Alexis Michelat

I am an Assistant Professor at the Mathematics Department at Gakushuin University, Japan since the 1st of April 2026.

Before that, I was a PhD student at ETH Zürich (2015-2019) under the supervision of Prof. Tristan Rivière, then a postdoc at the Université Paris Diderot (that keeps changing names) under the supervision of Prof. Frédéric Hélein (2019-2020), and a postdoc of the Swiss National Science Foundation at the University of Oxford (2020-2022), where Prof. Andrea Mondino was my mentor. Finally, I was Bernoulli Instructor at EPFL (Lausanne, Switzerland) between September 2022 and March 2026.

For more information on my career, please refer to my CV.

Research area

My research field is geometric analysis, with an emphasis on the analysis of partial differential equations (PDE) that arise from geometric problems, including Willmore surfaces, minimal surfaces, polyharmonic maps, Loewner energy, and Ginzburg–Landau vortices.

Publications

Articles

  1. (with Andrea Mondino). Quantization of the Willmore Energy in Riemannian Manifolds. Adv. Math. 489 (2026), Paper No. 110789, 118 pp. 2026
  2. (with Tristan Rivière). Morse Index Stability of Willmore Immersions. [memoir combining Morse Index Stability of Willmore Immersions I and Weighted Eigenvalue Problems for Fourth-Order Operators in Degenerating Annuli]. Memoirs of the European Mathematical Society, 300 p. to appear, 2026
  3. Morse Index Stability of Biharmonic Maps in Critical Dimension. J Geom Anal 35, 108, 158 p., 2025
  4. (with Yilin Wang). The Loewner Energy via the Renormalised Energy of Moving Frames. Arch Rational Mech Anal 248, no. 2, Paper No. 15, 60 p., 2024
  5. (with Tristan Rivière). Pointwise expansion of degenerating immersions of finite total curvature. J. Geom. Anal. 33, no. 1, Paper No. 24, 91 p., 2023
  6. (with Tristan Rivière). The Classification of branched Willmore spheres in the 3-sphere and the 4-sphere. Ann. Sci. de l’École Norm. Superieure, 4e série, t. 55, 2022, p. 1199 à 1288, 2022
  7. On the Morse Index of Critical Points in the Viscosity Method. Calc. Var. Partial Differ. Equ. 61:42, 42p., 2022
  8. On the Morse Index of Branched Willmore Spheres in 3-Space. Calc. Var. Partial Differ. Equ. 60:126, 97p., 2021
  9. On the Morse index of Willmore spheres in S^3. Comm. Anal. Geom., Vol. 28, No. 6, p. 1337–1406, 2020
  10. (with Tristan Rivière). A viscosity method for the min-max construction of closed geodesics. ESAIM: COCV Volume 22, Number 4, October-December, p. 1282-1324, 2016.

Preprints

  1. Morse Index Stability of Branched Willmore Immersions. arXiv:2506.09005, 2025
  2. On the Moduli Space of Null Curves in Klein’s Quadric. arXiv:1905.04942, 2019
  3. Morse Index Estimates of Min-Max Willmore Surfaces. arXiv:1808.07700, 2018

Teaching/演習

数学演習（化学科）

  1. ４月１３日—４月１９日：演習問題 No. 1
  2. ４月２０日—４月２６日：演習問題 No. 2
  3. ４月２７日—５月０３日：演習問題 No. 3
  4. ５月０４日—５月１０日：演習問題 No. 4
  5. ５月１１日—５月１７日：演習問題 No. 5
  6. ５月１８日—５月２４日：演習問題 No. 6
  7. ５月２５日—５月３１日：演習問題 No. 7
  8. ６月０１日—６月０７日：演習問題 No. 8
  9. ６月０８日—６月１４日：演習問題 No. 9
  10. ６月１５日—６月２１日：演習問題 No. 10
  11. ６月２２日—６月２８日：演習問題 No. 11
  12. ６月２９日—７月０５日：演習問題 No. 12
  13. ７月０６日—７月１２日：演習問題 No. 13
  14. ７月１３日—７月１９日：演習問題 No. 14

曲線と曲面

  1. ４月１３日—４月１９日：演習問題 No. 1
  2. ４月２０日—４月２６日：演習問題 No. 2
  3. ４月２７日—５月０３日：演習問題 No. 3
  4. ５月０４日—５月１０日：演習問題 No. 4
  5. ５月１１日—５月１７日：演習問題 No. 5
  6. ５月１８日—５月２４日：演習問題 No. 6
  7. ５月２５日—５月３１日：演習問題 No. 7
  8. ６月０１日—６月０７日：演習問題 No. 8
  9. ６月０８日—６月１４日：演習問題 No. 9
  10. ６月１５日—６月２１日：演習問題 No. 10
  11. ６月２２日—６月２８日：演習問題 No. 11
  12. ６月２９日—７月０５日：演習問題 No. 12
  13. ７月０６日—７月１２日：演習問題 No. 13
  14. ７月１３日—７月１９日：演習問題 No. 14

Contact

alexis "dot" michelat "at" gakushuin "dot" ac "dot" jp
(the email address should look like firstname.lastname@gakushuin.ac.jp)