Affine Invariant Submanifolds with Completely Degenerate Kontsevich-Zorich Spectrum

I will introduce the Lyapunov exponents of the Teichmueller
geodesic flow on the moduli space of Abelian differentials and give some
background on what is known about them. Then I will consider the problem
of classifying all affine invariant submanifolds with the property that
they have the maximal number of zero Lyapunov exponents with respect to
the Kontsevich-Zorich cocycle. I will prove that any such submanifold is
an arithmetic Teichmueller curve. By a result of Martin Moeller, it must
occur in genus 3, 4, or 5.