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Attend a lecture on "Progress Around the Boone-Higman Conjecture" by Matthew Zaremsky from the University at Albany as part of the Joint IAS/PU Groups and Dynamics Seminar. Explore the 50-year-old Boone-Higman conjecture (1973), which predicts that a finitely generated group has solvable word problem if and only if it embeds in a finitely presented simple group. While the "if" direction is proven, the "only if" direction remains an open challenge. Discover a new sufficient condition for groups to satisfy this conjecture that focuses on group actions with specific properties rather than simple groups directly. Learn about recent breakthroughs applying this approach to hyperbolic groups and Aut(F_n), involving "twisted Brin-Thompson groups" - interesting groups of Cantor space homeomorphisms. The talk will cover joint work with Jim Belk, Collin Bleak, Francesco Fournier-Facio, James Hyde, and Francesco Matucci. The one-hour seminar takes place at Simonyi 101 on March 25, 2025, at 4:30pm.
