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Explore a mathematics seminar that delves into the fascinating world of random matrices and word-distributions in matrix groups over finite fields. Learn about the probability distributions induced by words in free groups when applied to finite groups, with a particular focus on matrix groups over finite fields. Discover the surprising connection between these distributions and free group algebras, drawing interesting parallels with symmetric group cases. Gain a foundational understanding of free groups and free group algebras through a gentle introduction, followed by an exploration of new findings and compelling conjectures in this field. The presentation covers the collaborative research work with Danielle Ernst-West and Matan Seidel, building upon earlier established connections between distributions on symmetric groups and the poset of finitely generated subgroups of the free group.
