KAIST

< Professor Mikyoung Lim from KAIST Department of Mathematical Sciences >

Professor Mikyoung Lim from KAIST Department of Mathematical Sciences gave a plenary talk on "Research on Inverse Problems based on Geometric Function Theory" at AIP 2025 (12th Applied Inverse Problems Conference). AIP is one of the leading international conferences in applied mathematics, organized biennially by the Inverse Problems International Association (IPIA). This year's conference was held from July 28 to August 1 in Rio de Janeiro, Brazil, and consisted of plenary talks, over 40 mini-symposia, and poster sessions. The IPIA began in 2007 and was re-established in 2022 as a non-profit international academic organization officially registered in Germany. At that time, Professor Lim served as an executive committee member for the re-establishment.

During the lecture, Professor Lim's research team introduced a new geometric solution and its applications to boundary value problems for electric/elastic equations, which they have been working on for the past 10 years. In particular, they presented a method for reconstructing partial differential equation boundary value problems into matrix equations and applying them to inverse problems using geometric function theory, a classical theory of complex analysis. A representative achievement was the formalization of the relationship between conformal mappings for simply connected domains in a plane and the measured values of solutions to equations of inhomogeneous conductors into a closed-form expression.

This research led to the plenary talk, as it was recognized for pioneering a new methodology for inverse problem research by connecting geometric function theory and layer potential theory.