Research

My research topic mainly concerns geometry of Shimura varieties and level raising/lowering of automorphic forms.

Lever lowering for U(1,2)

Mazur’s principle provides simple conditions so that an irreducible unramified $\mathbb{F}\ell$ representation coming from a modular form of level \Gamma{0} (Np) also comes from a form of level $\Gamma_0 (N)$. We proof Mazur’s principle for $U(1,2)$ by studying the geometry of special fiber of Shimura varieties.

Explicit cycle from higher Chow group and arithmetic level raising for U(1,2)

Using higher Chow group we construct cycles in an explicit manner which realise the arithmetic level raising for $U(1,2).$