Syzygies of Algebraic Varieties

Algebraic geometers study geometric objects defined by algebraic equations. It is natural to study the relations among the defining equations, i.e. the syzygies of the varieties. One may ask can we detect geometric information about the variety from its syzygies. In this talk, I'll discuss some of the related questions and results that I worked on related to the problem. Most of the results that I'll talk about were joint work with R. Lazarsfeld.