Nic Banks, Department of Pure Mathematics, University of Waterloo
"Inverse Galois Theory of Elliptic Curves"
The Inverse Galois Problem asks which finite groups appear as Galois groups of extensions of the rational numbers. The problem was first systematically investigated in 1892 by Hilbert, but the essential ideas were in the mathematical community since Galois enunciated his groundbreaking theory in the 1830s.
Since then, many partial cases of the IGP have been solved, but the full problem remains open. Several geometric methods have been used to construct Galois groups. In this talk, we will investigate Galois groups arising from torsion points on elliptic curves. We will conclude by looking at Serre's celebrated Open Image Theorem, which quantifies the failure of certain Galois representations to be isomorphisms.
This seminar will be held jointly online and in person:
- Room: MC 5403
- Zoom information: Meeting ID: 817 1030 9714; Passcode: 063438