Projects per year
Personal profile
About
— Biography from the 2024 Spring Commencement program —
Dr. Ngai earned his BS in Mathematics and Physics (1987) from the University of Hong Kong. He then earned his MA (1989) and Ph.D. (1995), both in Mathematics, from the University of Pittsburgh. After successful postdoctoral and visiting appointments at institutions such as the Chinese University of Hong Kong, Cornell University, and Georgia Technical Institute, Dr. Ngai began his career at Georgia Southern University in 2000. His field of specialization is fractal geometry, and he has published more than 60 journal articles in this and related fields. Dr. Ngai’s most notable publications are his joint paper with Ka-Sing Lau entitled Multifractal Measures and a Weak Separation Condition (1999) and his joint paper with Yang Wang entitled Hausdorff Dimension of Self-similar Sets with Overlaps (2001). In the paper with Lau, the authors introduced a weaker separation condition on iterated function systems, called the weak separation property, which is strictly weaker than the well-known open set condition. By assuming the weak separation property, the authors proved that the multifractal formalism holds. In his joint work with Yang Wang, the authors introduced a finite type condition and described a scheme for computing the exact Hausdorff dimension of a self-similar set. This method not only extends previous ones, but also includes some new classes of self-similar sets. According to the American Mathematical Society’s MathSciNet Search, these two papers are among the top 10 most cited papers in subject areas 28A80 and 28A78, respectively. Dr. Ngai is also a quality teacher and has effectively supported graduate students throughout his career. Further, he is a strong contributor to the discipline, serving on editorial boards and organizing meetings and conferences, including an American Mathematical Society Southeastern Sectional Meeting held at Georgia Southern in Fall of 2024. In recognition of his noteworthy scholarship, teaching, and service to the discipline and the university, Dr. Ngai is deserving of the title of Professor Emeritus of Mathematics.*
Expertise related to UN Sustainable Development Goals
In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This person’s work contributes towards the following SDG(s):
Related links & documents
Education/Academic qualification
Ph.D. in Mathematics, University of Pittsburgh
… → 1995
M.A. in Mathematics, University of Pittsburgh
… → 1989
B.S. in Mathematics/Physics, The University of Hong Kong
… → 1987
Disciplines
- Other Mathematics
Research Interests
- Fractal Partial Differential Equations
- Fractal Sets
- Fractal Measures
- Self-affine Tiles
Fingerprint
- 1 Similar Profiles
Collaborations and top research areas from the last five years
Projects/Grants
- 2 Finished
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Induced Dirichlet forms on Self-similar sets
Feng, D.-J. D. (PI), Lau, K.-S. (CoPI) & Ngai, S.-M. (CoPI)
01/1/16 → 12/31/19
Project: Research
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Boundary Theory and Analysis on Fractals
Lau, K.-S. (PI) & Ngai, S.-M. (CoPI)
01/1/10 → 12/31/13
Project: Research
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Differential equations defined by Kreĭn–Feller operators on Riemannian manifolds
Ngai, S. M. & Ouyang, L., Mar 2026, In: Chaos, Solitons and Fractals. 204, 117773.Research output: Contribution to journal › Article › peer-review
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Iterated Relation Systems on Riemannian Manifolds
Liu, J., Ngai, S. M. & Ouyang, L., Sep 29 2025, In: Fractal and Fractional. 9, 10, 637.Research output: Contribution to journal › Article › peer-review
Open Access -
Nodal sets and continuity of eigenfunctions of Krein-Feller operators
Ngai, S. M., Zhang, M. K. & Zhao, W. Q., Feb 5 2025, In: Electronic Journal of Differential Equations. 2025, 12, p. 1-25 25 p.Research output: Contribution to journal › Article › peer-review
Open Access -
Existence of Lq-dimension and entropy dimension of self-conformal measures on Riemannian manifolds
Ngai, S. M. & Xu, Y., Feb 24 2023, In: Nonlinear Analysis, Theory, Methods and Applications. 230, 113226.Research output: Contribution to journal › Article › peer-review
1 Scopus citations -
Lq-SPECTRUM OF A CLASS OF SELF-SIMILAR MEASURES∗
Ngai, S. M. & Zhao, W. Q., Jan 1 2023, In: Asian Journal of Mathematics. 27, 6, p. 867-892 26 p.Research output: Contribution to journal › Article › peer-review