Johnson Jia
Department of Mathematics
University of Michigan
2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
Office: EH 4084
Phone: (734) 763-2502
I am a sixth year student in the Department of Mathematics at the University of Michigan.
My interest is in number theory. I am especially fascinated by the deep connections between certain automorphic forms and motives (and their realizations as Galois representations). Currently I am working using theta correspondence to produce interesting congruences between automorphic forms and their associated Galois representations (assuming they exist), a long the lines indicated in the works of Harris-Li-Skinner.
In the significance of "arithmetic" automorphic forms in arithmetic/number theory stems from the widely-held belief that the L-functions of a large family of well-behaved motives are automorphic; moreover, the special values of these L-functions are intimately related to the periods that arise from ratios of periods of automorphic forms. There is much work to be done.