Welcome to my homepage. I am currently research fellow of the institute of Mathematics, Academia Sinica, Taipei. My domain of research is Microlocal Analysis, Complex Geometry and CR (Cauchy-Riemann) Geometry. For more details about my research work, please peruse the Publications section. Mcrolocal Analysis is a term used to describe a technique developed from the 1950s by Kohn-Nirenberg, Hörmander, Sato, Boutet de Monvel, Sjöstrand, Guillemin, Melrose, and others, based on Fourier transforms related to the study of variable coefficients linear and nonlinear partial differential operators. This includes pseudodifferential operators, wave front sets, Fourier integral operators and WKB constructions. The term Microlocal implies localisation not just at a point, but in terms of contangent space directions at a given point. This gains in importance on manifolds. Microlocal Analysis is a powerful analytic tool in Complex Geometry, CR Geometry, Spectral Theory and Theoretical Physics. Complex Geometry is the study of complex manifolds and functions of many complex variables. Complex Geometry is a highly attractive branch of modern mathematics that has witnessed many years of active and successful research. CR Geometry is the study of manifolds equipped with a system of CR-type. CR Geometry is a relatively young and nowadays intensively studied research area having interconnections with many other areas of mathematics and its applications. It deals with restrictions and boundary values of holomorphic functions (CR functions) and of holomorphic mappings (CR mappings) to real submanifolds. A phenomenon arising in dimension higher than one is the rich intrinsic structure that leads to the existence of real submanifolds of different non-equivalent types. The systems of tangential Cauchy-Riemann equations for functions and mappings present important examples of systems of partial differential equations. A celebrated example of a system of this kind due to Hans Lewy played a crucial role in the development of the solvability theory for more general classes of PDEs. A full understanding of modern CR Geometry requires knowledge of various topics such as real (complex) differential and symplectic geometry, foliation theory, the geometry of PDE's and microlocal analysis. |