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Explore advanced topics in group theory through this comprehensive lecture series from the Hausdorff Center for Mathematics' trimester program on Logic and Algorithms in Group Theory. Delve into cutting-edge research areas including pseudofinite groups with Dugald Macpherson's three-part series, representation theory for groups of Lie type presented by Gerhard Hiss, and algorithmic approaches to finitely presented groups covered by Derek Holt. Examine stability theory and invariant random subgroups through Andreas Thom's lectures, and investigate non-commutative algebraic geometry with Zlil Sela's foundational work. Study amenable theories, Burnside groups of small odd exponent, growth phenomena in linear algebraic and permutation groups, and forking independence in free groups. Learn about first-order rigidity in high-rank arithmetic groups, group isomorphism problems, equations in groups and their connections to formal languages, relational complexity of finite permutation groups, and properties of small profinite groups. Discover arboreal structures and Poisson boundaries, computational methods for infinite linear groups, scale computation techniques, and applications of small cancellation theory to rings, concluding with model-theoretic approaches to rigidity in ergodic theory.
