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

Research

Publications

1. Branched SL(r, C)-opers

   with Inranil Biswas and Sorin Dumitrescu
   accpeted for publication in IMRN
   Preprint: arxiv:2109.07685

2. Real projective structures on Riemann surfaces and new hyper-Kähler manifolds

   
   Manuscripta Mathematica, doi.org/10.1007/s00229-022-01377-z, (2022)
   Preprint: arxiv:1906.10350

3. On the monodromy map for the logarithmic differential systems

   with Marian Aprodu, Indranil Biswas and Sorin Dumitrescu
   accepted for publication in Bulletin de la Societe Mathematique de France
   Preprint: arxiv: 2201.04095

4. Area estimates for high genus Lawson surfaces via DPW

   with Lynn Heller and Martin Traizet
   accepted for publication in Journal of Differential Geometry
   Preprint: arxiv: 1907.07139

5. Uniformization of branched surfaces and Higgs bundles

   with Indranil Biswas, Steven Bradlow and Sorin Dumitrescu
   Int. J. of Mathematics, Vol. 32, No. 13 (2021)
   Preprint: arxiv: 2101.03080

6. Branes and moduli spaces of Higgs bundles on smooth projective varieties

   with Indranil Biswas and Laura Schaposnik
   Research in the Mathematical Sciences, 8 (2021), no. 3, Paper No. 52
   Preprint: arxiv: 2005.02564

7. Stability properties of 2-lobed Delaunay tori in the 3-sphere

   with Lynn Heller and Cheikh B. Ndiaye
   Differential Geometry and its Applications, Volume 79, 2021, doi.org/10.1016/j.difgeo.2021.101805
   Preprint: arxiv: 1903.11830

8. Constant mean curvature surfaces based on fundamental quadrilaterals

   with Alexander Bobenko and Nicholas Schmitt
   Math. Physics, Analysis and Geometry 24, 37 (2021)
   Preprint: arxiv: 2102.03153

9. Isothermic constrained Willmore tori in 3-space

   with Lynn Heller and Cheikh B. Ndiaye
   Annals of Global Analysis and Geometry, 60 (2021), no. 2, 231-251
   Preprint: arxiv: 1903.11823

10. On certain Tannakian categories of integrable connections over Kaehler manifolds

    with Indranil Biswas, Sorin Dumitrescu, and Joao Dos Santos
    Canadian Journal of Mathematics, 1-28. https://www.doi.org/10.4153/S0008414X21000201
    Preprint: arxiv:2008.11483

11. Willmore spheres in the 3-sphere revisited

    
    accepted for publication in Communications in Analysis and Geometry
    Preprint: arxiv: 2003.06922

12. Irreducible flat SL(2, R)-connections on the trivial holomorphic bundle

    with Indranil Biswas and Sorin Dumitrescu
    Journal de Mathematiques Pures et Appliquees (9) 149 (2021), 28-46
    Preprint: arxiv: 2003.06997

13. Higher solutions of Hitchin?s self-duality equations

    with Lynn Heller
    Journal of Integrable Systems Volume 5, Issue 1, 2020, xyaa006
    Preprint: arxiv: 1801.02402

14. Energy of sections of the Deligne-Hitchin twistor space

    with Florian Beck and Markus Roeser
    Math. Annalen 380 (2021), no. 3-4, 1169-1214
    Preprint: arxiv:1903.02497

15. Minimal n-noids in hyperbolic and anti-de Sitter 3-space

    with Alexander Bobenko and Nicolas Schmitt
    Proceedings of the Royal Society A, DOI: 10.1098/rspa.2019.0173
    Preprint: arxiv: 1902.07992

16. Real holomorphic sections of the Deligne-Hitchin moduli space

    with Indranil Biswas and Markus Roeser
    Comm. Math. Phys., Volume 366, Issue 3 (2019), pages 1099- 1133
    Preprint: arxiv: 1802.06587

17. Branes through finite group actions

    with Laura P. Schaposnik
    J. Geom. Phys., Volume 129, July 2018, Pages 279-293
    Preprint: arxiv: 1611.00391

18. Navigating the Space of Symmetric CMC Surfaces

    with Lynn Heller and Nicholas Schmitt
    Journal of Differential Geometry, vol. 110, no. 3 (2018), pp. 413-455
    Preprint: arxiv: 1501.01929

19. Automorphisms of a rank one Deligne-Hitchin moduli space

    with Indranil Biswas
    SIGMA 13 (2017), 072, 19 pages.
    Preprint: arxiv: 1704.04924

20. 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

21. 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

22. 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

23. Conformally flat circle bundles over surfaces

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

24. 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

25. 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

26. 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

27. 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

28. 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

29. Harmonic morphisms on conformally flat 3-spheres

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

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    Preprints

    1. Loop group methods for the non-abelian Hodge correspondence on a 4-punctured sphere

       with Lynn Heller and Martin Traizet
       Preprint: arxiv: 2205.12106

    2. Affine thrice punctured spheres and SYZ geometry

       with Franz Pedit and Charles Ouyang
       Preprint: arxiv: 2203.04224

    3. Infinitesimal deformations of parabolic connections and parabolic opers

       with Indranil Biswas, Sorin Dumitrescu, and Christian Pauly
       Preprint: arxiv: 2202.09125

    4. Fuchsian DPW potentials for Lawson surfaces

       with Lynn Heller
       Preprint: arxiv: 2202.05184

    5. On the existence of holomorphic curves in compact quotients of SL(2,C)

       with Indranil Biswas, Sorin Dumitrescu and Lynn Heller
       Preprint: arxiv: 2112.03131

    6. Complete families of embedded high genus CMC surfaces in the 3-sphere

       with Lynn Heller and Martin Traizet
       Preprint: arxiv: 2108.10214

    7. Holomorphic sl(2,C)-systems with Fuchsian monodromy (with an appendix by Takuro Mochizuki)

       with Indranil Biswas, Sorin Dumitrescu and Lynn Heller
       Preprint: arxiv: 2104.04818

    8. Geometry of the space of sections of twistor spaces with circle action

       with Florian Beck, Inrdanil Biswas, and Markus Roeser
       Preprint: arxiv: 2102.10853

    9. Exploring the space of compact symmetric CMC surfaces

       with Lynn Heller and Nicholas Schmitt
       Preprint: arxiv: 1503.07838
    
    

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    Conference Proceedings

    1. 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

    2. 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).

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