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Explore the mathematical theory of profinite rigidity in crystallographic groups through this 49-minute conference talk from the Hausdorff Center for Mathematics. Survey collaborative research with R. Sklinos, S. André, and D. Carolillo that addresses profinite rigidity problems in crystallographic groups, building from model theoretic solutions for affine Coxeter groups. Examine the concept of profinite homogeneity within crystallographic groups, with special emphasis on affine Coxeter groups and their unique properties. Discover recent developments in elementary equivalence problems for spherical and affine Artin groups of type ˜A_n, representing cutting-edge research conducted with A. Cassella and Giovanni Paolini. Gain insights into advanced topics in geometric group theory, model theory, and algebraic structures that bridge abstract algebra with geometric applications.
