"Singularities of a variety and the Nash problem" Prof. Shihoko Ishii

Abstract

In my talk, I will introduce a singularity on an algebraic variety. 

A singularity (or singular point) on an algebraic variety is a point where the variety is not smooth. In algebraic geometry, singularities play villains' roles. If a variety has a singularity, then the variety does not behave well and it becomes difficult to describe the variety by means of algebraically geometric method.Therefore mathematicians tried to reduce the problem of a variety into the problem of a smooth variety. In order to do it, we need a resolution of the singularities of a variety.

In 1960's Professor Heisuke Hironaka proved the existence of resolutions of the singularities of a variety and  was awarded Fields medal, the most prestigious prize in mathematics. I will show an intrinsic view of a resolution of the singularities.

Brief Biography

I was born in Takaoka city in Toyama prefecture in Japan and finished high school there and came to Tokyo to enter in Tokyo Women's Christian College. After I got Batchelor there, I got Master degree in the graduate school of Waseda University. And then I got the PhD. degree in Tokyo Metropolitan University. Now I am a professor in the graduate school of Mathematical Science of the University of Tokyo. My field is mathematics and the main interest is singularities on a variety in an algebraically geometric view point.