Mathematical Sciences: Research in Geometric Analysis

9626427哈维这个项目位于微分几何和代数几何的交界处。研究人员计划进一步研究特征电流的理论、校准及其各种应用。特别值得注意的是对Riemann-Roch定理的可微版的研究。曲线空间上的刻度给出了体积最小化的子空间的无穷小版本。有一些“特殊”的校准与连续对称群密切相关。Riemann-Roch定理是代数几何中的一个重要定理，但它的适用性仅限于所谓的全纯范畴。这个项目的一个既定目标是将Riemann-Roch定理推广到只需要可微性假设的更一般的环境中。

9626427 Harvey This project lies in the interface of differential geometry and algebraic geometry. The investigator plans to further pursue the theory of characteristic currents, calibrations and their various applications. Of particular note is the research on the differentiable version of the Riemann-Roch theorem. Calibrations on a curved space give infinitesimal versions of volume-minimizing subspaces. There are certain 'exceptional' calibrations that are closely related to continuous symmetry groups. The Riemann-Roch theorem is an important theorem in algebraic geometry, but its applicability is restricted to the so-called holomorphic category. One of the stated goals of this project is to extend the Riemann-Roch theorem to a more general setting requiring only the differentiability assumption.