Talk page
Title:
Cubic Differentials and Convex Real Projective Structures
Speaker:
Abstract:
If $S$ is a closed oriented surface of genus at least 2, then the data of a pair $(\Sigma,U)$ of a conformal structure $\Sigma$ and holomorphic cubic differential $U$ is in one-to-one correspondence with a convex real projective structure $X$ on $S$, in which $X$ is the quotient of a bounded convex domain in $RP^2$ by a representation $\pi_1S$ whose quotient is $X$. This result is due independently to the speaker and Labourie. We'll explain the differential geometry and analysis behind this results, and investigate some more degenerate settings a the boundary of the moduli space. One may think of these results as a "higher" analog of the interplay of between hyperbolic and complex geometry in ordinary Teichmuller spaces.
Link:
Workshop: