相关领域的专家，以令人兴奋的最新发展为基础，并提供了一个论坛，以使这些领域的代数几何学和同义理论公开早期的数学家和同义理论。该奖项反映了NSF的法定任务，并通过评估了基金会的范围，并通过评估了基金会的范围。