Explore a comprehensive mathematics seminar where Joel Friedman from The University of British Columbia delves into the Hanna Neumann conjecture from the 1950s and its resolution through innovative graph theory tools. Learn about sheaf theory on graphs, Galois theory for graphs, and the preservation of local properties under base change, with potential additional applications of sheaves on graphs. Requiring only basic knowledge of graph theory and linear algebra, discover how these mathematical concepts intersect to solve a decades-old conjecture, with possible references to Chevalley's Theorem on constructible sets. While rooted in advanced mathematical concepts, the presentation maintains accessibility without extensive prerequisites in number theory or algebraic geometry.