Mathematics & Statistics visitor seminar

SPEAKER: Dr. Giovanni Rossol

(University of Cambridge, UK)

ABSTRACT:  L-functions are complex functions which are defined from interesting arithmetic objects, such as number fields and elliptic curves. These functions contain a lot of interesting information about the objects that interest us. During the talk, I shall give some examples of how this information can be recovered, stressing the importance of the p-adic and mod p behaviour of these functions. I shall conclude with an overview of related conjectures (Iwasawa Main Conjecture, Greenberg's conjecture on trivial zeroes, existence of eigenvarieties,...) and my results on these topics.