Prof. Miranda's main field of interest is Algebraic Geometry,
which is, broadly speaking, the study of curves, surfaces, etc.
which are defined by the vanishing of one or several polynomials.
He has written articles and/or directed research in the following areas.
- Elliptic Surfaces
- Geometric Invariant Theory
- Classification and Degenerations of Surfaces
- Coverings of Algebraic Varieties
- Integral Quadratic Forms
- Toric Geometry
- Gaussian Maps for Curves
- Graph Curves
- Fano Threefolds
- Quantum Cohomology