Conference Program: https://web.math.princeton.edu/~petero/Browder/Browder.html

9:30 AM — 10:30 AM
Speaker: Ishan Levy
Location: Lewis Library 120 (Registered Attendees) Lewis Library 121 (Overflow/Walk-In viewing)

The splitting of the Kervaire--Milnor sequence

The work of Kervaire--Milnor, along with the resolution of the Kervaire invariant one problem describes the group of homotopy spheres in dimensions at least 5 as an extension of two groups. One of these groups is a cyclic group that is understood, and the other is closely related to the stable homotopy groups of spheres. I will describe work in progress with Burklund and Crowley with the goal of showing this extension is always split, completing a program of Brumfiel, and thereby completely reducing the computation of these group of homotopy spheres to that of the stable homotopy groups of spheres. As in the work of Browder, this problem reduces to one in stable homotopy theory: one must prove the mod 2 analog of the Hill--Hopkins--Ravenel nonexistence result of the Kervaire classes.

11:00 AM — 12:00 PM
Speaker: Shmuel Weinberger
Location: Lewis Library 120 (Registered Attendees) Lewis Library 121 (Overflow/Walk-In viewing)

The Browder-Livesay invariant

The Browder-Livesay invariant was critical to the classification of manifolds homotopy equivalent to RP^n. For n = 3 mod 4 there are infinitely many such manifolds (when n isn’t 3). I will describe some later work (of many people) building on this — showing how to unconditionally prove some consequences of the Farrell-Jones conjecture and also how to get some geometric information on manifolds that surgery theory implies exist.