Nakai Conjecture for Homogeneous Isolated Hypersurface Singularity
Organizers
Speaker
Time
Thursday, June 20, 2024 3:00 PM - 4:00 PM
Venue
A6-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
The long-standing Nakai Conjecture concerns a very natural question: can differential operators detect singularities on algebraic varieties? On a smooth complex variety, it is well known that the ring of differential operators is generated by derivations. Nakai asked whether the converse holds: if the ring of differential operators is generated by derivations, is the variety smooth? We will first introduce the history and some important works about Nakai Conjecture. In our work, we prove the Nakai Conjecture for isolated homogeneous hypersurface singularities.
Speaker Intro
Stephen Yau received his PhD degree from the State University of New York at Stony Brook in 1976. He has served as a member of the Institute for Advanced Study at Princeton, an assistant professor at Harvard University under Benjamin Pierce, and later joined the University of Illinois at Chicago, where he taught for over 30 years in the departments of mathematics, statistics, and computer science.
Stephen Yau has made significant original contributions in international cutting-edge research fields, including mathematics, applied mathematics and control theory, computer science, financial mathematics, and bio informatics. He solved some famous conjectures in complex geometry and singularity theory, and was the first to successfully use Lie algebras to study hypersurface singularities in algebraic geometry, a algebra that is now known as Yau algebra among his peers. He solved the Mitter conjecture, completely solving the theoretical problem of nonlinear filters, which will have far-reaching implications for modern industries, including national defense. In the field of bio informatics, his work on the 2D representation of DNA and protein was published in the world's top journal, "Nucleic Acids Research". Recently, he pioneered the natural vector method for representing genomes and proteins. He has published over 200 academic papers, including top international mathematics journals such as PNAS, Annals of Mathematics, and Inventiones Mathematicae.
Stephen Yau has made significant original contributions in international cutting-edge research fields, including mathematics, applied mathematics and control theory, computer science, financial mathematics, and bio informatics. He solved some famous conjectures in complex geometry and singularity theory, and was the first to successfully use Lie algebras to study hypersurface singularities in algebraic geometry, a algebra that is now known as Yau algebra among his peers. He solved the Mitter conjecture, completely solving the theoretical problem of nonlinear filters, which will have far-reaching implications for modern industries, including national defense. In the field of bio informatics, his work on the 2D representation of DNA and protein was published in the world's top journal, "Nucleic Acids Research". Recently, he pioneered the natural vector method for representing genomes and proteins. He has published over 200 academic papers, including top international mathematics journals such as PNAS, Annals of Mathematics, and Inventiones Mathematicae.