Mid-Atlantic Topology Conference

University Of Pennsylvania, Philadelphia PA

Investigators

Abstract

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/home 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.