Bulletin Number Four 1986

As for career destinations, most of the graduates of the Department enter the teaching profession and about seventy percent of them teach in secondary schools. Others take up posts in various fields, such as computer and data processing, administration and management, or in finance and business. Many of our best students stay on to study for higher degrees in this University or work for PhD degrees abroad. There is an average of ten students working for MPhil degrees in the Department each year. They have to do course work, write a thesis and take an oral defence. Most of the MPhil graduates further their studies abroad. Some of our graduates have gained international reputation for their great success in mathematics, the most outstanding being the Fields medalist, Professor Shing Tung Yau. Research Activities Members of the Department are actively engaged in research. Their fields of research and recent research topics are summarized as follows: Dr. K,F. Lai Automorphic forms, algebraic groups, algebraic geometry - Eisenstein series, trace formula, algebraic cycles. Dr. K.F. Ng Functional analysis — Inverse functions, tangent cones, positive semigroups. Dr. W.L Chan Control theory - Nonsmooth optimization, China's population dynamics and control, KdV and K-P equations. Dr. Y.C Wong Functional analysis — Ordered topological vector spaces, theory of operator ideals geometry on Banach spaces. Dr. H .L . Chow Topological groups 一 Harmonic analysis. Dr. L.F. Ho Control theory —Exact controllability of wave equa tion, spectral assignability of linear feedback systems. Dr. S.P. Lam Algebraic topology — Algebraic K-theory, stable homotogy theory, maps between classifying spaces and unstable algebras over the steenrod algebra. Dr. K. W. Leung Classical groups — Isometrics of intrinsic metries on strictly convex domain. Dr. H.S. Luk Several complex variables — Geometry and analysis on Cauchy-Riemann manifolds. Dr. K.P. Shum Algebra —Semigroups, rings and lattices. Dr. P.K. Tam Functional analysis — Curitz algebra, extensions of derivations. Mr. L.O. Tse Differential geometry —Finsler spaces. Mr. K.W. Yip Functional analysis Looking Ahead Spectacular developments continue to take place in mathematics. Many long standing open pro blems have been solved. Close, unexpected relations between different areas have been discovered. Recent advances in number theory include the proofs of Riemann hypothesis over finite fields, Mordell-Weil conjecture on algebraic curves, the first case of the Fermat's last theorem about the equation: x p + y p = z p , the Langlands programme of applying Lie group theory to number theoretic problems (such as Hodge- Tate conjecture on algebraic cycles). Mathematics and physics once again interact to give far-reaching results, for example, the Yang-Mills equations in quantum field theory and the theory of fibre bundles, the instanton solutions and the geometry of four dimen sional space, the Kadomtsev-Petiashvilli equation in plasma physics and algebraic curves, the KdV equation and differential geometry, quantum physics and Conne's non-commutative differential geometry. As pointed out by Professor Sir Michael Atiyah, our classical picture: The boundary between pure and applied mathematics becomes much less distinct. The Department hopes to have these important developments reflected in the teaching of mathematics, so that students not only learn abstract and difficult mathematics, but also use mathematics widely and skilfully. It is a pleasure to point out that the work of Professor Shiing-Shen Chern and Professor Chen Ning Yang plays a decisive role in the interaction of mathe matics and physics mentioned above, and both pro fessors are closely related with this University. They have given the Department of Mathematics invaluable help and encouragement. RECENT DEVELOPMENTS 19