Conference: Cornell Topology

Cornell University, Ithaca NY

Investigators

Abstract

This award is to support speakers and participants at several meetings of the Cornell Topology Festival, an annual conference at Cornell University, starting with the conference planned for May 5-7, 2023. The conference has been a force in the mathematical life of topologists and geometers in the northeastern United States since 1963, providing an arena for the development and dissemination of a broad array of results from within algebraic, differential, and geometric topology and allied subjects. The activities are designed to encourage mathematical breadth and exchange of ideas between different branches of topology, as well as to welcome early career mathematicians into the field and promote interactions between junior and senior participants. Each year, several of the talks cluster around one significant theme, in order to communicated a recent research development in one subarea to topologists across other areas, and to educate graduate students and early career researchers on a subject of recent interest. Each iteration of the conference starts with a day of introductory talks by early junior speakers, and a colloquium talk on the history of the topic chosen for the main theme. It also includes a lightning session of short talks on exciting new research directions. All of these activities serve to counter recent trends towards increasing specialization, by showcasing developments across inter-related fields at an accessible level. The area of interest for the 2023 conference will be recent developments in the theory of 4-manifolds, a topic with deep connections to geometric, algebraic, and symplectic topology and geometry. About one third of the talks will be on this subject, in order to introduce topologists across sub-disciplines to this area in more detail than obtainable by attending a single talk or mini-course. Possible future themes include: high dimensional negatively curved manifolds, trace methods, and homotopy type theory; although the organizers remain flexible should a new exciting development come to light elsewhere. The remainder of talks at the conference showcase a broad range of recent developments in different areas of topology, selected with a view towards breadth. Additionally, all speakers participate in a “lightning round” consisting of short pitches of recent exciting work by others and speculation on future trends. This gives a forward-looking perspective on new developments and stimulates discussion. The opening introductory day of activities and graduate student talks provides a point of entry for interested non-experts and encourages graduate student involvement. The broader impacts of the activities include a more broadly-trained community of topologists, able to transcend the boundaries of subspecialties; a more diverse mathematical workforce; a more rapid integration of younger topologists into areas of current research; and the enhancement of collaboration among researchers in different areas of topology. The training effects of the conference will be extended by dissemination of lecture notes from the workshops and summaries of the panel discussion and problem session; the main vehicle for this is the conference web site, which has been maintained continuously since 1997. https://e.math.cornell.edu/sites/topology/ 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.