Algebraic Geometry is a field in mathematics that studies geometric objects defined by polynomials. Since polynomials are used in the definition, algebraic methods can be used to study the geometry.
The main objects that I am interested in are rlow dimensional objects such as algebraic curves and surfaces. I try to find “invariants” that can be used to distinguish similar curves, thnik of the “exsitence problem” which asks wheter curves satisfying given conditions exist, and once we know the existance, considr the “construction problem” in which the goal is to explicitely write down the equation. Since explicit equations appear, I sometimes use computers in order to execute my calculations.