(1) Ker (f,) is a characteristic subgroup of T,(M),(2) the group G leaves Ker (f*) invariant. This assumption is needed in the last two statements of Corollary 6,(vi) of Theorems 8, Theorem 11 and Theorem 13. In Theorem 12, the corresponding assumption can be stated as follows: Let H be the subspace of H,(M, I?) defined by {PIP U ai, U... U ai, _,= 0 for all ii}. Then G leaves H invariant.

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It is a great honor for me to be invited by Tsinghua University to talk today. Tsinghua has, in its history, made many contributions to mathematics. The two most famous mathematicians in modern Chinese history have both been closely related to Tsinghua University. One is Professor Hua Lo-Keng, the other is Prof essor Chern Shiing-Sheng. Especially since Professor Chern is my teacher, I feel proud to be able to say some words in the opening ceremony for the Center for Advanced Study. I chose the title of my talk also for this reason. Due to my critical comments, I have decided to spend most of my time in giving a general talk in English. The remainder of the talk will be in Chinese.

In this summary article, we review and discuss the non-existence of stationary black hole solutions for the Einstein-Dirac-Maxwell equations.

Narain lattices are unimodular lattices {\it in} $\R^{r, s} $, subject to certain natural equivalence relation and rationality condition. The problem of describing and counting these rational equivalence classes of Narain lattices in $\R^{2, 2} $ has led to an interesting connection to binary forms and their Gauss products, as shown in [HLOYII]. As a sequel, in this paper, we study arbitrary rational Narain lattices and generalize some of our earlier results. In particular in the case of $\R^{2, 2} $, a new interpretation of the Gauss product of binary forms brings new light to a number of related objects--rank 4 rational Narain lattices, over-lattices, rank 2 primitive sublattices of an abstract rank 4 even unimodular lattice U^ 2, and isomorphisms of discriminant groups of rank 2 lattices.