March Science and Technology Award, Professor Park Jin-hyung Who Solved the Secondary Variety Equation

Ministry of Science and ICT - Korea Research Foundation Joint Selection

[Asia Economy Reporter Kim Bong-su] Professor Jin-Hyung Park of the Department of Mathematics at Sogang University has been selected as the recipient of the March 'Scientist of the Month' award for solving the secant variety equation problem of algebraic curves, one of the greatest challenges in modern mathematics.

On the 3rd, the Ministry of Science and ICT and the National Research Foundation of Korea announced, "As the role of mathematics is emphasized as the foundation for the development of advanced technologies such as artificial intelligence and big data, Professor Park was highly praised for his contribution to the advancement of algebraic geometry and for elevating the status of the Korean mathematical community."

Geometry developed from ancient Egyptian land surveying to Euclidean geometry in ancient Greece. In the 17th century, based on Descartes' concept of coordinates, the interaction between geometry and algebra, expressing geometric objects as equations, began in earnest. Algebraic geometry is a field closely related to many core areas of modern mathematics, studying algebraic varieties, which are geometric objects defined by algebraic equations. In particular, the geometric properties and equations of secant varieties derived from algebraic varieties have been fundamental topics explored for over 100 years in algebraic geometry and have applications in statistics, computer science, and artificial intelligence.

Notably, March 14th is 'Mathematics Day (π-day),' and Professor Park's research achievements have attracted great attention as they provide a breakthrough for effectively improving tensor calculations of matrices necessary for machine learning, big data analysis, and solving optimization problems.

Through joint research with Professor Lawrence Ein of the University of Illinois and Professor Wenbo Niu of the University of Arkansas, Professor Park perfectly solved the challenging problems regarding the geometric properties of singularities of secant varieties and the algebraic properties of their equations. Specifically, by disproving a long-standing prejudice in the mathematical community and proving that the secant varieties of algebraic curves have normal singularities, it became possible to predict results about the singularities and equations of secant varieties of higher-dimensional algebraic varieties.

The research results of Professor Park and his colleagues were recognized as the most outstanding achievement on secant varieties and were published in Inventiones Mathematicae in November last year.

Professor Park stated, "This research is significant in that it developed a systematic research approach connecting the geometric properties of singularities of secant varieties of algebraic curves with the algebraic properties of their equations," adding, "It is expected to serve as a foundation for future follow-up studies on the singularities and equations of secant varieties of algebraic curves."