One (full) professor and three tenure-track assistant professors were hired during the 1999-2000 academic year. In addition, two associate professors and one tenure-track assistant professor have already been hired this year, to take effect beginning with the 2001-02 academic year.
Shi's research interests lie in the development and study of effective computational and mathematical methods for problems arising in a wide variety of physical and engineering problems. In particular, he is interested in numerical methods for fluid dynamics, rarefied gas dynamics, wave propagation and material sciences. Numerical and computational analysis is of strategic importance on our campus, and Dr. Jin is expected to play a major role. One of Shi's major achievements (with Z. Xin) was the design of relaxation schemes which allow a much simpler discretization of hyperbolic systems of conservation laws than the usual schemes. Basic to these schemes is the design of a linear supersystem with stiff relaxation terms that relax to the original nonlinear system. These schemes have been widely adopted and developed in many application areas. Recently he began the study of a nonlinear Schrodinger equation with random inhomogeneities. Like a true applied mathematician, he has developed collaborations with engineers and scientists.
Alexandru's research area is real analysis on Lie groups. This area involves several branches of mathematics including Fourier analysis, global and harmonic analysis, partial differential equations, differential geometry, and probability theory. One of his striking achievements is a dramatic improvement of the Kunze-Stein phenomenon for Lp. In the case of rank-one semi-simple Lie groups he obtained the optimal form that, in the setting of Lorentz spaces, the convolution of two L2,1 functions yields a L2,¥ function. Other aspects of his work concern Lrp ® Lsq estimates for the wave operator and the noncentered Hardy-Littlewood maximal operator.
Dr. Gong's main research interests are in several complex variables and dynamical systems. In collaboration with Dan Burns, he has been studying singular Levi-flat real analytic hypersurfaces. His most recent research work includes the normalization of holomorphic symplectic mappings admitting invariant Levi-flat real analytic sets, non-reversibilities of real analytic area-preserving mappings and Hamiltonian systems, and the existence of periodic points of symplectic and reversible holomorphic mappings near a fixed point. Gong brings a breadth of knowledge in a number of areas of mathematics that will significantly impact our research programs.
Tonghai's research interests are in number theory, arithmetic geometry and representation theory. He has worked extensively on the central values and derivatives of Hecke L-functions. One of his striking results is a formula for certain representation densities of quadratic forms. Recently he obtained a striking formula for the central derivative of the L-function of a canonical Hecke character, the derivation of which involved enormous insight and computational skill.
Dr. Seppäläinen's research interests are in probability theory, with special interests in interacting particle systems, large deviation theory, combinatorial probability, and statistical mechanics. His current main research concerns the large-scale behavior of interacting particle systems. In a series of papers, he has developed a method for studying certain asymmetric systems where an infinite family of processes is simultaneously constructed so that a complicated process can be represented as an envelope of simpler processes.
Sergey's research interests include variational methods in Hamiltonian systems, conditions for nonintegrability and chaotic behavior of Hamilton systems, billiards, rigid body dynamics, and celestial mechanics and inertial navigation. With Z. Z. Kozlov, he received the S. V. Kovalevskaya Prize of the Russian Academy of Sciences in 2000 for a series of papers on integrability and nonintegrability of Hamiltonian systems.
Dr. Borisov's research area is algebraic geometry and
currently he is working on problems related to mirror symmetry, a
byproduct of research by physicists in string theory. He has also
interests in number theory and, more recently, in protein folding
problems in mathematical biology. The ultimate goal in the latter
area is to predict a three-dimensional structure of a protein from
its amino acid sequence.