Probability and Statistics Seminar: A fixed-point theorem for face maps, or deletion-tolerant random finite sets

Event details Date: Wednesday, September 23, 2026 Time: 2:00 PM to 3:00 PM Location: Kaprielian Hall (KAP) - 414 - 3620 South Vermont Avenue, Los Angeles, CA 90089 Type: Lecture / Talk / Workshop Campus: University Park Campus Department: Mathematics About this event Omer Tamuz, Caltech Title: A fixed-point theorem for face maps, or deletion-tolerant random finite sets Abstract: Is there a way to choose a finite subset of the integers so that it’s approximately impossible to tell if the lowest one was removed? Or if the second or third lowest was removed? We show that such probability measures exist, by showing that there exists a finitely additive probability measure that is exactly invariant to these deletions. This problem is related to some interesting open questions, including the amenability of Thompson’s group F. (with Tom Hutchcroft and Nicholas Monod) Official event details: https://calendar.usc.edu/event/probability-and-statistics-seminar-a-fixed-point-theorem-for-face-maps-or-deletion-tolerant-random-finite-sets