The global geometry of moduli spaoes

中村证明了SL（2，C）的有限群G为单奇点C ~ 2/G的McKay对应的一个新定理。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图和G.的所有不可约表示的双向对应。这份文件现已付印。他还证明了退化拟阿贝尔簇的一个重要的消失定理。Weng正在构造一个新的重要的几何类场论理论，它是仿照Mumford的GIT稳定性，Seshadri-Narashiman的酉向量丛理论。在这个计划中，他定义nonabelian L-职能，并在某些情况下，他证明了一个定理类似于黎曼假设。加藤研究与藤原的基本理论的p进几何和刚性几何。他还证明了Mumford伪射影平面和其他已知的伪射影平面都属于Shimura变种。Kondo构造了射影直线的有序8点模的5维复球的一致化，松本利用真实的θ函数对S3中的环及其补函数给出了非常精确的描述，吉冈证明了一个计算环及其补函数个数的公式在某些复杂表面上的瞬子。

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.