Abstract

The long-standing Nakai Conjecture concerns a very natural question: can diferential operatorsdetect singularities on algebraic varieties? On a smooth complex variety, it is well known that theing of differential operators is generated by derivations. Nakai asked whether the converse holds: ifthe ring of differential operators is generated by derivations, is the variety smooth? We will firstintroduce the history and some important works about Nakai Coniecture. in our work, we prove theNakai Conjecture for isolated homogeneous hypersurface singularities.

Speaker Intro

Stephen Yau received his PhD degree from the State University of New York at Stony Brook in1976. He has served as a member of the Institute for Advanced Study at Princeton, an assistantprofessor at Harvard University under Benjamin Pierce, and later joined the University of linois atChicago, where he taught for over 30 years in the departments of mathematics, statistics, andcomputer science.Stephen Yau has made significant original contributions in international cutting-edge researchfields, including mathematics, applied mathematics and control theory, computer science, financialmathematics, and bio informatics. He solved some famous conjectures in complex geometry andsingularity theory, and was the first to successfully use Lie algebras to study hypersurfacesingularities in algebraic geometry, a algebra that is now known as Yau algebra among his peersHe 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 thefield of bio informatics, his work on the 2D representation of DNA and protein was published in theworld's top journal, "Nucleic Acids Research". Recently, he pioneered the natural vector method forrepresenting genomes and proteins. He has published over 200 academic papers, including topinternational mathematics journals such as PNAS, Annals of Mathematics, and InventionesMathematicae.