Current research

My research is focused on sharp inequalities and extremal problems in analysis and geometry. Particularly, I'm interested in problems from spectral theory, mathematical physics, PDE, and harmonic analysis that involve aspects of both analysis and geometry.

Publications & preprints

On a Hardy–Morrey inequality (with R. Hynd and E. Lindgren)
Preprint: arXiv:2401.05781 [math.AP].

Decay of extremals of Morrey's inequality (with R. Hynd and E. Lindgren)
Arkiv för Matematik (to appear).
Preprint: arXiv:2306.03471 [math.AP].

Quadrature domains for the Helmholtz equation with applications to non-scattering phenomena (with P. Z. Kow, M. Salo, and H. Shahgholian)
Potential Analysis, vol. 60 (2024), 387-424, DOI.
Preprint: arXiv:2204.13934 [math.AP].

An inequality for the normal derivative of the Lane–Emden ground state (with R. L. Frank)
Advances in Calculus of Variations, vol. 17 (2024), no. 2, 255-276, DOI.
Preprint: arXiv:2201.09605 [math.AP].

Discrete Schrödinger operators with decaying and oscillating potentials (with R. L. Frank)
Algebra i Analiz (St. Petersburg Mathematics Journal), vol. 35 (2023), no. 1, 304-320, link.
Preprint: arXiv:2108.05083 [math.SP].

On the spectrum of the Kronig–Penney model in a constant electric field (with R. L. Frank)
Probability and Mathematical Physics, vol. 3 (2022), no. 2, 431-490, DOI.
Preprint: arXiv:2104.10256 [math-ph].

A sharp multidimensional Hermite–Hadamard inequality
International Mathematics Research Notices, vol. 2022 (2022), 1297-1312, DOI.
Preprint: arXiv:2005.01853 [math.CA].

Two consequences of Davies's Hardy inequality (with R. L. Frank)
Functional Analysis and Its Applications, vol. 55 (2021), 174-177, DOI.
Preprint: arXiv:2011.11830 [math.CA].

Semiclassical asymptotics for a class of singular Schrödinger operators (with R. L. Frank)
Partial Differential Equations, Spectral Theory, and Mathematical Physics: The Ari Laptev Anniversary Volume, p. 155-176, DOI.
Preprint: arXiv:2010.05417 [math.SP].

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, vol. 31 (2021), 801-816, DOI.
Preprint: arXiv:1907.06122 [math.CA].

Lieb–Thirring inequalities for wave functions vanishing on the diagonal set (with D. Lundholm and P. T. Nam)
Annales Henri Lebesgue, vol. 4 (2021), 251-282, DOI (open access).
Preprint: arXiv:1901.04963 [math-ph].

On the error in the two-term Weyl formula for the Dirichlet Laplacian (with R. L. Frank)
Journal of Mathematical Physics, vol. 61 (2020), 043504, DOI.
Preprint: arXiv:2001.01876 [math.SP].

Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain (with R. L. Frank)
Journal für die reine und angewandte Mathematik, vol. 766 (2020), 195-228, DOI.
Preprint: arXiv:1901.09771 [math.SP].

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].

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, erratum.
Preprint: arXiv:1611.05680 [math.SP] (revised in accordance with the erratum).

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].

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].

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].

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].

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

Thesis

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 Professor Ari Laptev.