Algebraic combinatorics and its application to algebraic geometry and low dimensional topology

点击翻译按钮获取中文摘要

Since about the 1980's there has been a long period of remarkable and intense activity in modern geometry, spurred on by the deep connexions with mathematical physics. For the same reason, there were advances in Modern Knot Theory, prompted partly by the occurrence of a particular fundamental equation, the Yang-Baxter Equation, in both mathematical physics and knot theory. As research progressed in these areas, it became increasingly apparent that deeply within questions about individual knot invariants lay new questions of great complexity about Vassiliev invariants, and aggregates of new objects, or diagrams, constrained by complex relations. These new questions are essentially combinatorial in nature, and may be expressed abstractly, without reference to their original context. An instance of such a diagram is the Feynman diagram from quantum field theory.