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Meromorphic quadratic differentials, measured foliations, and harmonic maps to trees

Subhojoy Gupta (Indian Institute of Science, Bangalore)
Tirsdag, 31 maj, 2016, at 15:15, in Aud. D3 (1531-215)
A holomorphic quadratic differential on a Riemann surface S induces a singular foliation equipped with a transverse measure. When S is closed, the Hubbard-Masur Theorem asserts that this provides a bijective correspondence between holomorphic quadratic differentials and measured foliations on S. This establishes an important bridge between the complex-analytic and topological aspects of Teichmüller theory. In this talk I shall describe joint work with Michael Wolf, that generalizes this correspondence to the case of quadratic differentials with finite-order poles. Our proofs involve harmonic maps of the universal cover of S to R-trees, that have infinite energy.
Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen