现阶段我主要研究以下方向：

1. 度量测度空间上的Gel'fand反问题

2. 离散图上的反问题。

3. 自由边界反问题

Publications and preprints:

[16] Gel'fand's inverse problem under Ricci curvature bounds (with S. Honda), arXiv:2602.14527.    

[15] Stability of Gel'fand's inverse interior spectral problem for Schrodinger operators, arXiv:2507.15560.    

[14] An inverse Signorini obstacle problem (with M. de Hoop, M. Lassas, L. Oksanen, Z. Zhao), Arch. Ration. Mech. Anal. 250 (2026), no. 49.

[13] Inverse spectral problems for collapsing manifolds II: quantitative stability of reconstruction for orbifolds (with M. Lassas, T. Yamaguchi), arXiv:2404.16448.

[12] Inverse spectral problems for collapsing manifolds I: uniqueness and stability (with Y. Kurylev, M. Lassas, T. Yamaguchi), arXiv:1209.5875v3.

[11] Stable recovery of coefficients in an inverse fault friction problem (with M. de Hoop, M. Lassas, L. Oksanen), Arch. Ration. Mech. Anal. 248 (2024), no. 64.

[10] Quantum computing algorithms for inverse problems on graphs and an NP-complete inverse problem (with J. Ilmavirta, M. Lassas, L. Oksanen, L. Ylinen), Inverse Probl. Imaging 19 (2025), 660-692.

[9] Quantitative unique continuation for the elasticity system with application to the kinematic inverse rupture problem (with M. de Hoop, M. Lassas, L. Oksanen), Comm. PDE 48 (2023), 286-314.

[8] Inverse problems for locally perturbed lattices -- Discrete Hamiltonian and quantum graph (with E. Blåsten, P. Exner, H. Isozaki, M. Lassas), Ann. H. Lebesgue 7 (2024), 267-305.

[7] Reconstruction and interpolation of manifolds II: Inverse problems with partial data for distances observations and for the heat kernel (with C. Fefferman, S. Ivanov, M. Lassas, H. Narayanan), Amer. J. Math. 147 (2025), 1331-1382.

[6] Inverse problems for discrete heat equations and random walks for a class of graphs (with E. Blåsten, H. Isozaki, M. Lassas), SIAM J. Discrete Math. 37 (2023), 831-863.

[5] Gel'fand's inverse problem for the graph Laplacian (with E. Blåsten, H. Isozaki, M. Lassas), J. Spectral Theory 13 (2023), 1-45.

[4] Quantitative stability of Gel'fand's inverse boundary problem (with D. Burago, S. Ivanov, M. Lassas), Anal. PDE 18 (2025), 963-1035.

[3] Approximations of the connection Laplacian spectra (with D. Burago, S. Ivanov, Y. Kurylev), Math. Z. 301 (2022), 3185-3206.

[2] Graph approximations to the Laplacian spectra, J. Topol. Anal. 14 (2022), 111-145.

[1] How large isotopy is needed to connect homotopic diffeomorphisms (with D. Burago, T. Ozuch), J. Topol. Anal. 12 (2020), 1213-1222.