Seminar Details
Szemerédi’s Theorem, Primes, and Nilsequences
- Start Date: April 14, 2025
- Event Start Time: 2:00 PM
- Event End Time: 3:00 PM
- Seminar Series: Rutgers Discrete Mathematics Seminar
- Presenter(s): James Leng - University of California, Los Angeles
- Event Location: Conference Room 705 | Rutgers University | Hill Center | 110 Frelinghuysen Rd
- Event Additional Info: See: https://sites.google.com/view/rutgersdmseminar
- Presentation Type: Stand Alone Presentation
- Abstract:
Let $r_k(N)$ be the largest subset of $[N] = \{1, \dots, N\}$ with no k-term arithmetic progression. Szemerédi’s theorem states that $r_k(N) = o_k(N)$. We will go over the proof that achieves the best known upper bounds for $r_k(N)$ for general $k$. We will discuss how the mathematics behind the proof relates to counting primes along linear forms and the distribution of orbits on $G/\Gamma$ with $G$ nilpotent and $\Gamma$ discrete and cocompact. This is (partly) based on joint work with Ashwin Sah and Mehtaab Sawhney.