Qiongling Li

I am currently a research fellow at Chern Institute of Mathematics, Nankai University,  Tianjin, China. 

From 2006 to 2010, I was an undergraduate in Nankai University, China. Then I did my graduate studies in Rice University , USA under the supervision of Mike Wolf and got my PhD degree in Dec 2014. In the spring of 2015, I was a postdoc in MSRI, Berkeley.  From Aug 2015 to Jul 2018, I was a joint-position postdoc at Caltech and QGM-Aarhus University. 

Here is my CV.  

Email:       qiongling.li@gmail.com  qiongling.li@nankai.edu.cn     

Research Interests

      Higher Teichmueller Theory, Higgs Bundles, and Harmonic Maps

Papers

• 1. Teichmueller space is totally geodesic in Goldman space, Asian Journal of Mathematics, Vol 20 (2016) No. 1, pp. 21-46.

  2. Asymptotics of Higgs bundles in Hitchin Components, with Brian Collier, Advances in Mathematics, Vol 307 (2017), pp. 488–558, arXiv:1405.116.

  3. AdS 3-manifolds and Higgs bundles, with Daniele Alessandrini, Proc. Amer. Math. Soc. 146 (2018), pp. 845-860, arXiv:1510.07745.

  4. Minimal surfaces for Hitchin representations, with Song Dai,  Journal of Differential Geometry, Vol. 112, No. 1 (2019), pp. 47-77, arXiv:1605.09596.

  5. On the uniqueness of vortex equations and its geometric applications, The Journal of Geometric Analysis (2019) 29:105–120.

  6. On cyclic Higgs bundles, with Song Dai, Math. Ann. (2018). https://doi.org/10.1007/s00208-018-1779-4,  online version, arXiv:1710.10725.

  7. Harmonic maps for Hitchin representations, Geometric and Functional Analysis, (2019) 29 (2), 539-560.

  8. An introduction to Higgs bundles via harmonic maps, SIGMA 15 (2019), 035, 30 pages. 

Work in Progress

• • Projective structures with (quasi-)Hitchin holonomy, with Daniele Alessandrini, in preparation.

Notes

• • Lecture notes on metric geometry of Euclidean buildings. These are the note from an introductory talk at a GEAR log cabin Workshop on Compactifications of moduli spaces of representations.  (full notes from the workshop)

  • slides for the talk on "Cyclic Higgs bundles and minimal surfaces", Conference of Complex Analysis in China, Qufu, 2017

  • slides for the talk on "Asymptotics of certain families of Higgs bundles", AMS-EMS-SPM International Meeting in Porto, 2015

  • slides for the talk on "Teichmueller space is totally geodesic in Goldman space", Joint Mathematics Meetings in San Diego, 2013.

  • Lectures notes on Convex RP^2 structures. These are the note from a talk I gave at a GEAR log cabin Workshop on Higher Teichmueller-Thurston Theory.

（ 2019 at Sisteron, France)

Conference (co-organized)

• • 2020 Frontier of Analysis and Geometry of Teichmüller spaces, TSIMF, Sanya, Jan 06-10, 2020. 

  • Workshop on Teichmüller theory and Related topics, Tsinghua University, Beijing, Aug 24-26, 2018.  

  • Workshop on Surface Group Representations, Mar 17-20, 2016.

  • Workshop on Higgs bundles and Harmonic Maps, Jan 3-10, 2015.