Mathematical Sciences: Research in Algebraic Geometry and Related Topics

尤辛教授将研究复杂代数变种的奇点。他将研究来自交上同调的L-2上同调分解与来自微分算子环上的模的L-2上同调分解之间的关系。他还打算研究牛顿多面体与奇点分解之间的关系。这是代数几何领域的研究。代数几何是现代数学中最古老的部分之一，但在过去的25年里，它已经有了革命性的发展。在它的起源中，它处理的图形可以用最简单的方程，即多项式，在平面上定义。如今，该领域不仅使用代数的方法，还使用分析和拓扑的方法，相反，它在这些领域以及物理学、理论计算机科学和机器人技术中也得到了应用。

Professor Youssin will investigate singularities of complex algebraic varieties. He will study the relationship between decompositions of the L-2 cohomology that come from intersection cohomology and those that come from modules over rings of differential operators. He also intends to study relations between Newton polyhedra and resolution of singularities. This is research in the field of algebraic geometry. Algebraic geometry is one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter- century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics.