Title: The weight part of Serre's conjecture for GL_n and GSp_4
Abstract: The phenomenon of congruences between q-expansions of modular forms played a large role in the development of the theory of Galois representations and eventually to modularity. The weight part of Serre's conjecture asks when two cuspidal eigenforms of different weights can be congruent. A rather complete answer has been given in terms of Galois representations for classical and Hilbert modular forms. We will discuss recent generalizations to higher rank in several joint works with B.V. Le Hung, H. Lee, B. Levin, and S. Morra.