Study of Discrete Subgroups of Rank 1 Simple Groups by Geometric Methods

Shin Nayatani和Hiroyasu Izeki研究了组合调和映射理论及其在超刚性和不动点定理中的应用，并证明了CAT（O）空间上离散群等距作用的不动点定理。Shin Nayatani和Hiroyuku Kamada研究了四元数CR几何，阐明了规范伪厄米联络的表示论意义，Norio Ejiri研究了2g维平坦环面中亏格g的非面积极小化稳定极小曲面的存在性问题，并证明了在某个8-Ryoichi小林研究了作为Nevanlinna理论离散化的丢番图逼近几何理论的构造，并证明了全纯曲线在保护代数簇中的对数导数引理始终保持相同的形式，Toshihiro Nakanishi引入了一个参数复化R. C. Penner 关于我们 的λ长度在从曲面群到SL（2，C）的忠实表示的等价类空间上，边界分支到抛物元的映射同伦类。利用这一点，他成功地代表了映射类群体作为群体的合理转变。元子小谷研究了大偏差的随机行走的晶格，即一个无限图形上的阿贝尔群的行为及其几何意义。她确定了渐近项，阐明了代表衰变阶的速率函数与晶格无穷远切锥之间的关系。太田浩完全确定了简单奇异点和简单椭圆奇异点链接的辛填充变形类。他还利用滤子A_∞代数研究了Floer上同调的阻塞和形变理论，佐藤武用各种模函数得到了计算π值的新算法，Kamada研究了含有标量平坦Kahler度量的紧致复曲面，并根据具有某种对称性的度量的存在性来刻画复射影线的乘积。行为的变形空间的拟Fuchsian群的完整表示的投影结构的表面。他证明了戈德曼的嫁接定理适用于边界群，表现出某种连续性和离散性，从而解决了布朗伯格猜想。少

Shin Nayatani and Hiroyasu Izeki studied combinatorial harmonic map theory and its application to super-rigidity and fixed point theorem, and proved fixed point theorems for isometric actions of discrete groups on CAT(O) spaces. Shin Nayatani and HIroyuku Kamada studied quaternionic CR geometry, and clarified the representation-theoretic meaning of the canonical pseudohermitian connection.Norio Ejiri studied the existence problem for non-area-minimizing stable minimal surface of genus g in 2g-dimensional flat tori, and proved that there exists a non-holomorphic stable minimal surface of genus【greater than or equal】4 in a certain 8-dimensional torus.Ryoichi Kobayashi srudied the construction of geometric theory of Diophantine approximation as discretization of the Nevanlinna theory, and showed that the lemma of logarithmic derivative for holomorphic curves in protective algebraic varieties hold always with the same form.Toshihiro Nakanishi introduced a parameter complexifying R.C.Penner … More 's λ length on the spaces of equivalence classes of faithful representations from surface groups into SL(2,C) mapping homotopy classes of boundary components to parabolic elements. Using this he succeeded in representing the mapping class groups as groups of rational transformations.Motoko Kotani studied the large deviation of the random walk on a crystal lattice, that is, an infinite graph on which an abelian group acts and its geometric meaning. She determined asymptotic terms and clarified the relation between the rate function representing decay order and the tangent cone at infinity of a crystal lattice.Hiroshi Ohta completely determined the deformation classes of symplectic fillings of the links of simple singularities and simple elliptic singularities. He also studied the obstruction and deformation theories of the Floer cohomology using filtered A_∞ algebras.Takeshi Sato obtained some new algorithms to compute the value of π using various modular functions.Hiroyuki Kamada studied compact complex surfaces admitting scalar flat Kahler metrics, and characterized the product of complex projective lines in terms of the existence of such metrics with a certain type of symmetry.Kentaro Ito studied the boundary behavior of the deformation space of quasi-Fuchsian groups by means of the holonomy representations of projective structures on surfaces. He proved that Goldman's grafting theorem holds for the boundary groups by showing a certain kind of continuity and discreteness, thus resolving Bromberg's conjecture. Less