Algebraic geometry is the study of objects defined by polynomial equations, called varieties. These equations can be studied algebraically (e.g. solving the equation to find all solutions) or geometrically (e.g. graphing the shape defined by the equation) and algebraic geometry uses the tools from both perspectives to analyze varieties. An overarching goal of the field to be explored in this project is to classify all possible varieties, which is done through the construction of moduli spaces, or parameter spaces for varieties of a given type. The study of moduli spaces has a rich history and these spaces arise naturally in algebraic geometry, symplectic geometry, differential geometry, enumerative geometry and combinatorics, mirror symmetry, number theory, and physics. The work involved with this project has connections to each of these fields. The PI will mentor both undergraduate and graduate students and continue with a variety of activities that encourage the participation of women in mathematics. The main objective of the PI is to research moduli spaces of higher dimensional algebraic varieties, specifically to study degenerations of hypersurfaces (varieties defined by a single polynomial equation). The PI will approach two related questions: studying smooth limits of hypersurfaces from a moduli-theoretic perspective, focusing on when such limits are again hypersurfaces, and also an explicit classification of singular varieties appearing in these moduli spaces