Objective
Dynamics on polygonal billiard tables is best understood by unfolding the table and studying the resulting flat surface. The moduli space of flat surfaces carries a natural action of SL(2,R) and all the questions about Lie group actions on homogeneous spaces reappear in this
non-homogeneous setting in an even more interesting way.
Closed SL(2,R)-orbits give rise to totally geodesic
subvarieties of the moduli space of curves, called
Teichmueller curves. Their classifcation is a major goal over the coming years. The applicant's algebraic characterization of Teichmueller curves plus the comprehension of the Deligne-Mumford compactification of Hilbert modular varities
make this goal feasible.
on polygonal billiard tables is best understood
unfolding the table and studying the resulting
surface. The moduli space of flat surfaces carries
action of SL(2,R) and all the questions about
group actions on homogeneous spaces reappear in this homogeneous setting in an even more interesting way.
SL(2,R)-orbits give rise to totally geodesic
of the moduli space of curves, called
curves. Their classifcation is a major goal
the coming years. The applicant's algebraic characterization Teichmueller curves plus the comprehension of the Mumford compactification of Hilbert modular varities this goal feasible.
Fields of science
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques.
Call for proposal
ERC-2010-StG_20091028
See other projects for this call
Funding Scheme
ERC-SG - ERC Starting GrantHost institution
60323 Frankfurt Am Main
Germany