Sze Man Ngai

Group: Analysis and Geometry

Office: A15-203

Email: ngai@bimsa.cn

Research Field: Fractal Geometry

Education Experience

1984 - 1987 University of Hong Kong Mathematics/Physics
1988 - 1989 University of Pittsburgh Mathematics Master
1988 - 1995 University of Pittsburgh Mathematics Ph.D (Supervisor: Ka-Sing Lau)

Work Experience

1995 - 1995 Chinese University of Hong Kong Instructor
1996 - 1997 Chinese University of Hong Kong Postdoctoral Fellow
1998 - 1998 Cornell University Visiting Assistant Professor
1998 - 2000 Georgia Institute of Technology Visiting Assistant Professor
2000 - 2006 Georgia Southern University Assistant Professor
2006 - 2011 Georgia Southern University Associate Professor
2008 - 2009 Chinese University of Hong Kong Visiting Scholar
2016 - 2017 Harvard University Visiting Scholar
2011 - 2024 Hunan Normal University Adjunct Professor
2011 - 2024 Georgia Southern University, USA Professor

Publication

[1] Sze-Man Ngai and Wen-Quan Zhao, Lq-spectrum of a class of self-similar measures, Asian J. Math., 27(6), 867-892 (2023)
[2] Sze-Man Ngai and Wei Tang, Schrodinger equations defined by a class of self-similar measures, J. Fractal Geom., 10(2023), 3/4, 209-241
[3] Guotai Deng, Chuntai Liu, and Sze-Man Ngai, Self-affine tiles generated by a finite number of matrices, Discrete Comput. Geom., 70(2023), 602-644
[4] Yong Lin, Sze-Man Ngai, and Shing-Tung Yau, Green's function of a subgraph of a complete graph, Int. Math. Res. Not. IMRN, 2023(2023), 13, 11145-11171
[5] Sze-Man Ngai and Yangyang Xu, Separation conditions for iterated function systems with overlaps on Riemannian manifolds, J. Geom. Anal. , 33(2023), 262
[6] Sze-Man Ngai and Yangyang Xu, Existence of Lq-dimension and entropy dimension of self-conformal measures on Riemannian manifolds, Nonlinear Anal., 230(2023), 113226
[7] Sze-Man Ngai, Wei Tang, Anh Tran, and Shuai Yuan, Orthogonal polynomials de ned by self-similar measures with overlaps, Exp. Math, 31(2022), 3, 1026-1038
[8] Guotai Deng, Chuntai Liu, and Sze-Man Ngai, A class of self-affine tiles in Rd that are d-dimensional tame balls, Adv. Math., 410(2022), 108716
[9] Da-Wen Deng, Yulan Huang, and Sze-Man Ngai, Continuous maps that preserve Hausdor measure, J. Math. Anal. Appl. , 516(2022), 126485
[10] Wei Tang and Sze-Man Ngai, Heat equations defined by self-similar measures with overlaps, Fractals , 30(3), 2250073 (2022)
[11] Y. Lin, S.-M. Ngai, and S.-T. Yau, Heat kernels on forms defined on a subgraph of a complete graph, Math. Ann., 380, 1891-1931 (2021)
[12] D.-W. Deng and S.-M. Ngai, Estimates for sums and gaps of eigenvalues of Laplacians on measure spaces, Proc. Roy. Soc. Edinburgh Sect. A, 151, 842-861 (2021)
[13] S.-M. Ngai and Y. Xie, Spectral asymptotics of Laplacians associated with a class of higherdimensional graph-directed self-similar measures, Nonlinearity, 34, 5375{5398. (2021)
[14] Q. Gu, J. Hu and S.-M. Ngai, , Geometry of self-similar measures on intervals with overlaps and applications to sub-Gaussian heat kernel estimates, Commun. Pure Appl. Anal., 19, 641-676 (2020)
[15] S.-M. Ngai, Measures essentially of finite type and spectral asymptotics of fractal Laplacians, Fractals and Dynamics in Mathematics, Science, and the Arts: Theory and Applications. Analysis, Probability and Mathematical Physics on Fractals, 337-362 (2020)
[16] S.-M. Ngai and Y. Xie, Spectral asymptotics of one-dimensional graph-directed self-similar measures with overlaps, Ark. Mat., 58, 393{435. (2020)
[17] C.-Y. Chu and S.-M. Ngai, Dimensions in in nite iterated function systems consisting of bi-Lipschitz mappings, Dyn. Syst., 549-583 (2020)
[18] S.-M. Ngai, W. Tang, and Y. Xie, Wave propagation speed on fractals, J. Fourier Anal. Appl., 26(31) (2020)
[19] G. Deng, C. Liu, and S.-M. Ngai, Topological properties of a class of higher-dimensional self-affine tiles, Canad. Math. Bull., 62, 727--740 (2019)
[20] S.-M. Ngai and W. Tang, Eigenvalue asymptotics and Bohr's formula for fractal Schr"odinger operators, Pacific J. Math., 300, 83-119 (2019)
[21] S.-M. Ngai and Y. Xie, $L^q$-spectrum of self-similar measures with overlaps in the absence of second-order identities, J. Aust. Math. Soc., 106, 56-103 (2019)
[22] S.-M. Ngai, W. Tang, and Y. Xie, Spectral asymptotics of one-dimensional fractal Laplacians in the absence of second-order identities, Discrete Contin. Dyn. Syst., 38, 1849-1887 (2018)
[23] G. Deng, C. Liu, and S.-M. Ngai, Topological properties of a class of self-affine tiles in ${\mathbb R}^3$, Trans. Amer. Math. Soc., 370, 1321-1350 (2018)
[24] G. Deng and S.-M. Ngai, Differentiability of $L^q$-spectrum and multifractal decomposition by using infinite graph-directed IFSs, Adv. Math., 311, 190-237 (2017)
[25] S.-M. Ngai and J.-X. Tong, Infinite iterated function systems with overlaps, Ergodic Theory Dynam. Systems, 36, 890-907 (2016)
[26] G. Deng, C. Liu and S.-M. Ngai, Dimensions of the boundary of a graph-directed self-similar set with overlaps, Houston J. Math., 42, 179-210 (2016)
[27] J. Liu, S.-M. Ngai, and J. Tao, Connectedness of a class of two-dimensional self-affine tiles associated with triangular matrices, J. Math. Anal. Appl., 435, 1499-1513 (2016)
[28] J. F.-C. Chan, S.-M. Ngai, and A. Teplyaev, One-dimensional wave equations defined by fractal Laplacians, J. Anal. Math., 127, 219--246 (2015)
[29] D.-W. Deng and S.-M. Ngai, Eigenvalue estimates for Laplacians on measure spaces, J. Funct. Anal., 268, 2231-2260 (2015)
[30] D.-W. Deng and S.-M. Ngai, Fractal tiles and quasidisks, Math. Z., 279, 359-387 (2015)
[31] Q.-R. Deng and S.-M. Ngai, Dimensions of fractals generated by bi-Lipschitz maps, Abstr. Appl. Anal. (2014)
[32] K.-S. Lau and S.-M. Ngai, Boundary theory on the Hata tree, Nonlinear Anal., 95, 292-307 (2014)

Update Time: 2025-03-28 01:57:07