Song Shao
songshao@ustc.edu.cn
Education
2001-2004 Ph.D. in Math, USTC
1999-2001 Master's Degree in Math, USTC
1995-1999 Bachelor's Degree in Math, USTC
Experience
2010-Present Professor, USTC
2006-2010 Associate Professor, USTC
2001-2006 Lecturer, USTC
Overview of Academic Research
Prof. Shao’s research interest is topological dynamics and ergodic theory. Together with his collaborators, they have made a series of achievements in the problems of multiple ergodic averages in dynamical systems and related issues. His main academic achievements in recent years include: establishing the structural theorem for minimal systems involving nilpotent factors; systematically developing the characteristic factor theory of topological dynamical systems and applying it to combinatorial number theory; and studying the pointwise convergence problem of multiple ergodic averages, proving the pointwise multiple ergodic theorem for disjoint systems and weakly mixing PID systems, among others. The relevant results have been published in journals such as J. Eur. Math. Soc., Mem. Amer. Math. Soc., and Adv. Math.
Research Directions/Fields:
Topological dynamics
Ergodic theory
Major Honors and Awards
2018 Second Prize of the National Natural Science Award
Representative Publications
1. E. Glasner, W. Huang, S. Shao, B. Weiss and X.D. Ye , Topological characteristic factors and nilsystems, J. Eur. Math. Soc., 27 (2025), no. 1, 279-331.
2.W. Huang, S. Shao and X.D. Ye, Parallels Between Topological Dynamics and Ergodic Theory, Ergodic theory, 389–426, Encycl. Complex. Syst. Sci., Springer, New York, (2023).
3.Y. Cao and S. Shao, Almost proximal extensions of minimal flows, Ergodic Theory Dynam. Systems, 43 (2023), no. 12, 4041–4073.
4.W. Huang, Z. Lian, S. Shao and X.D. Ye, Minimal systems with finitely many ergodic measures，J. Funct. Anal., Volume 280, Issue 12, (2021), 109000，42 pp
5.W. Huang, S. Shao and X.D. Ye, Pointwise convergence of multiple ergodic averages and strictly ergodic models, J. Anal. Math. 139 (2019), no. 1, 265–305.