Publications by Research Area

Inverse Geometric Diffraction

• G. Bao, X. Chen, S. Lu, K. Xiong; Inverse geometric diffraction by a cone, arXiv:2608.04675.

• G. Bao, X. Chen, S. Lu, K. Xiong; Inverse scattering by diffracted waves, arXiv:2607.22174.

Computational Wave Propagation in Anisotropic Media

• Y. Cai, Z. Qiu, Y. Shu, J. Wu, Y. Li, T. Wang, X. Chen; Windowed Fourier propagator: A frequency-local neural operator for wave equations in inhomogeneous media, arXiv:2603.14289.

Calderón's Problem of Anisotropic Media

• X. Chen, Z. Jin; The Calderón problem for quasilinear conductivities of conformally transversally anisotropic media, Inverse Problems 42(2026), 035003.

• T. Cai, X. Chen; Inverse problem for fractional Schrödinger equations with drift on closed Riemannian manifolds, accepted for publication in CSIAM Trans. Appl. Math., arXiv:2508.16879.

Inverse Problems of Nonlinear Wave Equations and Applications to the Standard Model of Particle Physics

• X. Chen, S. Lu, R. Zhang; Unique inversion of smooth nonlinearity in semilinear wave equations on Lorentzian manifolds, arXiv:2607.17501.

• X. Chen, M. Lassas, L. Oksanen, G. Paternain; An inverse problem for the Standard Model of particle physics, arXiv:2505.24454.

• X. Chen, S. Lu, R. Zhang; Stable inversion of potential in nonlinear wave equations with cubic nonlinearity, Math. Ann. 392(2025), 4283-4314.

• X. Chen, M. Lassas, L. Oksanen, G. Paternain; Retrieving Yang–Mills–Higgs fields in Minkowski space from active local measurements, Math. Ann., 391(2025), 2385-2428.

• X. Chen, M. Lassas, L. Oksanen, G. Paternain; Inverse problem for the Yang–Mills equations, Comm. Math. Phys. 384(2021), 1187-1225.

• X. Chen, M. Lassas, L. Oksanen, G. Paternain; Detection of Hermitian connections in wave equations with cubic non-linearity, J. Eur. Math. Soc.(JEMS) 24(2022), 2191-2232.

Geometric Microlocal Analysis and Interactions with Harmonic Analysis, Spectral and Scattering Theory

• X. Chen; The semiclassical resolvent on conic manifolds and application to Schrödinger equations, Comm. Math. Phys. 390(2022), 757-826.

• X. Chen, The Sobolev inequalities on real hyperbolic spaces and eigenvalue bounds for Schrödinger operators with complex potentials, Anal. PDE 15 (2022), No. 8, 1861-1878.

• X. Chen, A. Hassell; The heat kernel on asymptotically hyperbolic manifolds, Comm. Partial Differential Equations 45 (2020), no. 9, 1031-1071. 

• X. Chen; Stein–Tomas restriction theorem via spectral measure on metric measure spaces, Math. Z. 289(2018), no. 3-4, 829-835.

• X. Chen;  Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds III: Global-in-time Strichartz estimates without loss, Ann. Inst. H. Poincaré Anal. Non Linéaire 35(2018), 803-829.

• X. Chen,  A. Hassell;  Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds II: Spectral measure, restriction theorem, spectral multipliers, Ann. Inst. Fourier (Grenoble) 68(2018), 1011-1075.

• X. Chen,  A. Hassell;  Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds I: Resolvent construction at high energy, Comm. Partial Differential Equations 41(2016), 515-578.

Harmonic Analysis of Multilinear Integral Operators

• X. Chen; Weighted estimates for maximal operator of multilinear singular integral, Bull. Polish Acad. Sci. Math. 58 (2010), 129-135.

• X. Chen, Q. Xue, K. Yabuta; On multilinear Littlewood-Paley operators, Nonlinear Anal. 115 (2015), 25-40.

• X. Chen, Q. Xue; Weighted estimates for a class of multilinear fractional type operators, J. Math. Anal. Appl. 36 (2010), 355-373.

Publications in Reverse Chronological Order

[21] G. Bao, X. Chen, S. Lu, K. Xiong; Inverse geometric diffraction by a cone, arXiv:2608.04675.

[20] X. Chen, S. Lu, R. Zhang; Unique inversion of smooth nonlinearity in semilinear wave equations on Lorentzian manifolds, arXiv:2607.17501.

[19] G. Bao, X. Chen, S. Lu, K. Xiong; Inverse scattering by diffracted waves, arXiv:2607.22174.

[18] Y. Cai, Z. Qiu, Y. Shu, J. Wu, Y. Li, T. Wang, X. Chen; Windowed Fourier propagator: A frequency-local neural operator for wave equations in inhomogeneous media, arXiv:2603.14289.

[17] X. Chen, Z. Jin; The Calderón problem for quasilinear conductivities of conformally transversally anisotropic media, Inverse Problems 42(2026), 035003.

[16] T. Cai, X. Chen; Inverse problem for fractional Schrödinger equations with drift on closed Riemannian manifolds, accepted for publication in CSIAM Trans. Appl. Math., arXiv:2508.16879.

[15] X. Chen, M. Lassas, L. Oksanen, G. Paternain; An inverse problem for the Standard Model of particle physics, arXiv:2505.24454.

[14] X. Chen, S. Lu, R. Zhang; Stable inversion of potential in nonlinear wave equations with cubic nonlinearity, Math. Ann. 392(2025), 4283-4314.

[13] X. Chen, M. Lassas, L. Oksanen, G. Paternain; Retrieving Yang–Mills–Higgs fields in Minkowski space from active local measurements, Math. Ann., 391(2025), 2385-2428.

[12] X. Chen; The semiclassical resolvent on conic manifolds and application to Schrödinger equations, Comm. Math. Phys. 390(2022), 757-826.

[11] X. Chen, M. Lassas, L. Oksanen, G. Paternain; Inverse problem for the Yang–Mills equations, Comm. Math. Phys. 384(2021), 1187-1225.

[10] X. Chen, M. Lassas, L. Oksanen, G. Paternain; Detection of Hermitian connections in wave equations with cubic non-linearity, J. Eur. Math. Soc. (JEMS) 24(2022), 2191-2232.

[9] X. Chen, The Sobolev inequalities on real hyperbolic spaces and eigenvalue bounds for Schrödinger operators with complex potentials, Anal. PDE 15 (2022), No. 8, 1861-1878.

[8] X. Chen, A. Hassell; The heat kernel on asymptotically hyperbolic manifolds, Comm. Partial Differential Equations 45 (2020), no. 9, 1031-1071. 

[7] X. Chen; Stein–Tomas restriction theorem via spectral measure on metric measure spaces, Math. Z. 289(2018), no. 3-4, 829-835.

PhD Thesis

[6] X. Chen;  Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds III: Global-in-time Strichartz estimates without loss, Ann. Inst. H. Poincaré Anal. Non Linéaire 35(2018), 803-829.

[5] X. Chen,  A. Hassell;  Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds II: Spectral measure, restriction theorem, spectral multipliers, Ann. Inst. Fourier (Grenoble) 68(2018), 1011-1075.

[4] X. Chen,  A. Hassell;  Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds I: Resolvent construction at high energy, Comm. Partial Differential Equations 41(2016), 515-578.

Master’s Thesis 

[3] X. Chen; Weighted estimates for maximal operator of multilinear singular integral, Bull. Polish Acad. Sci. Math. 58 (2010), 129-135.

[2] X. Chen, Q. Xue, K. Yabuta; On multilinear Littlewood-Paley operators, Nonlinear Anal. 115 (2015), 25-40.

[1] X. Chen, Q. Xue; Weighted estimates for a class of multilinear fractional type operators, J. Math. Anal. Appl. 36 (2010), 355-373.