The global geometry of moduli spaoes

Nakamura证明了简单奇点C2/G的McKay对应的一个新定理，其中G是SL（2，C）的有限群。该定理证明了某些自然模V和Vdagger具有简单的结构。其中，Vdagger的结构完全解释了已知的扩展Dynkin图的双射对应关系和G的所有不可约表示。这份报纸现在正在印刷。他还证明了一个重要的退化拟阿贝尔变的消失定理。他以Mumford的GIT稳定性、Seshadri-Narashiman的酉向量束理论为模型，构建了一个新的重要的几何类场论理论。在这个程序中，他定义了非阿贝尔l函数，在某些情况下，他证明了一个类似黎曼假设的定理。加藤和藤原一起学习了p进几何和刚性几何的基本理论。他还证明了芒福德假射影平面和其他已知的假射影平面都属于志村变种。近藤用Borcherds模形式构造了一个5维复球的均匀化，该复球是射影线上有序的8个点的模。Matsumoto在S3中使用实函数给出了一个非常精确的链接及其补的描述。吉冈和Nakajima一起证明了一个计算某些复杂表面上的瞬子数的公式。

Nakamura proved a new theorem on McKay correspondence of a simple singularity C2/G, G being a finite group of SL(2,C). The theorem shows certain natural modules V and Vdagger have simple structures. Among others, the structure of Vdagger explains completely the known bijetive correspondence of the extended Dynkin diagram and all the irreducible representations of G.. The paper is now in print. He also proved an important vanishing theorem for degenerate quasi-abelian varieties.Weng is constructing a new important theory of geometric class field theory, which is modeled after Mumford's stability of GIT, Seshadri-Narashiman's theory of unitary vector bundles. In this program he defined nonabelian L-functions, and in some cases he proved a theorem analogous to Riemann hypothesis.Kato studied with Fujiwara the fundamental theory of p-adic geometry and rigid geometry. He proved also that Mumford fake projective plane and the other known fake projective planes are among Shimura varieties.Kondo constructed a uniformization by a 5-dimensional complex ball of the moduli of ordered 8 points of the projective line, by using Borcherds modular forms.Matsumoto gave a very precise description of a link and its complement in S3 by using real theta functions.Yoshioka proved a formula of counting the number of instantons on certain complex surfaces with Nakajima.