Geometry Seminar

---

A necessary and sufficient condition for k-transversals

Speaker: Daniel McGinnis, Princeton U

Location: Warren Weaver Hall 1314

Date: Tuesday, September 16, 2025, 6 p.m.

Synopsis:

We solve a long-standing open problem posed by Goodman & Pollack in 1988 by establishing a necessary and sufficient condition for a family of convex sets in \(\mathbb{R}^d\) to admit a \(k\)-transversal (a \(k\)-dimensional affine subspace that intersects each set in the family) for any \(0 \le k \le d-1\). This result is a common generalization of Helly's theorem (\(k=0\)) and the Goodman-Pollack-Wenger theorem (\(k=d-1\)). Our approach is topological and employs a Borsuk-Ulam-type theorem on Stiefel manifolds.

Notes:

In person.  Plz contact Boris Aronov for if you are not NYU-affiliated and want to attend in person.