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会议的参与者提供资金。会议重点讨论了代数拓扑学中目前处于研究前沿的领域：算术拓扑学，色同伦理论，应用拓扑学，流形拓扑学和几何表示理论。优先资助将给予研究生和没有其他资金来源的初级研究人员，其中包括数学代表性不足的群体的成员。代数拓扑学正在享受越来越多的多样性，本次会议将通过选择发言者和与会者来促进。这次会议是相当及时的研究增长在代数拓扑看到东海岸近年来和由此产生的增长的学生团体在这个问题上。 现代代数拓扑学与许多领域密切相关。从Thom的论文到Madsen-Weiss定理，稳定同伦理论在流形的研究中一直扮演着至关重要的角色。最近，复杂的技术等变稳定同伦理论带来了承担的解决方案的Kervaire不变的问题有关奇异光滑结构的领域，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应用（如抽象剪刀同余K-理论对经典Grothendieck簇环的应用）与代数几何相联系。此外，代数拓扑最近在新兴的拓扑数据分析领域的数据研究中得到了显着的应用。本次会议的目的之一是提供一个样本的新方向代数拓扑和互动与其他领域，如几何拓扑，算术几何，应用拓扑。会议在两天内举行了9场45分钟的特邀演讲。会议的科学重点无疑是前瞻性的：演讲者是该领域的新兴领导者，包括早期的职业研究人员;每个演讲者都代表了未来拓扑结构的一个独特而重要的方面。更多信息可以在以下网页上找到：https://sites.google.com/view/mid-atlantic-topology/homeThis奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

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.