University Researcher
Department of Mathematics and Statistics
University of Helsinki, Finland
Office: Exactum C329
Email: jinpeng.lu@helsinki.fi
About me:
I am currently university researcher at the University of Helsinki. During 2019-2023 I was postdoc at the University of Helsinki working with Matti Lassas. I received my Ph.D. from Penn State University in 2019 under the supervision of Dmitri Burago. My research interests are geometric analysis and inverse problems. My recent research focuses on the effect of curvature on the unique solvability and stability of inverse problems. I am also interested in geometry of manifold learning and inverse problems on graphs, especially their connections with manifolds.
Publications and Preprints:
[13] (with M. Lassas, T. Yamaguchi) Inverse spectral problems for collapsing manifolds II: quantitative stability of reconstruction for orbifolds, arXiv:2404.16448.
[12] (with Y. Kurylev, M. Lassas, T. Yamaguchi) Inverse spectral problems for collapsing manifolds I: uniqueness and stability, arXiv:1209.5875v3.
[11] (with M. de Hoop, M. Lassas, L. Oksanen) Stable recovery of coefficients in an inverse fault friction problem, Arch. Ration. Mech. Anal. 248 (2024), no. 64. doi
[10] (with J. Ilmavirta, M. Lassas, L. Oksanen, L. Ylinen) Quantum computing algorithms for inverse problems on graphs and an NP-complete inverse problem, to appear in Inverse Probl. Imaging. doi
[9] (with M. de Hoop, M. Lassas, L. Oksanen) Quantitative unique continuation for the elasticity system with application to the kinematic inverse rupture problem, Comm. PDE 48 (2023), 286-314. doi
[8] (with E. Blåsten, P. Exner, H. Isozaki, M. Lassas) Inverse problems for locally perturbed lattices -- Discrete Hamiltonian and quantum graph, Ann. H. Lebesgue 7 (2024), 267-305. doi
[7] (with C. Fefferman, S. Ivanov, M. Lassas, H. Narayanan) Reconstruction and interpolation of manifolds II: Inverse problems for Riemannian manifolds with partial distance data, to appear in Amer. J. Math., arXiv:2111.14528.
[6] (with E. Blåsten, H. Isozaki, M. Lassas) Inverse problems for discrete heat equations and random walks for a class of graphs, SIAM J. Discrete Math. 37 (2023), 831-863. doi
[5] (with E. Blåsten, H. Isozaki, M. Lassas) Gel'fand's inverse problem for the graph Laplacian, J. Spectral Theory 13 (2023), 1-45. doi
[4] (with D. Burago, S. Ivanov, M. Lassas) Quantitative stability of Gel'fand's inverse boundary problem, to appear in Anal. PDE, arXiv:2012.04435v4.
[3] (with D. Burago, S. Ivanov, Y. Kurylev) Approximations of the connection Laplacian spectra, Math. Z. 301 (2022), 3185-3206. doi
[2] Graph approximations to the Laplacian spectra, J. Topol. Anal. 14 (2022), 111-145. doi
[1] (with D. Burago, T. Ozuch) How large isotopy is needed to connect homotopic diffeomorphisms, J. Topol. Anal. 12 (2020), 1213-1222. doi
Teaching:
At University of Helsinki, I taught
$\bullet$ Riemannian Geometry, Fall 2024
$\bullet$ Introduction to Differential Geometry, Fall 2023
$\bullet$ Calculus IA, Fall 2022
$\bullet$ Calculus IA, Fall 2021