Marc Burger (ETH Zurich)

Title:

Compactifications of Teichmueller Spaces in the light of real Algebraic Geometry

Abstract:

In 1988, in a little noticed paper, G.Brumfiel defined a compactification RSp(S) of the Teichmueller space T(S) of a closed surface S using the real spectrum of a ring of suitable coordinates of T(S). He then related RSp(S) to Thurston's compactification via projectivized length functions. In this talk we will recall the construction of RSp(S), give an interpretation of its boundary points, and show how it canonically projects to Bonahon's compactification of T(S) by geodesic currents. This will lead to a striking property of the action of the mapping class group of S on RSp(S). Joint work with A. Iozzi, A. Parreau and B. Pozzetti.