Priv.-Doz. Dr. Sebastian Heller


GeometrieWerkstatt
Mathematisches Institut
Auf der Morgenstelle 10
72076 Tübingen

Office: 2 P 31
Telephone: +49-7071-29-78596
E-mail: heller@mathematik.uni-tuebingen.de



Three views of a constant mean curvature surface in the 3-sphere. Images by Nick Schmitt based on the joint paper 'Deformations of symmetric CMC surfaces in the 3-sphere'.


Office Hours

open door policy

Teaching

Winter term 2016/17:
Riemannsche Flächen

Summer term 2016:
Ausgewählte Kapitel der Differentialgeometrie

Winter term 2015/16:
Mathematik für Physiker 3

Summer term 2015:
Mathematik für Physiker 2

Winter term 2014/15:
Ausgewälte Kapitel der Differentialgeometrie

Summer term 2014:
Seminar Geometrie von Flächen

Winter term 2013/14:
Einführung in Mannigfaltigkeiten
Seminar Riemannsche Flächen

Summer term 2013:
on parental leave

Winter term 2012/13:
Liegruppen und Liealgebren
Projektive Geometrie

Research

My research interests are global surface geometry, integrable systems and the geometry of moduli space of flat connections. I have developed a spectral curve theory for compact symmetric CMC surfaces of genus greater or equal two. Currently, I am generalizing the spectral curve theory to all CMC surfaces of genus 2. I am also studying a generalized Whitham flow on the spectral data of CMC surfaces which is used to construct new surfaces and to study the moduli space of CMC surfaces of higher genus.
I am the principal investigator in the DFG programme "Constant mean curvature surfaces with non-abelian fundamental groups: theory and experiments".

Publications

  1. The asymptotic behavior of the monodromy representations of the associated families of compact CMC surfaces

    Bulletin of the London Mathematical Society 2016; doi: 10.1112/blms/bdw036
    Preprint: arXiv:1505.00747

  2. The spectral curve theory for (k,l)-symmetric CMC surfaces

    with Lynn Heller and Nicholas Schmitt
    J. Geom. Phys. 98 (2015), 201-213. http://dx.doi.org/10.1016/j.geomphys.2015.08.010
    Preprint version

  3. Abelianization of Fuchsian Systems on a 4-punctured sphere and applications

    with Lynn Heller
    Journal of Symplectic Geometry, Vol. 14, No. 4 (2016), pp. 1059-1088
    Preprint version

  4. Conformally flat circle bundles over surfaces

    Diff. Geom. Appl. 40 (2015), 103-110.
    Preprint version

  5. Deformations of symmetric CMC surfaces in the 3-sphere

    with Nick Schmitt
    Experimental Mathematics , Volume 24, Issue 1 (2015), pp 65-75.
    Preprint: arxiv: 1305.4107

  6. A spectral curve approach to Lawson symmetric CMC surfaces of genus 2

    Math. Annalen, Volume 360, Issue 3 (2014), pp 607-652.
    DOI: 10.1007/s00208-014-1044-4
    Preprint: arxiv: 1209.3200

  7. Lawson's genus two minimal surface and meromorphic connections

    Math. Z., Volume 274 (2013), pp 745-760.
    DOI: 10.1007/s00209-012-1094-9
    Preprint version

  8. Higher genus minimal surfaces in S^3 and stable bundles.

    J. Reine Angew. Math. (Crelle's Journal), Volume 685 (2013), pp 105-122.
    DOI: 10.1515/crelle-2012-0011
    Preprint version
    Review

  9. Higher genus CMC surfaces via integrable systems

    Abresch U, Pedit F, Umehara M.: Progress in Surface Theory. Oberwolfach Rep. Volume 10 (2013), pp 1253-1312.
    DOI: 10.4171/OWR/2013/21

  10. Conformal fibrations of S3 by circles.

    Harmonic maps and differential geometry, Contemp. Math., Amer. Math. Soc., Providence, RI, Volume 542 (2011), pp 195-202.
    Preprint version
    Review

  11. Harmonic morphisms on conformally flat 3-spheres

    Bull. Lond. Math. Soc., Volume 43 (2011), no. 1, 137-150.
    Preprint version

  12. Global aspects of integrable surface geometry

    with A. Gerding, F. Pedit and N. Schmitt
    in Systèmes intégrables et théorie des champs quantiques, eds: P. Baird, F. Hélein, J. Kouneiher, F. Pedit, V. Roubtsov, collection Travaux en Cours en Physique-Mathématiques, no 75, Hermann (2009).

Preprints

  1. Branes through finite group actions

    with Laura P. Schaposnik
    Preprint: arxiv: 1611.00391

  2. Exploring the space of compact symmetric CMC surfaces

    with Lynn Heller and Nicholas Schmitt
    Preprint: arxiv: 1503.07838

  3. Navigating the Space of Symmetric CMC Surfaces

    with Lynn Heller and Nicholas Schmitt
    Preprint: arxiv: 1501.01929

Theses

Integrable systems methods for higher genus CMC surfaces in the 3-sphere

Habilitationsschrift, Universität Tübingen, 2013

Conformal Submersions of the 3-sphere

PhD thesis, Humboldt Universität Berlin, 2008

Articles in Preparation

Abelianization of flat special linear connections on n-punctured spheres (with C. Meneses)
Integrable systems methods for CMC surfaces of genus 2