Mid-Atlantic Topology Conference

该奖项为2020年4月18日至19日在费城宾夕法尼亚大学举行的中大西洋拓扑学会议的参与者提供资金。会议集中讨论了目前处于研究前沿的代数拓扑学领域：算术拓扑学、色同伦论、应用拓扑学、流形拓扑学和几何表示论。将优先资助研究生和没有其他资金来源的初级研究人员，以及那些在数学方面代表性不足的群体的成员。代数拓扑学的多样性正在不断增强，本次会议将通过挑选发言者和与会者来促进这一点。鉴于近年来在东海岸看到的代数拓扑学的研究增长以及由此导致的该学科学生群体的增长，这次会议是相当及时的。现代代数拓扑学与许多领域密切相关。从Thom的命题到Madsen-Weiss定理等等，稳定同伦理论在流形的研究中一直扮演着重要的角色。近年来，在球面上奇异光滑结构的Kervaire不变问题的求解中，引入了等变稳定同伦理论的成熟技术，开辟了新的研究方向和应用。另一方面，同伦理论通过动机同伦理论和抽象剪刀同余K-理论在经典的Grothendieck环上的应用而与代数几何相联系。此外，在新兴的拓扑数据分析领域，代数拓扑学最近在数据研究中得到了显著的应用。这次会议的目的之一是提供代数拓扑学的新方向以及与其他领域的互动的样本，如几何拓扑学、算术几何和应用拓扑学。这次会议有9个45分钟的应邀演讲，为期两天。会议的科学重点无疑是前瞻性的：演讲者是该领域正在崛起的领导者，其中包括早期的职业研究人员；每一位演讲者代表着未来拓扑结构的一个独特和至关重要的方面。更多信息可在网页上找到：https://sites.google.com/view/mid-atlantic-topology/homeThis奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award provides funding for participants in the Mid-Atlantic Topology Conference taking place April 18-19, 2020 at the University of Pennsylvania in Philadelphia. The conference focuses on a confluence of areas in algebraic topology that are currently at the forefront of research: arithmetic topology, chromatic homotopy theory, applied topology, manifold topology, and geometric representation theory. Priority for funding will be given to graduate students and to junior researchers without other funding sources, and among those to members of underrepresented groups in mathematics. Algebraic topology is enjoying a growing diversity, which this conference will foster through the selection of speakers and participants. This conference is quite timely in light of the research growth in algebraic topology seen on the East Coast in recent years and the resulting growth of student groups in the subject. Modern algebraic topology is intimately tied to a host of fields. From Thom's thesis to the Madsen-Weiss theorem and beyond, stable homotopy theory has long played a crucial role in the study of manifolds. More recently, sophisticated techniques of equivariant stable homotopy theory were brought to bear in the solution of the Kervaire invariant problem concerning exotic smooth structures on spheres, opening new research directions and applications. On the other hand, homotopy theory is connected to algebraic geometry via motivic homotopy theory and applications such as those of abstract scissors congruence K-theory to the classical Grothendieck ring of varieties. Moreover, algebraic topology has seen notable recent application to the study of data in the emerging field of topological data analysis. One of the aims for this conference is to provide a sample of new directions in algebraic topology and interactions with other fields such as geometric topology, arithmetic geometry, and applied topology. The conference features nine 45-minute invited talks over two days. The scientific focus of the conference is decidedly forward-looking: the speakers are rising leaders in the field and include early career researchers; each speaker represents a distinct and vital aspect of the topology of the future. More information can be found on the webpage: https://sites.google.com/view/mid-atlantic-topology/homeThis 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.