Daniel L. Stern
I am an assistant professor of mathematics at Cornell University. Before coming to Cornell, I held postdoctoral positions at the University of Chicago and 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, 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: daniel.stern [at] cornell.edu
Publications and preprints:
(with M. Karpukhin, R. Kusner, and P. McGrath) Embedded minimal surfaces in S^3 and B^3 via equivariant eigenvalue optimization, arXiv:2402.13121
(with D. Parise and A. Pigati) The parabolic U(1)-Higgs equations and codimension-two mean curvature flows, accepted in GAFA, arXiv:2307.15134
(with M. Karpukhin) Existence of harmonic maps and eigenvalue optimization in higher dimensions, accepted in Invent. Math., arXiv:2207.13635
(with A. Pigati) Quantization and non-quantization of energy for higher-dimensional Ginzburg--Landau vortices, Ars Inven. Analytica. June '23, arXiv:2204.06491
(with M. Karpukhin) From Steklov to Laplace: free boundary minimal surfaces with many boundary components, accepted in Duke Math. J., arXiv:2109.11029
(with M. Karpukhin, M. Nahon, and I. Polterovich) Stability of isoperimetric inequalities for Laplace eigenvalues on surfaces, accepted in J. Diff. Geom., arXiv:2106.15043
(with D. Parise and A. Pigati) Convergence of the self-dual U(1)-Yang-Mills-Higgs energies to the (n-2)-area functional, CPAM 77 (2024), arXiv:2103.14615
(with M. Karpukhin) Min-max harmonic maps and a new characterization of conformal eigenvalues, accepted in J. Eur. Math. Soc., arXiv:2004.04086
(with H. Bray) Scalar curvature and harmonic one-forms on three-manifolds with boundary, accepted in Comm. Anal. Geom., arXiv:1911.06803
(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
Scalar curvature and harmonic maps to S^1, J. Diff. Geom. 122(2) (2022), arXiv:1908.09754
(with A. Pigati) Minimal submanifolds from the abelian Higgs model, Invent. Math. 223 (2021) arXiv:1905.13726
Mountain pass energies between homotopy classes of maps, preprint, arXiv:1809.03361
p-Harmonic maps to S^1 and stationary varifolds of codimension 2, Calc. Var. 59 (2020), arXiv:1802.03053
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:
Cornell University
Spring 2024: Math 6160--Partial Differential Equations (see Canvas for information and resources)
Fall 2023: Math 3210--Manifolds and Differential Forms
University of Chicago
Spring 2023: Math 207200--Basic Functional Analysis
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