Seminar Details
A Necessary and Sufficient Condition for $k$-transversals
- Start Date: March 31, 2025
- Event Start Time: 2:00 PM
- Event End Time: 3:00 PM
- Seminar Series: Rutgers Discrete Mathematics Seminar
- Presenter(s): Daniel McGinnis - Princeton University
- Event Location: Conference Room 705 | Rutgers University | Hill Center | 110 Frelinghuysen Rd
- Event Additional Info: <p>See: <a href="https://sites.google.com/view/rutgersdmseminar">https://sites.google.com/view/rutgersdmseminar</a></p>
- Presentation Type: Stand Alone Presentation
- Abstract:
We solve a long-standing open problem posed by Goodman and Pollack in 1988 by establishing a necessary and sufficient condition for a finite family of convex sets in $\mathbb{R}^d$ to admit a $k$-transversal (a $k$-dimensional affine subspace that intersects each set) 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 ($k=d-1$).
This is joint work with Nikola Sadovek.