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Explore the mathematical structure and properties of free Burnside groups B(r, n) in this 51-minute conference talk from the Hausdorff Center for Mathematics. Delve into the historical context of Burnside's 1902 question about whether these groups are necessarily finite, and examine the groundbreaking 1968 proof by Novikov and Adian showing that B(r, n) is infinite for sufficiently large odd exponents when r > 1. Investigate the central problem of understanding equations in B(r, n), specifically determining conditions under which every solution to a given set of equations S in B(r, n) originates from a solution in the free group of rank r. Discover additional aspects of periodic groups, including quotients of free Burnside groups, while examining their Hopf and co-Hopf properties, isomorphism problems, and automorphism groups. Learn about research conducted during the 2018 HIM program "Logic and Algorithms in Group Theory" through this collaborative work with Z. Sela that advances understanding of these complex algebraic structures.
