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。会议的重点是代数拓扑中目前处于研究前沿的领域的融合：算术拓扑、色同伦理论、应用拓扑、流形拓扑和几何表示理论。研究生和没有其他资金来源的初级研究人员将优先获得资助，其中包括数学领域代表性不足的群体的成员。代数拓扑学正享受着日益增长的多样性，这次会议将通过选择演讲者和参与者来促进这种多样性。鉴于近年来在东海岸看到的代数拓扑研究的增长以及该主题的学生群体的增长，这次会议非常及时。现代代数拓扑学与许多领域密切相关。从Thom的论文到Madsen-Weiss定理等，稳定同伦理论在流形研究中一直扮演着至关重要的角色。近年来，将等变稳定同伦理论的复杂技术应用于求解球面上奇异光滑结构的Kervaire不变量问题，开辟了新的研究方向和应用领域。另一方面，同伦理论通过动力同伦理论和抽象剪子同余k理论在经典Grothendieck变异环上的应用与代数几何联系起来。此外，代数拓扑在拓扑数据分析这一新兴领域的数据研究中也有显著的应用。本次会议的目的之一是提供代数拓扑以及与其他领域（如几何拓扑、算术几何和应用拓扑）相互作用的新方向的样本。会议在两天内举行了9场45分钟的受邀演讲。会议的科学焦点无疑是前瞻性的：演讲者是该领域的新兴领导者，包括早期的职业研究人员；每一位演讲者都代表着未来拓扑学的一个独特而重要的方面。更多信息可在以下网页找到：https://sites.google.com/view/mid-atlantic-topology/homeThis该奖项反映了美国国家科学基金会的法定使命，并通过基金会的知识价值和更广泛的影响审查标准进行评估，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.