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This lecture explores the stability properties of maximum cuts in binomial random graphs. Discover how the family of largest cuts in the binomial random graph G_{n,p} demonstrates a remarkable stability property: when 1/n ≪ p ≤ 1-Ω(1), with high probability, there exists a set of n-o(n) vertices that is partitioned identically by all maximum cuts. Learn how this property extends to nearly-maximum cuts as well, and how these findings can be applied to show that certain properties of G_{n,p} that hold in a fixed cut simultaneously hold in all maximum cuts. The presentation covers joint research with Ilay Hoshen (Tel Aviv University) and Maksim Zhukovskii (University of Sheffield). Delivered by Wojciech Samotij, a faculty member at Tel Aviv University's School of Mathematical Sciences who previously studied at the University of Wrocław and the University of Illinois at Urbana-Champaign.
