In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. Partial Differential Equations (PDEs) describe many different physical systems, ranging from gravitation to fluid dynamics, and have a great variety of applications to mechanics, electrostatics, quantum mechanics and many other fields of physics as well as to finance. They also appear in stochastic game theory, non-Newtonian fluids, glaceology, rheology, nonlinear elasticity, flow through a porous medium, and image processing.
Alexander Bukhgeim - Integral geometry, Volterra integral equations,stability of difference
schemes,tomography, Carleman estimates
Thalia Jeffres - Complex and Riemannian differential geometry
Xiaolong Li - Geometric Analysis
Yueh-Ju Lin - Conformal geometry, Geometric Analysis
Ziqi Sun - Anisotropic Calderon’s Problem, Quasilinear inverse boundary value problems