Noncommutative Geometry

Wodzicki PI将继续研究代数K理论、算子代数和算子理想的循环和Hochschild同调;他将研究算子不变量的构造（例如，更高的指数不变量和调节器）。他还将研究异国情调的痕迹和由此产生的不变量;古典以及分形和非交换几何的应用;狄利克雷级数理论的分支及其在狄利克雷级数临界线附近的行为。 他还打算研究非对易几何中与特殊导子和奇异链同伦等价有关的新现象，这些导子和奇异链同伦等价取代了德拉姆理论的Koszul分解方法，特别感兴趣的是量子群，量子齐性空间和非对易流形的可能应用。除了前一段提到的领域，代数学和解析几何，奇点理论，分形几何和MathematicalPhysics是拟议的调查的影响将是最显着的领域。

AbstractWodzickiThe PI will continue his investigation of algebraic K-theory, cyclic and Hochschild homology of operator algebras and operator ideals; he will be studying constructions of invariants of operators (e.g., higher index invariants and regulators). He will also study exotic traces and resulting invariants; the applications to Classical as well as Fractal, and Noncommutative Geometry; ramifications for the theory of Dirichlet series and their behavior in the vicinity of the critical line of Dirichlet series. He also intends to investigate new phenomena in Noncommutative Geometry related to special derivations and exotic chain homotopy equivalences that replace Koszul resolution approach to de Rham theory, with a particular interest in possible applications to quantum groups, quantum homogeneous spaces and noncommutative manifolds.Besides the areas mentioned in the previous paragraph, Algebraic andAnalytic Geometry, Singularity Theory, Fractal Geometry and MathematicalPhysics are the areas where the impact of the proposed investigations will be most significant.