Seminar Details
An Exotic Growth Rate in Ramsey Theory
- Start Date: April 29, 2024
- Event Start Time: 2:00 PM
- Event End Time: 3:00 PM
- Seminar Series: Rutgers Discrete Mathematics Seminar
- Presenter(s): Xiaoyu He - 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:
The vast majority of natural Ramsey numbers studied to date have polynomial or exponential growth rates. We give a hypergraph Ramsey number - perhaps the simplest of its kind - with an unusual intermediate growth rate. Namely, let S_n be the 3-uniform star (with n+1 vertices and (n choose 2) edges) and let K_4 be the complete 3-uniform hypergraph on 4 vertices. We show 2^{c(\log n)^2} < r(K_4, S_n) < 2^{n^{2/3+o(1)}}.
Based on joint work with David Conlon, Jacob Fox, Dhruv Mubayi, Andrew Suk, and Jacques Verstraete.