Publications

Manuscripts Submitted for Publication

1.  (with Y. Canzani, J. Marzuola) Uniform upper bounds on Courant sharp Neumann eigenvalues of chain domains, https://arxiv.org/abs/2305.16452

2. (with M. Gupta, J. Marzuola) Nodal Set Openings on Perturbed Rectangular Domains, https://arxiv.org/abs/2204.12009.

Publications

3. (with F. Azad, K. Lokaj) The isoperimetric inequality for convex subsets of the sphere, Involve, a Journal of Mathematics 16 no. 2 (2023), 343–364.

4. (with Y. Canzani, J. Marzuola) Quantitative bounds on Impedance-to-Impedance operators with applications to fast direct solvers for PDEs, Pure and Applied Analysis 4 no. 2 (2022), 225–256.

5. (with D. Jerison) The Friedland-Hayman inequality and Caffarelli’s contraction theorem, Journal of Mathematical Physics, 62, 101504 (2021).

6. (with I. Bors, G. Conte, G. Cox, J. Marzuola) Limiting eigenfunctions of Sturm-Liouville operators subject to a spectral flow, Ann. Math. Québec, 45 (2020), 249–269.

7. (with D. Jerison, S. Raynor) Two-phase free boundary problems in convex domains, J. Geom. Anal. 31 (2021), 6845–6891.

8. (with Y. Canzani, J. Marzuola) Nodal line estimates for the second Dirichlet eigenfunction, Journal of Spectral Theory 11 no. 1 (2021), 323–353.

9. Localization of the first eigenfunction of a convex domain, Communications in PDE 46 no.3 (2020), 1–18.

10. (with B. Brandolini, K. Burdzy, A. Henrot, J. Langford, S. Larson, S. Steinerberger, and R. Smits) Improved Bounds for Hermite-Hadamard Inequalities in Higher Dimensions, J. Geom. Anal. (2019), 1–16.

11. The torsion function of convex domains of high eccentricity, Potential Analysis (2019), 1–26.

12. Uniform level set estimates for ground state eigenfunctions, SIAM J. Math. Anal. 50-4 (2018), 4483–4502.

13. (with B. Hanin) Level spacings and nodal sets at infinity for radial perturbations of the harmonic oscillator, International Math Research Notices, (2018).

14. (with S. Becker-Kahn, B. Hanin) Nodal sets of smooth functions with finite vanishing order and p-sweepouts, Calc. Var. 57:140 (2018).

15. The shape of the level sets of the first eigenfunction of a class of two dimensional Schrödinger operators, Trans. Amer. Math. Soc. 370 (2018), 3197–3244.

16. Level set shape for ground state eigenfunctions on convex domains, PhD Thesis, Princeton University (2015).

17. (with F. Pusateri, P. Sosoe, P. Wong) On global solutions of a Zakharov type system, Nonlinearity 28 (2015), 3419–3441.

18. (with P. Sosoe, P. Wong) Duchon-Robert solutions for the Rayleigh-Taylor and Muskat problems, Journal of Differential Equations, Vol. 256, 1 (2014), 206–222.