Congruences between modular forms

Contact: Christian Kaiser (kaiser @ mpim-bonn.mpg.de)

The resolution of Serre's conjecture for modular forms by Khare-Wintenberger in the mid-2000s was a major achievement in the field of number theory. In this talk, I will begin by describing Serre's conjecture and its origins in the theory of congruences between modular forms. I will then describe how the conjecture is connected to representation theory in finite characteristic. This will naturally lead to higher dimensional analogues of the conjecture.  Finally, I will discuss results on these higher dimensional conjectures joint with Daniel Le, Bao V. Le Hung and Stefano Morra.