Current research

Currently my research is focused on problems related to shape optimization problems for eigenvalues of the Laplace operator on domains in d-dimensional Euclidean space. In particular I'm interested in the behaviour of such problems in semiclassical limits (see papers [4, 6, 7, 8, 11]).


[1] A bound for the perimeter of inner parallel bodies
Journal of Functional Analysis, vol. 271 (2016), no. 3, 610-619, DOI
Preprint: arXiv:1508.06414 [math.MG].

[2] Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domains in the Heisenberg group
Bulletin of Mathematical Sciences, vol. 6 (2016), no. 3, 335-352, DOI (open access)
Preprint: arXiv:1603.01379 [math.AP].

[3] On the remainder term of the Berezin inequality on a convex domain
Proceedings of the American Mathematical Society, vol. 145 (2017), no. 5, 2167-2181, DOI
Preprint: arXiv:1509.06705 [math.SP].

[4] Asymptotic behaviour of cuboids optimising Laplacian eigenvalues (with K. Gittins)
Integral Equations and Operator Theory, vol. 89 (2017), no. 5, 607-629, DOI
Preprint: arXiv:1703.10249 [math.SP].

[5] Exclusion bounds for extended anyons (with D. Lundholm)
Archive for Rational Mechanics and Analysis, vol. 227 (2018), no. 1, 309-365, DOI (open access)
Preprint: arXiv:1608.04684 [math-ph].

[6] Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domains
Journal of Spectral Theory, vol. 9 (2019), no. 3, 857-895, DOI
Preprint: arXiv:1611.05680 [math.SP].

[7] Maximizing Riesz means of anisotropic harmonic oscillators
Arkiv för Matematik, vol. 57 (2019), no. 1, 129-155, DOI (open access)
Preprint: arXiv:1712.10247 [math.SP].

[8] Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain (with R. L. Frank)
Journal für die reine und angewandte Mathematik (published online), DOI.
Preprint: arXiv:1901.09771 [math.SP].

[9] Improved bounds for Hermite-Hadamard inequalities in higher dimensions (with T. Beck, B. Brandolini, K. Burdzy, A. Henrot, J. Langford, R. Smits, and S. Steinerberger)
The Journal of Geometric Analysis (to appear)
Preprint: arXiv:1907.06122 [math-CA].


[10] Lieb-Thirring inequalities for wave functions vanishing on the diagonal set (with D. Lundholm and P. T. Nam)
Preprint: arXiv:1901.04963 [math-ph].


[11] Asymptotic and universal spectral estimates with applications in many-body quantum mechanics and spectral shape optimization PDF
PhD thesis from Royal Institute of Technology, Stockholm. Defended 5th of June 2019.
Main advisor Prof. Ari Laptev.
Opponent Prof. Stefan Steinerberger, Yale University.
Corrections: PDF