Wireless networks: I mainly concentrate on designing energy efficient protocols and topogies for wireless ad hoc networks. It combines computational geometry, algorithm design, and wireless netwokrs into one.

Non-cooperative Computing in selfish environment: A large part of research in computer science is concerned with protocols and algorithms for inter­connected collections of computers. An implicit assumption often made by the designer of such an algorithm or protocol is that the participating computers will act as instructed -- except, perhaps, for the faulty or malicious ones. With the emergence of the computer networking as the platform of computation, e.g., grid computing, wireless networks and peer-to-peer networks, this assumption can no longer be taken for granted. Computing devices and communication terminals belong to different persons or organizations, and will likely do what is the most beneficial to their owners, i.e., act selfishly. We cannot simply expect them to faithfully follow the designed protocols or algorithms without any deviation. It is more reasonable to expect that each selfish computer will try to manipulate it for its owners' benefit. An algorithm or protocol intended for selfish computers must therefore be designed in advance for this kind of behavior! Such protocols and algorithms will likely involve incentives to the selfish participants. In this area, I basically study how to design some theoretical tools that could be used by systems' engineers to achieve certain system goals for the global behavior of the network.

CRYPTOGRAPHY is the state-of-the-art about the information security. There are two kinds of cryptosystems: symmetric and asymmetric. Symmetric cryptosystems use the same key (the secret key) to encrypt and decrypt a message, while asymmetric cryptosystems use one key (the public key) to encrypt a message and a different key (the private key) to decrypt it. Asymmetric cryptosystems are also called public key cryptosystems. Symmetric cryptosystems have a problem: how do you transport the secret key from the sender to the recipient securely and in a tamper-proof fashion? If you could send the secret key securely, you wouldn't need the symmetric cryptosystem in the first place (because you would simply use that same secure channel to send your message). Frequently, trusted couriers are used as a solution to this problem. Another, more efficient and reliable solution is a public key cryptosystem, such as RSA, which is used in the popular security tool PGP.

Human-machine identification is an important problem in cryptography that has applications in network access, electronic commerce, and smart-card design. It is a hard problem largely because human users have a very limited capacity in memorizing secrets and in performing protocols. Therefore, in addition to the requirement that a human-machine identification scheme must be provably secure, the scheme has to be practical in the sense that it must be feasible for a human user to participate.

MESHING can be defined as the process of breaking up a domain into a collection of elements. It has a wide range of applications in physical simulation, computer graphics, computer vision, geographic information systems, and elsewhere. Surface domains may be subdivided into triangle or quadrilateral shapes, while volumes may be subdivided primarily into tetrahedra or hexahedra shapes. The shape and distribution of the elements is ideally defined by automatic meshing algorithms. The automatic mesh generation problem is that of attempting to define a set of nodes and elements in order to best describe a geometric domain, subject to various element size and shape criteria. Geometry is most often composed of vertices, curves, surfaces and solids as described by a CAD or solids modeling package.

Surface reconstruction (reconstruct a surfaces representation from a set of sampled points) and surface simplification (simplify originally very dense representation by using less vertices) are two of the hot area for computer graphics.

Anisotropic mesh generation and hexahedral mesh generation are two of the most difficult mesh generation questions that are still lack of theoretical sound algorithms.