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Probability and Dynamical Systems Seminar
Probability and Dynamical Systems Seminar
A short proof of the Komlos conjecture
A short proof of the Komlos conjecture
Organizers
Speaker
Time
Tuesday, October 20, 2026 3:15 PM - 4:15 PM
Venue
A3-3-301
Online
Zoom 482 240 1589
(BIMSA)
Abstract
Komlos conjectured that there exists an absolute constant $C$ such that for every $d > 0$ and every finite collection of vectors $v_1,...,v_n \in \mathbb{R}^d$, there exists $c_1,...,c_n \in \{-1,1\}$ for which the sum of $c_iv_i$ is has infinity norm at most $C$. In September of 2026 Guo, Fang, and Liu gave an AI-assisted proof of this conjecture with $C = 3\sqrt{2\pi}$. Soon afterwards, Karingula and Lovett gave a simpler proof at the expense of enlarging $C$ to 36. We will discuss the simpler proof of Karingula and Lovett.