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My current mathematical research is in the area of number theory, in particular arithmetic geometry with techniques from analytic number theory. Some key words: elliptic curves; modular forms; abelian varieties; Drinfeld modules; L-functions; sieve methods; the Chebotarev density theorem. While I was a doctoral student, my mentors were Professors Ernst Kani and M. Ram Murty; as such, my mathematical grandfathers are Professors Dorian Goldfeld, Peter Roquette, Jean-Pierre Serre, and Harold Stark. My collaborators are: Antal Balog; Manjul Bhargava; Pete Clark; Chantal David; William Duke; Etienne Fouvry; David Grant; Chris Hall; Nathan Jones; Ernst Kani; Ron Livne; Florian Luca; M. Ram Murty; Igor Shparlinski; Arpad Toth. My research is currently supported by the University of Illinois at Chicago and NSF grant DMS-0636750. |