I am a Gibbs Assistant Professor in Applied Mathematics at Yale University. 

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, and my Curriculum Vitae can be found [here] (updated 28 February 2022).

Affiliation: Department of Mathematics, Yale University

Address: 51 Prospect Street, AKW 103,  New Haven CT 06511, USA

Email: erik.hiltunen (at) yale.edu

Research

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

Peer-reviewed papers

1. H. Ammari, S. Barandun, J. Cao, B. Davies and E. O. Hiltunen, Mathematical foundations of the non-Hermitian skin effect. To appear in Archive for Rational Mechanics and Analysis, [link] 

2. E. O. Hiltunen, J. Kraisler, J. C. Schotland and M. I. Weinstein, Nonlocal PDEs and Quantum Optics: Bound States and Resonances. To appear in SIAM Journal on Mathematical Analysis. [link] 

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

4. 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] 

5. 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] 

6. 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] 

7. 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] 

8. 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] 

9. 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]

10. 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]

11. 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] 

12. 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] 

13. 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] 

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

15. 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] 

16. 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] 

17. 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] 

18. 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]

19. 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] 

20. 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. 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. arXiv:2403.12546 

2. H. Ammari, S. Barandun, B. Davies, E. O. Hiltunen, T. Kosche, and P. Liu, Exponentially localised interface eigenmodes in finite chains of resonators. arxiv:2312.09667

3. 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

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

5. 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. arXiv:2311.10521 

6. H. Ammari, S. Barandun, B. Davies, E. O. Hiltunen, and P. Liu, Stability of the non-Hermitian skin effect. arxiv:2308.06124 

7. H. Ammari, B. Davies, and E. O. Hiltunen, Spectral convergence in large finite resonator arrays: the essential spectrum and band structure. arxiv.org:2305.16788 

8. 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. arXiv:2106.12301 

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]