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Explore the geometric aspects of the conjugacy problem for finitely presented groups in this mathematical lecture. Learn about the well-established relationship between the word problem for finitely presented groups and the geometry of disc-filling loops in compact manifolds with fundamental group G, which led to comprehensive understanding of Dehn Functions in the 1990s and 2000s. Discover why the geometry of the conjugacy problem presents greater challenges and remains less understood compared to the word problem. Survey current knowledge in this field before delving into recent research highlights on Conjugator Length Functions, which provide optimal bounds on the size of conjugating elements in finitely presented groups. Gain insights from collaborative research with Tim Riley from Cornell University that advances understanding of this complex mathematical topic.
