This month’s Science and Technology Award has been awarded to Professor Lee Sang-hyuk of the Department of Mathematical Sciences at Seoul National University for March. The 'Science and Technology Award of the Month' honors a researcher each month who has contributed to the advancement of science and technology through outstanding research and development achievements, presenting them with a Minister's award and a prize of 10 million won.
Professor Lee identified for the first time in the world the boundedness of extreme functions related to space curves, one of the important challenges in the field of harmonic analysis, which do not diverge to infinity and have limits between certain values. A space curve is a concept defined only in three-dimensional space or higher, in contrast to a planar curve.
Extreme functions are a central concept in classical analysis and harmonic analysis that enable quantitative measurement of the maximum values of a given physical quantity. This concept is applied in various fields, including signal processing, quantum mechanics, and neuroscience.
Since the 1970s, active research has been conducted in harmonic analysis to clarify the boundedness of extreme functions on surfaces and curves; however, the extreme functions of curves have been more complex to analyze, making them less accessible. Even after Professor Bourgain, a Fields Medalist, proved the boundedness of extreme functions for planar curves, the case of space curves remained unresolved.
Professor Lee proposed a new methodology to prove the boundedness of extreme functions on space curves by developing inductive methods and a multilinear approach. He identified that a necessary and sufficient condition for the extreme function to be bounded for curves in three-dimensional space with non-zero curvature and torsion is that the Lebesgue space has an integral index greater than 3. Lebesgue space refers to the space of functions classified based on their integrability.
Professor Lee's discovery has been evaluated as opening significant possibilities for application in the fields of mathematics and science. The research results were published in the May 2022 issue of Inventiones Mathematicae, one of the influential international journals in the field of mathematics.
Professor Lee noted, "Artistic passion for mathematics itself is paramount," and emphasized that one must pursue what one is genuinely drawn to and interested in. To create innovative research, one must find what they truly wish to explore.