Detecting Primitivity and Free-splittings in the Free Group Algebra

Explore a 47-minute mathematics seminar lecture that delves into the intricacies of the free group algebra and its relationship with free groups. Learn about the fundamental properties of free group algebra, including its parallels with the Nielsen-Schreier theorem, and discover a novel algorithm for detecting primitive elements within ideals - analogous to Whitehead's algorithm in free groups. Understand why the free group algebra serves as a crucial tool in addressing free group problems, despite having fewer algorithmic solutions compared to free groups. Follow along as the speaker presents collaborative research findings developed with Matan Seidel and Danielle Ernst-West, demonstrating the practical applications and theoretical significance of this mathematical concept in group theory.