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  • 姓名:饶辉
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    数理逻辑与数学基础

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个人简介


Name:RAO Hui
Sex:Male
Date and Place of Birth: September 26, 1969 Hubei
Nationality: Chinese
Address: Mathematics Department, Tsinghua University, Beijing 100084, China
Email: hrao@math.tsinghua.edu.cn
Present Position: Associate professor of Tsinghua University.

EDUCATION
1985-1989: B.S. (Probability Theory)
Sichuan University, Chengdu, China
1989-1992: M.S. (Fractal Geometry)
Wuhan University, Wuhan, China
1992-1995: Ph.D. (Fractal Geometry)
Wuhan University

ACADEMIC EXPERIENCES
1995.11-1997.07: Postdoc of Nanjing University, Nanjing, China.
1997.11-1998.06: Posdoc of the Chinese University of Hong Kong, Hong Kong, China.
1998.07-2001.02: Associated Professor of Wuhan University.
2001.02-2003.02: Postdoc of Japan Science Promotion Society.
2003.03-2003.09: Visitor of Laboratory of Informatics, Robotics and Microelectronics in Montpellier, France.
2004.02-2004.08: Visitor of Greifswald University, Germany.
2004.08- : Associated Professor of Tsinghua University.

RESEARCH INTERESTS
Dimensions and measure. He started his research by working on dimensions and measures of fractal sets, particularly on self-similar sets and self-similar measures with overlapping structures. Under a assumption of the so called weak separation condition, using self-similar tilings as auxiliary systems, They work out a rather general method to derive the graph-directed structures of self-affine sets with overlaps; many applications are found, for example, to study the smoothness of the density of a self-similar measure.
Self-similar tilings. Since 1998 he has been interested in tiling theory. He mainly study two kinds of self-similar tilings.
The first is the self-affine tiling, which is generated by an expanding matrix and a digits set. They describe the structure of the translation sets and characterize the IFS's which generates tilings (i.e., satisfy open set condition).
The second is tilings by atomic surface of Pisot unit substitution. Atomic surfaces are also called Rauzy fractals. They use atomic surfaces to construct self-similar tilings and Markov partitions. He is interested in the applications of tiling theory in number theory, for example, the arithmetic properties of beta-expansions. The relation between the combinatorial properties of substitutions, the dynamical properties and tiling properties of the atomic surface is an interesting object.
Words and complexity. He is interested in the complexities of words, especially words with low complexities. The theory of atomic surfaces is used to study the properties of Sturmian sequence. I also work on pattern complexity, a new complexity introduced by T. Kamae.

TEACHINGS
Undergraduate Course:
1. Advanced calculus
1993.09-1994.01, Huazhong University of Science and
Technology.
2005.02-2005.07, Tsinghua University.
2. Linear algebra
1994.02-1994.07, Huazhong University of Science and
Technology.
3. The continued fractions
1998.02-1998.04, The chinese Univeristy if Hong Kong.
4. Fractal geometry
1998.09-1999.01, Wuhan University.
5. Mathematical analysis
2000.01-2000.07, Wuhan University.
6. Complex analysis
2004.09-2005.01, Tsinghua University.
Graduate Courses:
6. Tiling and algebra
1998.09-1999.01, Wuhan University.
7. Fourier analysis
2000.02-2000.07, Wuhan University.

Personal web page: http://faculty.math.tsinghua.edu.cn/~hrao/

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