Abstract:
The study of the equations defining projective varieties and the relations amongst them, known as the theory of syzygies, dates back to the very beginnings of algebraic geometry in the work of Sylvester and Hilbert. Much more recently, deep connections have been found between syzygies and the intrinsic geometry of an abstract curve. This talk will explore this connection and explain how it relates to K3 surfaces as well as the birational geometry of the moduli spaces of curves.
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