A Borel Local Lemma for Finite Asymptotic Separation Index

Explore a 28-minute lecture on the Borel Local Lemma for Finite Asymptotic Separation Index, presented by Felix Weilacher at the Centre de recherches mathématiques (CRM) as part of the Measured Group Theory conference. Delve into the concept of asymptotic separation index (asi), a recently introduced Borel combinatorial parameter related to Gromov's asymptotic dimension. Examine the Lovasz Local Lemma and its applications in classical combinatorics for solving problems with local constraints on graphs. Discover recent developments in finding analogues of the local lemma in Borel and measurable combinatorics, including work by Csoka et al. and Bernshteyn. Learn about the speaker's proof of a Borel version of the Lovasz Local Lemma for Borel graphs with finite asi, which improves exponents for the measurable local lemma in hyperfinite settings and provides the first instances of a Borel version for groups of exponential growth with a polynomial inequality. Gain insights into this joint work with Anton Bernshteyn, advancing the field of Borel combinatorics.