RUI: Motivic, Operadic, and Combinatorial Homotopy Theory

RUI：动机、操作和组合同伦理论

• 批准号: 2204365
• 负责人: Kyle Ormsby
• 金额: $ 34.5万
• 依托单位: Reed College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-08-15 至 2025-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2204365&HistoricalAwards=false
• 关键词: RUI; Motivic; Operadic; Combinatorial; Homotopy

The scope of contemporary homotopy theory — the mathematics of shape and deformation — has expanded dramatically in recent years, and new tools and perspectives are needed to understand its features and potential. The PIs will explore homotopy theory through the lenses of combinatorics (enumerating structures), operads (parametrizing operations), and algebraic geometry (shapes described by polynomial equations). The PIs will also support the participation of a diverse group of undergraduate students in their research by organizing the Collaborative Mathematics Research Group (CMRG). CMRG participants will produce novel research results and also engage their local community in mathematics outreach efforts.The PIs will investigate operadic, combinatorial, and motivic aspects of homotopy theory with the aim of producing structural, enumerative, and computational results. Their projects include the following:(1) Further explore the combinatorics of model structures on finite categories, especially with an eye towards Catalan combinatorics of arbitrary type (in the sense of cluster algebras).(2) Uncover additional structure in the Balmer spectrum of the stable motivic homotopy category by leveraging a recollement with its étale variant.(3) Extend our computational understanding of stable motivic homotopy theory by computing the slice spectral sequence for the Bachmann-Hopkins connective Hermitian image-of-J spectrum.(4) Construct a rigid model for E_n-spaces as commutative monoids in a certain diagram category.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.

近年来，当代同质理论的范围（形状和变形的数学）急剧扩展，需要新的工具和观点来了解其特征和潜力。 PIS将通过组合镜（枚举结构），操作员（参数操作）和代数几何形状（由多项式方程描述的形状）探索同质理论。 PI还将通过组织协作数学研究小组（CMRG）来支持一群多样化的本科生研究。 CMRG参与者将产生新颖的研究结果，并参与其当地社区的数学外展工作。PIS将研究同型理论的运营，组合和主题方面，目的是产生结构性，枚举和计算结果。他们的项目包括以下内容：（1）进一步探索有限类别的模型结构的组合，尤其是在关注加泰罗尼亚类型的加泰罗尼亚组合（从集群代数的意义上）。（2）在Balmer频谱中发现额外的结构，通过利用其稳定的综述类别来审查其稳定的综述。 Bachmann-Hopkins结缔组织J频谱的切片光谱序列。（4）在特定图类别中构建一个刚性模型作为E_N空间的刚性模型，作为交换性的单粒型。该奖项反映了NSF的法定任务，并通过使用基金会的知识优点和广泛的影响来评估NSF的法定任务。

项目成果

Self-duality of the lattice of transfer systems via weak factorization systems

通过弱分解系统的传递系统格的自对偶性

• DOI: 10.4310/hha.2022.v24.n2.a6
• 发表时间: 2022
• 期刊: Homotopy and Applications
• 作者: Franchere, Evan E.;Ormsby, Kyle;Osorno, Angélica M.;Qin, Weihang;Waugh, Riley
• 通讯作者: Waugh, Riley

Model structures on finite total orders

有限总阶数的模型结构

• DOI: 10.1007/s00209-023-03287-6
• 发表时间: 2023
• 期刊: Mathematische Zeitschrift
• 影响因子: 0.8
• 作者: Balchin, Scott;Ormsby, Kyle;Osorno, Angélica M.;Roitzheim, Constanze
• 通讯作者: Roitzheim, Constanze

Multiplicative equivariant K-theory and the Barratt-Priddy-Quillen theorem

乘法等变 K 理论和 Barratt-Priddy-Quillen 定理

• DOI: 10.1016/j.aim.2023.108865
• 发表时间: 2023
• 期刊: Advances in Mathematics
• 影响因子: 1.7
• 作者: Guillou, Bertrand J.;May, J. Peter;Merling, Mona;Osorno, Angélica M.
• 通讯作者: Osorno, Angélica M.

Saturated and linear isometric transfer systems for cyclic groups of order pq

pq 阶循环群的饱和线性等距传递系统

• DOI: 10.1016/j.topol.2022.108162
• 发表时间: 2022
• 期刊: Topology and its Applications
• 影响因子: 0.6
• 作者: Hafeez, Usman;Marcus, Peter;Ormsby, Kyle;Osorno, Angélica M.
• 通讯作者: Osorno, Angélica M.