The Second Transatlantic Transchromatic Homotopy Theory Conference

第二届跨大西洋跨色同伦理论会议

• 批准号: 1955705
• 负责人: Nathaniel Stapleton
• 金额: $ 1.5万
• 依托单位: University of Kentucky Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-04-01 至 2024-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1955705&HistoricalAwards=false
• 关键词: Second; Transatlantic; Transchromatic; Homotopy; Theory

This National Science Foundation award provides travel funds for US based junior researchers to travel to "The Second Transatlantic Transchromatic Homotopy Theory Conference" that will take place at the University of Regensburg, Germany from August 2-7, 2020. This five day event will include talks by world experts as well as talks by junior researchers. The aim of this conference is to bring experts in transchromatic homotopy theory together with both junior researchers and graduate students working in the area as well as experts in closely associated fields including arithmetic geometry and differential geometry. A second aim is to give very early career researchers (i,e,. graduate students and postdocs) a chance to describe their research in the form of shorter talks. In doing this, not only will graduate students receive personal mentoring, but mathematicians outside of the field will be exposed to what is going on in transchromatic homotopy theory. We hope that this will significantly raise awareness of both the techniques that have been developed and also the problems that are faced.Transchromatic homotopy theory is a rapidly emerging subarea of chromatic homotopy theory. Chromatic homotopy theory organizes the stable homotopy category by decomposing it into "chromatic layers". In studying these layers, algebraic topologists have found deep relationships between homotopy theory and algebraic geometry, number theory, higher category theory, and supersymmetric field theories. To assemble results at each chromatic layer into global results about the stable homotopy category, the relationship between the chromatic layers must be understood. This is the primary goal of transchromatic homotopy theory. Since the first Transatlantic Transchromatic Homotopy Theory conference, which occurred at the University of Regensburg in June, 2017, real applications of transchromatic homotopy theory to other areas have begun to appear. In particular, fundamental calculations in transchromatic homotopy theory have been applied very successfully to better understand the equivariant stable homotopy category. The primary scientific aim of this conference is to describe work on the forefront of this area, explain applications to other mathematical areas, and also to get input from experts in related areas. Our speakers consist of established world experts in chromatic homotopy theory, arithmetic geometry, differential geometry, and group theory, all of whose work is related in some way to transchromatic homotopy theory, as well as early career mathematicians who are rapidly pushing the field forward. More information is available at https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/SFB_transchromatic_2020.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.

该国家科学基金会奖为美国的初级研究人员提供了旅行资金，将前往2020年8月2日至7日在德国雷根斯堡大学举行的“第二跨大西洋跨色素同型理论会议”。这项五天的活动将包括世界专家的演讲以及初级研究人员的谈判。这次会议的目的是将跨色素同质理论的专家与在该地区工作的初级研究人员和研究生一起，以及密切相关领域的专家，包括算术几何和差异几何学。第二个目的是让非常早期的职业研究人员（I，E，研究生和博士后）有机会以较短的演讲形式描述他们的研究。这样一来，研究生不仅会获得个人指导，而且该领域以外的数学家将暴露于跨性同型理论中的情况。我们希望这将显着提高人们对已经开发的技术以及面临的问题的认识。染色同义理论是一个迅速新兴的色素同型理论的亚细分区。色度同型理论通过将其分解为“色层”来组织稳定的同型类别。在研究这些层次时，代数拓扑师发现了同质理论与代数几何学，数字理论，高级类别理论和超对称场理论之间的密切关系。要将每个色层的结果组装到有关稳定同型类别的全局结果中，必须了解色层之间的关系。这是跨性同义理论的主要目标。自2017年6月在雷根斯堡大学举行的第一次跨大西洋跨色素同质理论会议以来，跨性同义理论的真实应用已开始出现。特别是，经跨性同义理论中的基本计算已被非常成功地应用于更好地了解稳定同型类别。这次会议的主要科学目的是描述该领域最前沿的工作，向其他数学领域解释应用程序，并从相关领域的专家那里获得投入。我们的演讲者由既定的色素同态理论，算术几何，差异几何学和群体理论组成，他们的工作都与跨性同型理论以及正在迅速推动领域前进的早期职业数学家相关。请访问https://www-app.uni-regensburg.de/fakultaeten/mat/sfb-higher-invariants/index.php/sfb_transchromatic_2020.this Award。该奖项反映了NSF的法定任务，并已通过评估概念概述了，该奖项已被评估和概述。