The Inverse Galois Problem is easily stated— “does every finite group occur as the automorphism group of some finite Galois extension of ” While this is still unsolved, if we replace by , the statement is true. The proof of this fact highlights an interesting boundary between Algebra and Geometry. In this talk, I will discuss Complex manifolds and Covering spaces—two of the key ingredients that go into the proof.
A geometric approach to a 200 year old problem in Algebra