Speaker: Aftab Pande, Cornell

Title: Deformations of Galois representations and some distribution conjectures

Dec. 8, 4:00 - 5:00 pm in MS 5148

Abstract: We start with a 2 dimensional mod p Galois representation and deform it to a Z_p representation (\rho), which is ramified at infinitely many primes (a method due to Ramakrishna). Such representations can be modified such that the distributions of the a_l ( = trace(\rho(frob_l)) are in contrast to the statements due to Sato-Tate, Lang-Trotter and others. If time permits, I'll also outline a method where residual representations of G_K (K a number field) have deformations with very large image.