Michael Kemeny, Special Colloquium

Title: The equations defining curves and moduli spaces

Abstract: A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures, which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.