Mathematical Sciences: Presidential Young Investigator Award

这项总统青年研究员奖将支持 Wodzicki教授在非对易领域的研究 微分几何 本研究的主要主题将 是一个非交换的Riemann-Roch定理，更高的指标 不变量，与算术代数几何的联系， 非对易微分几何的正特征 同调代数的平行方向量子化 到量子群。 微分几何可以被认为是 流形 这些是表面和它们的高维 类似物 上的微分算子代数 流形可以进一步抽象，直到没有流形 只剩下代数。 这是一个深远的 微分几何的一种推广叫做非对易 微分几何 该地区利用和吸收了所有的 数学的主要领域：代数、几何和分析。

This Presidential Young Investigator award will support the research of Professor Wodzicki in the area of noncommutative differential geometry. The dominant themes in this research will be a noncommutative Riemann-Roch theorem, higher index invariants, connections with arithmetic algebraic geometry via noncommutative differential geometry in positive characteristic, and quantization of homological algebras in a direction parallel to quantum groups. Differential geometry can be thought of as calculus on manifolds. These are surfaces and their higher dimensional analogues. The algebra of differentiation operators on the manifold can be further abstracted until there is no manifold left but just the algebra. This is the far reaching generalization of differential geometry called noncommutative differential geometry. The area draws on and nourishes all the major fields of mathematics: algebra, geometry and analysis.