Vanishing cycles and almost toric fibrations by Jie Min

Series
Geometry Topology Seminar
Time
Monday, March 10, 2025 - 2:00pm for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jie Min – University of Massachusetts Amherst – jmin@umass.eduhttps://sites.google.com/site/jieminmath/home
Organizer
Randy Van Why

Vanishing cycles of Lefschetz fibrations give examples of Lagrangian spheres in the fiber. A natural question, first raised by Donaldson, is whether all Lagrangian spheres arise this way. We focus on this problem for positive rational surfaces, which were shown to admit a geometric structure called almost toric fibrations. I will talk about a work-in-progress showing all Lagrangian spheres here are visible in an almost toric fibration and thus are vanishing cycles of a nodal degeneration.