Daniel L. Stern

I am a Dickson Instructor and NSF postdoctoral fellow at the University of Chicago. From 2019-2020, I was a postdoctoral fellow at the University of Toronto. I completed my PhD at Princeton University in 2019, under the supervision of Fernando Codá Marques.

I am interested primarily in differential geometry, as well as partial differential equations and variational problems of a geometric flavor. In recent years, I've been working on problems related to minimal submanifolds, harmonic maps, scalar curvature, spectral geometry and the Ginzburg--Landau equations.

Click here for a recent cv.


Email: dstern [at] uchicago.edu

Publications and preprints:

  1. (with M. Karpukhin) Existence of harmonic maps and eigenvalue optimization in higher dimensions, arXiv:2207.13635

  2. (with A. Pigati) Quantization and non-quantization of energy for higher-dimensional Ginzburg--Landau vortices, arXiv:2204.06491

  3. (with M. Karpukhin) From Steklov to Laplace: free boundary minimal surfaces with many boundary components, submitted, arXiv:2109.11029

  4. (with M. Karpukhin, M. Nahon, and I. Polterovich) Stability of isoperimetric inequalities for Laplace eigenvalues on surfaces, submitted, arXiv:2106.15043

  5. (with D. Parise and A. Pigati) Convergence of the self-dual U(1)-Yang-Mills-Higgs energies to the (n-2)-area functional, submitted, arXiv:2103.14615

  6. (with M. Karpukhin) Min-max harmonic maps and a new characterization of conformal eigenvalues, submitted, arXiv:2004.04086

  7. (with H. Bray) Scalar curvature and harmonic one-forms on three-manifolds with boundary, to appear in Comm. Anal. Geom., arXiv:1911.06803

  8. (with H. Bray, D. Kazaras, and M. Khuri) Harmonic functions and the mass of 3-dimensional asymptotically flat Riemannian manifolds, J. Geom. Anal. 32 (2022), arXiv:1911.06754

  9. Scalar curvature and harmonic maps to S^1, to appear in J. Diff. Geom., arXiv:1908.09754

  10. (with A. Pigati) Minimal submanifolds from the abelian Higgs model, Invent. Math. 223 (2021) arXiv:1905.13726

  11. Mountain pass energies between homotopy classes of maps, preprint, arXiv:1809.03361

  12. p-Harmonic maps to S^1 and stationary varifolds of codimension 2, Calc. Var. 59 (2020), arXiv:1802.03053

  13. Existence and limiting behavior of min--max solutions of the Ginzburg--Landau equations on compact manifolds, J. Diff. Geom. 118(2) (2021) (supersedes preprints arXiv:1612.00544 and arXiv:1704.00712)

Teaching:

University of Chicago

  • Fall 2022: Math 20510--Analysis in R^n III (accelerated)

  • Fall 2021: Math 15910--Introduction to Proofs in Analysis

University of Toronto at Mississauga

  • Spring 2020: Math 136--Integral Calculus

  • Fall 2019: Math 135--Differential Calculus

Princeton University

  • Fall 2017: Math 103--Calculus I