CORDIS
EU research results

CORDIS

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

Project information

Grant agreement ID: 257137

Status

Closed project

  • Start date

    1 October 2010

  • End date

    30 September 2015

Funded under:

FP7-IDEAS-ERC

  • Overall budget:

    € 1 005 600

  • EU contribution

    € 1 005 600

Hosted by:

JOHANN WOLFGANG GOETHE-UNIVERSITATFRANKFURT AM MAIN

Germany

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.
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Principal Investigator

Martin Moeller (Prof.)

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

Project information

Grant agreement ID: 257137

Status

Closed project

  • Start date

    1 October 2010

  • End date

    30 September 2015

Funded under:

FP7-IDEAS-ERC

  • Overall budget:

    € 1 005 600

  • EU contribution

    € 1 005 600

Hosted by:

JOHANN WOLFGANG GOETHE-UNIVERSITATFRANKFURT AM MAIN

Germany