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Research in Global Differential Geometry and Geometric Analysis

The group not only pays attention to the fundamental and important problems in the field of Differential Geometry, but also cares about the physical phenomena which closely relate to the development of mathematics, inculding the global differential geometry properties, the topology structure of submanifolds, the methods of geometry and analysis to study some physical phenomena, such as the relativity and quantum field theory.There are 8 doctors in the group, including 3 professors and 3 associate professors. Prof. Chuanxi wu, as the academic leader of the group, a national expert, one of the first and second class candidates of national million talents project and national excellent overseas study scholars. He has won the Hubei youth prize for science & technology and taken, nurtured by some old international famous mathematicians such as Shiing-Shen Chern and Quanzhi Xiong. Moreover he has established a wide academic links with domestic and foreign mathematicians.The group deeply studied the spectral theory, curvature flows, ideal immersion and conformation of minimizing submanifolds, and obtained a series important results, such as the generalization of the mean curvature flow thoery, developing the method to study the curvature flow of high order homogeneous curvature functor in hyperbolic space, Cheng-type eigenvalue comparisons, heat kernel comparisons. These results were published in J. Math. Pures Appl., Calc. Var. PDEs, J. Differ. Equations, J. Geom. Anal., Math.Z., J. Geom. Phys., Isr. J. Math., Z. Angew Math.Phys., Sci. China Math., and other important international academic journals.Furthermore, the group has successively obtained over more than 20 national natural science funds of China or provincial research funds, has won a second class prize of natural science in Hubei province, and has published over 60 papers or book, of which more than 30 articles indexed by SCI.

Research in Algebra and Graph Theory

The research team of Algebra and Graph Theory has a long-standing academic tradition and has distinctive features in teaching and research. There are three professors and two associate professors working on this field. They can carry out substantive exchanges and collaborations with each other. Professor Liu Heguo, an academic leader, is an excellent expert in middle-aged and young group theory in China. He has been supported by the National Natural Science Foundation of China for 6 times, won the Third Prize for Scientific and Technological Progress of the State Education Commission (Cooperation), and won the Youth Science and Technology Award of Hubei Province. In 2007 and 2008, he was invited to give 45-minute talk at the 10th Congress of the Chinese Mathematical Society and to give 60-minute invited lecture at the 11th National Algebra Academic Conference, respectively. In 2009, he was invited to give lectures on group and its representation at the 14th National Postgraduate Summer School. Lennox-Robinson cited his 12 papers in the monographThe Theory of Infinite Soluble Groups. Characterizing Wells mapping explicitly in group extension, which is a troublesome issue since 1971, the group theorist Professor Derek John Scott Robinson has highly praised this work for several times; given the structure of several classes of fusion systems. The computational problem of the Hochschild cohomology group of cross-section algebras over arbitrary domains was completely solved. Professor Liu Huiqing, a graph theory expert, is engaged in the research of graph theory and combinatorial optimization. She proved the conjecture proposed by Li, Satio and Schelp in J. Graph Theory. A sufficient condition for fault-tolerant Hamiltonian connectivity of a special network was obtained and three types of optimal matching preclusion sets of this network were also characterized. The matching property of K_{1,7}-free 3-vertex-critical graphs was completely characterized. This results solved a conjecture on 3-vertex-critical graphs, which is proposed by Ananchuen et al. (2005) on Networks. These conclusions provide a theoretical basis for the reliability study of interconnection networks. Since 2006, this direction has been supported by more than 10 National Natural Science Foundation projects and provincial or ministerial level research projects. It has won one Hubei Provincial Natural Science Second Prize and Hubei Provincial Natural Science Third Prize, more than 100 papers or monographs were published, of which more than 40 were included in SCI.

Research in Fractal geometry and its application

The team has 3 professors, 2 associate professors. Professor Wen Shengyou as theacademic leader has high popularity in the domestic research on fractal geometry. He hosted on two national natural science foundation projects. The research team has achieved creative results in the study of fractal dimensions and the geometry of doubling measures. They have solved several important cross problems of doubling measures and fractal geometry. Especially, the result on double measures has the international leading position in the field of doubling measures. They gave the sufficient and necessary conditions of thick and thin sets about doubling measures in Euclidean space. They dealed with a series of problems of double measures in the Whitney correction sets, self-similar sets and self-affine sets. Since 2006, the team hosted on 5 national natural science foundation projects, published more than 30 papers, of which more than 20 were included by SCI. One graduate student won a silver medal of Qiu Chengtong for new world mathematics master's thesis.

Research in Pattern Recognition and Information Processing

This group consists of three professors and three associate professors. The group leader, Prof. Luoqing Li, is interested in the development of novel theoretical results and algorithms in the fields of harmonic analysis, approximation theory, and statistical learning theory. He has implemented 5 projects from the National Natural Science Foundation of China (NSFC) and several projects from the Natural Science Foundation of Hubei Province and Doctoral Program Foundation of Education Ministry. Prof. Li is now the Managing Editor of an SCI journal “International Journal of Wavelets, Multiresolution and Information Processing”. The group focuses on the design of novel machine learning and information processing algorithms, the theoretical analysis of these algorithms, and their applications in different fields, such as signal decomposition, image recognition and classification, and big data analysis, etc. In detail, the group has made significant contributions on the following topics: the construction of multi-dimensional wavelets, signal decomposition and Hilbert-Huang transform, machine learning theory on non-iid data, Markov subsampling for big data, atomic representation theory, information theoretical learning, and hyperspectral image classification, etc. The group has won one Third Prize award of Science and Technology of Hubei Province for the contribution on multi-dimensional wavelets construction and application, and has published more than 80 peer-reviewed papers on famous journals, such as IEEE TPAMI, IEEE TSP, IEEE TIP, IEEE TNNLS, IEEE TC, IEEE TGRS, Neural Computation, Neural Networks, Pattern Recognition, and has funded by more than 20 projects from NSFC and from Hubei Province or Ministry.