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SL(2,R)-action on flat surfaces and geometry of extremal subvarieties of moduli spaces

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.

Field of science

  • /natural sciences/mathematics/pure mathematics/geometry
  • /natural sciences/mathematics/pure mathematics/algebra/algebraic geometry

Call for proposal

ERC-2010-StG_20091028
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

JOHANN WOLFGANG GOETHE-UNIVERSITATFRANKFURT AM MAIN
Address
Theodor W Adorno Platz 1
60323 Frankfurt Am Main
Germany
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 005 600
Principal investigator
Martin Moeller (Prof.)
Administrative Contact
Kristina Wege (Ms.)

Beneficiaries (1)

JOHANN WOLFGANG GOETHE-UNIVERSITATFRANKFURT AM MAIN
Germany
EU contribution
€ 1 005 600
Address
Theodor W Adorno Platz 1
60323 Frankfurt Am Main
Activity type
Higher or Secondary Education Establishments
Principal investigator
Martin Moeller (Prof.)
Administrative Contact
Kristina Wege (Ms.)