Motivic Symmetries

动机对称性

基本信息

批准号：
2304151
负责人：
Jeremiah Heller
金额：
$ 25.23万
依托单位：
University of Illinois at Urbana-Champaign
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：
2023-09-01 至 2026-08-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2304151&HistoricalAwards=false
关键词：
Motivic Symmetries

项目摘要

Over the past century, algebraic topology has developed many sophisticated methods and tools to study geometric "shapes". Motivic homotopy theory, provides a framework to apply tools from algebraic topology, to the study of algebraic varieties and to important algebro-geometric invariants such as vector bundles, quadratic forms, algebraic cycles, and rational points. This project will study structural and computational aspects of homotopy theory for algebraic varieties with an emphasis on geometric applications. Broader impacts of this project include work with incarcerated individuals, as well as work with undergraduate and graduate students. In this project, the PI will combine equivariant and higher categorical techniques to study ramifications of recent developments within motivic homotopy theory. In the first part of the project, the PI proposes to further develop tools to study normed motivic spectra, with a focus on orientations. In the second part, the PI proposes to focus on computations of equivariant motivic invariants and slice spectral sequences. In the third the PI proposes to develop a theory of equivariant framed correspondences and apply this to the study of equivariant motivic loop spaces.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.

在过去的一个世纪中，代数拓扑已经开发了许多复杂的方法和工具来研究几何“形状”。动机同义理论提供了一个框架，可以将代数拓扑的工具应用于代数品种的研究以及重要的代数几何不变式，例如向量束，二次形式，代数循环和理性点。该项目将研究代数品种的同型理论的结构和计算方面，重点是几何应用。该项目的更广泛影响包括与被监禁的人一起工作，以及与本科生和研究生合作。在该项目中，PI将结合模棱两可的分类技术，以研究动机同型理论中最新发展的后果。在项目的第一部分中，PI建议进一步开发研究规范动机的工具，重点是方向。在第二部分中，PI提议专注于模棱两可的动机不变性和切片频谱序列的计算。在第三个PI中，PI提议开发一项模棱两可的框架对应理论，并将其应用于模棱两可的动机循环空间的研究。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的智力优点和更广泛影响的评估标准通过评估来支持的。