I am an Associate Professor in Applied Mathematics at the University of Oslo

My research aims at developing the mathematical understanding of wave propagation in materials governed by local or non-local PDEs.  The goal is to be able to manipulate and guide waves, using very small devices which are robust to imperfections of their design. My mathematical study of these systems lies in the intersection of PDE theory, harmonic analysis and solid-state physics.

I finished my doctoral studies under the supervision of Prof. Dr. Habib Ammari, ETH Zürich, in May 2021.

My research activity is detailed more below.

Affiliation: Department of Mathematics, University of Oslo

Address:  Moltke Moes vei 35, 0851 Oslo, Norway

Email: erikhilt (at) math.uio.no

Research

My research focuses mainly on Partial Differential Equations (PDEs), Wave Propagation, Metamaterials and Topological Insulators.

Peer-reviewed papers

1. K. Alexopoulos, B. Davies, E. O. Hiltunen, Topological interface modes in systems with damping, to appear in SIAM Journal on Applied Mathematics. [link] 

2. E. O. Hiltunen, Perturbation theory for dispersion relations of spacetime-periodic materials. Physical Review B 111, L140102. [link]

3. Y. De Bruijn, E. O. Hiltunen, Complex Band Structure for Subwavelength Evanescent Waves. Studies in Applied Mathematics 154.2: e70022 (2025). [link] 

4. B. Davies, S. Barandun, E. O. Hiltunen, R. V. Craster, H. Ammari, A two-scale effective model for defect-induced localization transitions in non-Hermitian systems. Physical Review B 111.3: 035109 (2025). [link] 

5. H. Ammari, E. O. Hiltunen and L. Rueff, Space-Time Wave Localisation in Systems of Subwavelength Resonators. Proceedings of the Royal Society A  481: 20240698 (2025). [link]

6. H. Ammari, B. Davies, and E. O. Hiltunen, Spectral convergence in large finite resonator arrays: the essential spectrum and band structure. Bulletin of the London Mathematical Society 57.3: 730-747 (2025). [link] 

7. E. O. Hiltunen and B. Davies, Coupled harmonics due to time-modulated point scatterers. Physical Review B, 110, 184102 (2024). [link] 

8. H. Ammari, S. Barandun, J. Cao, B. Davies, E. O. Hiltunen, and P. Liu, The Non-Hermitian Skin Effect With Three-Dimensional Long-Range Coupling. To appear in Journal of the European Mathematical Society. [link] 

9. H. Ammari, S. Barandun, B. Davies, E. O. Hiltunen, T. Kosche, and P. Liu, Exponentially localised interface eigenmodes in finite chains of resonators. Studies in Applied Mathematics 153.4: e12765 (2024). [link]

10. H. Ammari, S. Barandun, J. Cao, B. Davies and E. O. Hiltunen, Mathematical foundations of the non-Hermitian skin effect. Archive for Rational Mechanics and Analysis 248, 33 (2024). [link] 

11. E. O. Hiltunen, J. Kraisler, J. C. Schotland and M. I. Weinstein, Nonlocal PDEs and Quantum Optics: Bound States and Resonances. SIAM Journal on Mathematical Analysis 56(3), 3802-3831 (2024). [link] 

12. H. Ammari, S. Barandun, B. Davies, E. O. Hiltunen, and P. Liu, Stability of the non-Hermitian skin effect. SIAM Journal on Applied Mathematics 84(4), 1697-1717 (2024). [link] 

13. H. Ammari, J. Cao, E. O. Hiltunen and L. Rueff, Scattering from time-modulated subwavelength resonators.  Proceedings of the Royal Society A 480.2289: 20240177 (2024). [link] 

14. H. Ammari, B. Davies, and E. O. Hiltunen, Anderson Localization in the subwavelength regime. Communications in Mathematical Physics 405 (1), 1 (2024). [link] 

15. H. Ammari, J. Cao, E. O. Hiltunen and L. Rueff, Transmission properties of time-dependent one-dimensional metamaterials. Journal of Mathematical Physics, 64.12 (2023). [link] 

16. H Ammari, T. Kosche and E. O. Hiltunen, Design of defected non-hermitian chains of resonator dimers for spatial and spatio-temporal localizations. SIAM Journal on Applied Mathematics 83.6: 2443-2468, 2023. [link] 

17. H. Ammari, B. Davies, and E. O. Hiltunen, Convergence rates for defect modes in large finite resonator arrays. SIAM Journal on Mathematical Analysis 55.6: 7616-7634, 2023. [link] 

18. H. Ammari, B. Davies, E. O. Hiltunen, H. Lee and S. Yu, Exceptional points in parity-time-symmetric subwavelength metamaterials. SIAM Journal on Mathematical Analysis  54.6, 6223-6253, 2022. [link] 

19. H. Ammari, J. Cao and E. O. Hiltunen, Non-reciprocal wave propagation in space-time modulated media. Multiscale Modeling and Simulalation, 20.4, 1228-1250, 2022. [link] 

20. H. Ammari, F. Fiorani and E. O. Hiltunen, On the validity of the tight-binding method for describing systems of subwavelength resonators. SIAM Journal on Applied Mathematics, 82.4, 1611-1634, 2022. [link]

21. H. Ammari, B. Davies and E. O. Hiltunen, Robust edge modes in dislocated systems of subwavelength resonators. Journal of the London Mathematical Society, 106.3, 2075-2135, 2022. [link]

22. H. Ammari, E. O. Hiltunen and S. Yu, Subwavelength guided modes for acoustic waves in bubbly crystals with a line defect. Journal of the European Mathematical Society, 24, 2279–2313, 2022. [link] 

23. H. Ammari, T. Kosche and E. O. Hiltunen, Asymptotic Floquet theory for first order ODEs with finite Fourier series perturbation and its applications to Floquet metamaterials. Journal of Differential Equations. 319, 227–287, 2022 [link] 

24. H. Ammari, B. Davies, E. O. Hiltunen, H. Lee and S. Yu, Bound states in the continuum and Fano resonances in subwavelength resonator arrays. Journal of Mathematical Physics, 62, 101506, 2021. [link] 

25. H. Ammari and E. O. Hiltunen, Time-dependent high-contrast subwavelength resonators. Journal of Computational Physics, 445, 110594, 2021. [link] 

26. H. Ammari, B. Davies, E. O. Hiltunen, H. Lee and S. Yu, High-order exceptional points and enhanced sensing in subwavelength resonator arrays. Studies in Applied Mathematics, 146, 440–462, 2021. [link] 

27. H. Ammari, B. Davies, E. O. Hiltunen, and S. Yu. Topologically protected edge modes in one-dimensional chains of subwavelength resonators. Journal de Mathématiques Pures et Appliquées, 144, 17–49, 2020. [link] 

28. H. Ammari, E. O. Hiltunen and S. Yu, A high-frequency homogenization approach near the Dirac points in bubbly honeycomb crystals. Archive for Rational Mechanics and Analysis, 238, 1559–1583, 2020. [link] 

29. H. Ammari, B. Fitzpatrick, E. O. Hiltunen, H. Lee and S. Yu, Honeycomb-lattice Minnaert bubbles. SIAM Journal on Mathematical Analysis, 52(6), 5441–5466, 2020. [link]

30. H. Ammari, B. Fitzpatrick, E. O. Hiltunen, H. Lee and S. Yu, Subwavelength resonances of encapsulated bubbles. Journal of Differential Equations, 267(8), 4719–4744, 2019. [link] 

31. H. Ammari, B. Fitzpatrick, E. O. Hiltunen and S. Yu, Subwavelength localized modes for acoustic waves in bubbly crystals with a defect. SIAM Journal on Applied Mathematics, 78(6), 3316–3335, 2018. [link] 

Preprints

1. Y. De Bruijn, E. O. Hiltunen, Complex Band Structure and localisation transition for tridiagonal non-Hermitian k-Toeplitz operators with defects, arXiv:2505.23610 

2. E. O. Hiltunen, J. C. Schotland, Optical theorem and generalized energy conservation for scattering of time-modulated waves, arXiv:2506.07789 

3. Y. De Bruijn, E. O. Hiltunen, Complex Brillouin Zone for Localised Modes in Hermitian and Non-Hermitian Problems, arXiv:2502.06620 

4. H. Ammari, J. Cao, E. O. Hiltunen and L. Rueff, Effective Medium Theory for Time-modulated Subwavelength Resonators, arXiv:2412.13545 

5. E. O. Hiltunen, J. Kraisler, J. C. Schotland and M. I. Weinstein, Nonlocal PDEs and Quantum Optics: band structure of periodic atomic sytems, arXiv:2311.12632

6. P. Wang, E. O. Hiltunen, J. C. Schotland, Rotating wave approximation and renormalized perturbation theory. arXiv:2311.02670 

7. H. Ammari and E. O. Hiltunen, Edge modes in non-Hermitian systems of subwavelength resonators. arXiv:2006.05719 

Review articles

1. H. Ammari, B. Davies, E. O. Hiltunen, Functional analytic methods for discrete approximations of subwavelength resonator systems. Pure and Applied Analysis 6-3, 873–939, 2024. [link]

2. H. Ammari, B. Davies, E. O. Hiltunen, H. Lee and S. Yu, Wave interaction with subwavelength resonators. Applied Mathematical Problems in Geophysics: Cetraro, Italy 2019. Springer International Publishing, 2022. 23–83. [link]

Selected conference presentations and seminar talks

• Spectral and Resonance Problems for Imaging, Seismology and Materials Science Conference, Reims (France), November 2023.

• Math Department Colloquium, Hong Kong University of Technology, August 2023.

• Numerical Analysis Seminar, Lund University (Sweden), August 2023.

• Arctic Quasiperiodic Workshop 2023, Luleå University of Technology (Sweden), June 2023.

• Summer school lecture series "Functional analytic methods for discrete approximations of subwavelength resonator systems", Gdańsk (Poland), July 2022.  [link]

• Online seminar "MetaMAT", London (UK), June 2022. [link] 

• ECCOMAS Congress (PhD Award Presentation), Oslo (Norway), June 2022. [link] 

• Online conference "SIAM Conference on Mathematical Aspects of Materials Science", Bilbao (Spain), May 2021.

• Online conference "International Conference on Partial Differential Equations Related to Material Science'', Beijing (China), May 2021.

• Online conference "Theory and Computational Methods for Inverse and Ill-posed Problems", Novosibersk (Russia), October 2020. [link]

• Applied Inverse Problems Conference, Grenoble (France), July 2019. [link]