HHigher Genus Curves in Mathematical Physics and Arithmetic GHigher Genus Curves in Mathematical Physics and Arithmetic Geometryde Andreas Malmendier, Tony ShaskaMateriasGeometryMathematical physicsNumber theoryArithmetical algebraic geometryCongressesNumber theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Curves of arbitrary genus or genus $\ne 1$ over global fieldsNumber theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Heights