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| Mr. Yu-Chia Li (Class of 1971) |
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- Between 1979 and 1985, conducted pioneering research in calculus on infinite-dimensional spaces and path integrals, introducing methods involving Fourier–Wiener transforms and studying the existence, uniqueness, and regularity of solutions to higher-order infinite-variable differential equations—making important contributions to the mathematical theory of infinite-dimensional spaces.
- From 1985 to 1998, reconstructed the theory of white noise analysis (Hida Calculus), proposing a formulation of white noise distinct from Hida’s original definition and expanding the theory’s potential applications in quantum probability, quantum field theory, and stochastic analysis.
- Proved that Hida test functionals in infinite-dimensional spaces possess analytic modifications, establishing foundational results that significantly advanced research in Hida Calculus.
- Extended several classical mathematical theorems to infinite-dimensional spaces, including generalizations of the Riesz Representation Theorem, the Weierstrass Approximation Theorem, and the Heisenberg Uncertainty Principle—demonstrating exceptional theoretical innovation.
- Since 1999, collaborated with Professor Shin-Hong Shih on Non-Gaussian white noise analysis, continuing to broaden the theoretical boundaries of the field and exhibiting sustained passion for mathematical research.
- Served in key academic administration roles, including Vice President of the first NCKU Mathematics Alumni Association and Chair of the Department of Mathematics for both the 5th and 7th terms, contributing to departmental development and academic engagement.。
- Demonstrated deep commitment to academic mentorship and heritage; encouraged by Professor Lin Yi-Hsi, he returned to teach at his alma mater and maintained close connections with senior scholars while cultivating new generations of mathematicians through teaching and research.
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