Explore the intricacies of local fields through the lens of the Lean theorem prover in this comprehensive 56-minute lecture by María Inés de Frutos-Fernández from the Hausdorff Center for Mathematics. Delve into the formalization of local field theory using Lean, gaining insights into both the mathematical concepts and their implementation in a proof assistant. Discover how advanced algebraic structures are represented and manipulated within the Lean framework, enhancing your understanding of local fields and their properties. Engage with cutting-edge research at the intersection of mathematics and computer science, and learn how formal verification tools like Lean are revolutionizing mathematical proofs and theory development.