Research directions in number theory

Explicit construction of Ramanujan bigraphs.- Classifications of Elliptic Fibrations of K3 surfaces.- Classifications of Elliptic Functions of a singular K3 Surface.- Shalika Germs for Sl(n) and Sp(2n) are Motivic.- The Conjectural Relation Between Generalized Shalika Models on SO4n(F) and Symplectic Linear Models on Sp4n(F): A Toy Example.- Bad Reduction of Genus Three Curves with Complex Multiplication.- Symmetries of Rational Functions Arising in Ecalle's Study of Multiple Zeta Values.- On T-Li Coefficients for Rankin-Selberg L-Functions.- Galois Representations and Galois Groups over Q.