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Dr. Lynn Heller
Mathematisches Institut
Auf der Morgenstelle 10
72076 Tübingen

Office: 2 P 25
Telephone: +49-7071-29-78594
E-mail: lynn-jing.heller@uni-tuebingen.de


Here is my Curriculum Vitae.

I am funded by the European Social Fund and by the Ministry of Science, Research and the Arts Baden-Württemberg. Further, I am indebted to the Baden-Württemberg Foundation for supporting my research through the "Eliteprogramm für PostdoktorandInnen".

Teaching

SS 16: Gewöhnliche Differentialgleichungen

SS 15: Klassifikation kompakter Flächen

WS 15/16: Quaternionische Flächentheorie

Research


My research lies in the field of Global Surface Geometry. I am investigating constrained Willmore tori, i.e., critical points of the Willmore energy with prescribed conformal class, and CMC surfaces (of higher genus) using the Integrable Systems approach, where moduli spaces of flat connections naturally appear.

I am particularly interested in the interplay between Algebraic Geometric data of the surfaces coming from Integrable Systems (e.g., Higgs bundles, spectral curves) and their analytic properties (e.g., non degeneracy and stability) studied in Geometric Analysis.

In my thesis I classified equivariant constrained Willmore tori in the 3-sphere under supervision of Prof. Dr. F. Pedit.


Work in progress:

  1. Deformation theory for symmetric CMC surfaces of higher genus.
    With S. Heller and N. Schmitt.
    The aim is to show that the moduli space of symmetric CMC surfaces with low Willmore energy is (generically) 1-dimensional.

  2. Constrained Willmore Minimizers - Theory and Experiments.
    With N. Schmitt and F. Pedit.
    We want to give an rigorous overview of all (often vague) conjectures about conformally constrained Willmore minimizers in 3-space that are circulating in the Integrable Systems community and connect these to results from Geometric Analysis.

  3. Experimental energy profile for the minimum Willmore energy of elliptic curves.
    With N. Schmitt and U. Wagner.

Publications

Accepted and published

    With Sebastian Heller and Nicholas Schmitt
  1. The spectral curve theory for (k,l)-symmetric CMC surfaces. J. Geom. Phys., vol 98, pp 201-213, 2015.
    Preprint: arXiv:1503.00969.

    2. With Sebastian Heller:
  2. Abelianization of Fuchsian systems on a 4-punctured sphere and applications. Accepted for publication in Journal of Symplectic Geometry. Preprint: arXiv:1404.7707.

  3. Constrained Willmore and CMC tori in the 3-sphere. Differ. Geom. Appl., vol. 40, pp 232-242, 2015.
    Preprint: arXiv:1212.2068

  4. Equivariant Constrained Willmore Tori in the 3-Sphere. Math. Z., vol. 278, no. 3, pp 955-977, 2014.
    Preprint: arXiv:1211.4137.

  5. Constrained Willmore Tori and Elastic Curves in 2-Dimensional Space Forms. Comm. Anal. Geom., vol. 22, no. 2, pp 343-369, 2014.
    Preprint: arXiv:1303.1445.

  6. Constrained Willmore Hopf tori.
    Oberwolfach Reports, vol. 10, no. 2., 2013.

  7. Equivariant Constrained Willmore Tori in S^3. PhD Thesis, Eberhard Karls University Tübingen, 2012.

Preprints

    With Cheikh Birahim Ndiaye:
  1. First explicit constrained Willmore minimizers of non-rectangular conformal class
    Preprint, 2016.

    With Sebastian Heller and Nicholas Schmitt:
  2. Exploring the Space of Compact Symmetric CMC Surfaces.
    Preprint: arXiv:1503.07838, 2015.

    With Sebastian Heller and Nicholas Schmitt:
  3. Navigating the Space of Symmetric CMC Surfaces.
    Preprint: arXiv:1501.01929, 2015.

  4. Dirac Tori.
    Preprint: arXiv:1401.7449, 2014.