DLGAPS (279893)

  https://cordis.europa.eu/project/id/279893

  FP7 (2007-2013)

  Dynamics of Lie group actions on parameter spaces

  ERC Starting Grant - Mathematical foundations (ERC-SG-PE1)

  topology  ·  geometry  ·  algebraic geometry

  2011-10-01 Start Date (YY-MM-DD)

  2016-09-30 End Date (YY-MM-DD)

  € 850,000 Total Cost

  Description

There are many parallels between Lie group actions on homogeneous spaces and the action of $\SL_2(\R)$ and its subgroups on strata of translation or half-translation surfaces. I propose to investigate these two spaces in parallel, focusing on the dynamical behavior, and more specifically, the description of orbit-closures. I intend to utilize existing and emerging measure rigidity results, and to develop new topological approaches. These should also shed light on the geometry and topology of the spaces. I propose to apply results concerning these spaces to the study of diophantine approximations (approximation on fractals), geometry of numbers (Minkowski's conjecture), interval exchanges, and rational billiards.

  Complicit Organisations

2 Israeli organisations participate in DLGAPS.