Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards.
Teichmüller space is not Gromov hyperbolic.
Teichmüller spaces are not starlike.
Teichmüller spaces with variable bases in the universal Teichmüller space.
Teichmüllerraum für total degenerierte Kurven.
The classification of punctured-torus groups.
The conformal structure of Riemann surfaces with boundary parametrizing minimal surfaces.
The equivariant fundamental group, uniformization of real algebraic curves, and global complex analytic coordinates on Teichmüller spaces
The extended Schottky space.
The Extended Teichmüller Space.
The geometric quantization of the moduli space of Riemann surfaces with even spin structure.
The geometry of Teichmüller space via geodesic currents.
The geometry of the period mapping on cyclic covers of P1
The mapping class group of a generic quadratic rational map and automorphisms of the 2-shift.
The moduli space of Riemann surfaces is Kähler hyperbolic.
The monodromy groups of Schwarzian equations on closed Riemann surfaces.
The Mumford conjecture
The Mumford Conjecture asserts that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra on the Mumford-Morita-Miller characteristic classes; this can be reformulated in terms of the classifying space derived from the mapping class groups. The conjecture admits a topological generalization, inspired by Tillmann’s theorem that admits an infinite loop space structure after applying Quillen’s plus construction. The text presents the proof by Madsen and...
The outside of the Teichmüller space of punctured tori in Maskit's embedding.
The Picard group of the moduli of higher spin curves.
The Poisson Boundary of the Mapping Class Group and of Teichmüller Space