Mathematical Sciences: Invariants of Singular Germs and Polynomials

点击翻译按钮获取中文摘要

This awards supports the research of Professor A. Nemethi to work in algebraic geometry. He will work on invariants of singularities and global polynomials. He plans to study the behavior of the signature for composed singularities. He hopes to see the connections between the signature of surface singularities and the Casson invariant of links. The research is in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which blossomed to the point where it has, in the past 10 years, solved problems that have stood for centuries. Originally, it treated figures defined in the plane by the simplest of equations, namely polynomials. Today, the field uses methods not only from algebra, but also from analysis and topology, and conversely it is extensively used in those fields. Moreover, it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics.