Overview

Ziqi Sun is a Professor of Mathematics and Chair for the Department of Mathematics, Statistics, and Physics. After obtaining his PhD in Mathematics at UCLA in 1987, he started his research and teaching career as an Assistant Professor at the University of Washington in Seattle and then became a faculty member at 麻豆传媒映画出品 in 1990 with promotions to Associate Professor in 1992 and Professor in 1997.

Ziqi Sun studies inverse problems in partial differential equations and related topics with conformal geometry. His research areas include inverse boundary value problems for elliptic equations and the inverse scattering theory. A number of classical issues related the isotropic and anisotropic Calderon's problems and the inverse scattering problems with scalar and vector potentials have been solved by Sun and his collaborators. His research was supported by three NSF grants from 1990 to 1998. His current research is concentrated in a nonlinear type of inverse boundary value problems that arise naturally in nonlinear materials and the nonlinear elasticity theory. A geometric framework has been developed to link the nonlinear problems to the existing linear theory that leads to a number of uniqueness results for the nonlinear anisotropic elliptic inverse boundary value problems.

Information

Academic Interests and Expertise
  • PDEs
  • Inverse Problems
  • Differential Geometry
Areas of Teaching Interest
  • Partial Differential Equations
  • Real Analysis
  • Functional Analysis
Publications
  • Some special properties of umbilic submanifolds of Riemannian manifolds with constant curvatures, J. Univ. Sci. Tech. Chin., 14 (2), (1984), 187-194.
  • Submanifolds with constant mean curvature in spheres, Adv. in Math. (Beijing), 16 (1), (1987), 91-96.
  • On complete hypersurfaces in with constant scalar curvature, Chin. Ann. of Math., Ser. A8 (1987), No.1, 1-8.
  • On compact hypersurfaces in with constant scalar curvature, Chin. Ann. Of Math., Ser. A8 (1987), No.3, 273-286.
  • On the uniqueness for a multidimensional hyperbolic inverse problem, Comm. in PDE, 13 (10), (1988), 1189-1208.
  • On an inverse boundary value problem in two dimensions, Comm. in PDE, 14 (8&9), (1989), 1101-1113.
  • On the continuous dependence for an inverse initial boundary value problem, J. Math. Anal. and Appl. 150 (1), (1990), 188-204.
  • The inverse conductivity problem in two dimensions, J. Diff. Equations, 87 (2), (1990), 227-255.
  • Generic uniqueness for an inverse boundary value problem, Duke Math. J., 62 (1), (1991), 131-155. (with G. Uhlmann)
  • Uniqueness for formally determined inverse boundary value problems, Comp. Math. Applic., 22 (4/5), (1991), 67-80.
  • Generic uniqueness for formally determined inverse problems, Inverse Problems in Engineering Sciences, ICM-90 Satellite Conf. Proc., Springer- Verlag, 145-152. (with G. Uhlmann)
  • An inverse boundary value problem for Schrodinger operators with vector potentials, (1991), Trans. of AMS, 338 (2), (1993), 953-969.
  • An inverse boundary value problem for Maxwell's equations, Archive Rat. Mech. Anal., 119, (1992), 71-93. (with G. Uhlmann)
  • Stability estimates for hyperbolic inverse problems with local boundary data, Inverse Problems, 8, (1992), 193-206. (with V. Isakov)
  • Inverse scattering for singular potentials in two dimensions, Trans. of AMS, 338 (1), (1993), 363-374. (with G. Uhlmann)
  • An inverse boundary value problem for Schrodinger operators with vector potentials in two dimensions, Comm. in PDE, 18 (1&2), (1993), 83-124.
  • Recovery of singularities for formally determined inverse problems, Comm. in Math. Physics, 153, (1993), 431-445. (with G. Uhlmann)
  • Inverse boundary value problems for Schrodinger operators, Inverse Problems in Mathematical Physics, Lecture Notes in Physics, 422, (1993), Springer-Verlag, 216-230.
  • An inverse boundary value problem for St. Venant-Kirchhoff's materials, Inverse Problems, 10 (1994), 1159-1163. (with G. Nakamura)
  • A global identifibility theorem for the Schrodinger equation in magnetic field, Math. Ann., 303 (1995), 377-388. (with G. Nakamura and G. Uhlmann)
  • The inverse scattering at fixed energies in two dimensions, Indiana Univ. Math. Journal, 44 (3), (1995), 883-896. (with V. Isakov)
  • On a quasilinear inverse boundary value problem, Math. Z, 221 (2), (1996), 293-305.
  • Electrical impedance tomography in nonlinear materials, Journees 鈥淓quations aux Derivees Partielles" (Saint-Jean-de-Monts, 1996), Exp. No. XIV, 11pp., Ecole Polytech., Palaiseau, 1996. (with G. Uhlmann)
  • Inverse problems in quasilinear anisotropic medium, Amer. Journal of Math. 19 (40), (1997), 771-797. (with G. Uhlmann)
  • Inverse boundary value problems for nonlinear elasticity, Inverse Problems in Engineering Sciences, Proc. of IPES, (1999), Springer-Verlag. (with G. Nakamura)
  • An inverse boundary value problem for quasilinear elliptic equations. Comm. in PDE, 27 (2002), 11&12, 2449-2490. (with D. Hervas)
  • An inverse problem for inhomogeneous conformal Killing field equations, Proc. Amer. Math. Soc. 131 (2003), 1583-1590.
  • Anisotropic inverse problems in two dimensions, Inverse Problems, 19 (2003) 1001-1010. (with Gunther Uhlmann)
  • A pinching theorem on submanifolds with parallel mean curvature vectors, Colloquium Mathematicum, 98 (2), (2003), 189-199.
  • Inverse boundary value problems for a class of semilinear elliptic equations, Advances in Applied Mathematics, 32 (4), (2004), 791-800.
  • Note on exponentially growing solutions to the Schrodinger equations, Communications in Applied Math, 9 (2005), 327-336.
  • Conjectures in inverse boundary value problems for quasilinear elliptic equations, CUBO Journal, 7 (3), (2005), 65-73.
  • Anisotropic inverse problems for quasilinear elliptic equations, Journal of Physics, 12 (2005), 156-164.
  • Inverse boundary value problems for elliptic equations, Advances in Mathematics and Its Applications, USTC, (2008), 149-171.
  • An inverse boundary value problem for semilinear elliptic equations, Electron. J. Diff. Equ., Vol. 2010 (2010), No. 37, 1-5.
  • A Method for searching for prime pairs in the Goldbach conjecture, International J. Math & Comp. 10 (2015), No 2, 115-126. (with W. Zeng)
  • Stability theorems for an inverse problem for inhomogeneous conformal Killing field equations, to be submitted.
  • Inverse problems with the conformal Killing field equations in higher dimensions. In preparation.
  • Conformal geometry and inverse problems. In preparation.