Modular Arithmetic Geometry

Modular Curves

Modular curve creation and attributes.

Modular Curves

Small Modular Curves

Explicit models, projections and automorphisms of small modular curves.

Small Modular Curves

Congruence Subgroups of PSL2(R)

Congruence subgroups, their structure and group elements.

Congruence Subgroups of {\operatorname{PSL}}_2({\mathbb{R}})

Arithmetic Fuchsian Groups and Shimura Curves

Fuchsian groups, fundamental domains and triangle groups.

Arithmetic Fuchsian Groups and Shimura Curves

Modular Forms

Spaces of modular forms, bases and q-expansions.

Modular Forms

Modular Symbols

Modular symbols spaces, creation and bases.

Modular Symbols

Brandt Modules

Brandt modules, subspaces and Hecke operators.

Brandt Modules

Supersingular Divisors on Modular Curves

Supersingular divisors: creation, basis and properties.

Supersingular Divisors on Modular Curves

Modular Abelian Varieties

Modular abelian varieties, homology and morphisms.

Modular Abelian Varieties

Hilbert Modular Forms

Hilbert modular forms: creation and basic properties.

Hilbert Modular Forms

Modular Forms over Imaginary Quadratic Fields

Bianchi modular forms, basic properties and Hecke operators.

Modular Forms over Imaginary Quadratic Fields

Algebraic Modular Forms

Algebraic modular forms: creation, properties and elements.

Algebraic Modular Forms

Representations of Local Fields

Admissible representations of GL\ :sub:2\ (Q\ :sub:p\ ) and local Langlands.

Admissible Representations of {\operatorname{GL}}_2({\mathbb{Q}}_p)