Conference: Cornell Topology Festival

This award is to support speakers and participants at The Cornell Topology Festival, an annual conference at Cornell University, to be held May 1-3, 2026. The festival 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 of the festival are designed to encourage mathematical breadth and exchange of ideas between different branches of topology, as well as to welcome young 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 communicate a recent research development in one subarea to topologists across other areas, and to educate graduate students and junior researchers on a subject of recent interest; this year, the theme is "Degenerations and moduli spaces," and there are additional talks ranging from homotopy theory to geometric topology. The festival starts with a day of introductory talks by junior speakers, and a colloquium talk on the history of the topic chosen for the main theme. At the end of the second day there is a lightning session of short talks on exciting new research directions. All these activities serve to showcase developments across interrelated fields at an accessible level. The area of interest for the 2026 festival is degenerations and moduli spaces. About 1/3 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. The remainder of talks at the festival 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 to provide a point of entry for interested non-experts and to encourage 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 rapid integration of early career topologists into areas of current research; and the enhancement of collaboration among researchers in different areas of topology. The training effects of the Festival 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 Festival web site, which has been maintained continuously since 1997. https://e.math.cornell.edu/sites/topology/2026/index_2026.php 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.