School profile, Shanghai Normal University.
Shanghai Normal University is a comprehensive university with the coordinated development of arts and crafts. It is good at arts and has the characteristics of normal education. The school has entered the ranks of universities supported by the comprehensive education reform department of Shanghai, and is a pilot unit for the construction of high-level local universities (disciplines) in Shanghai.
The school has a complete range of disciplines and fruitful teaching results. At present, there are 10 disciplines such as philosophy, economics, law, education, literature, history, science, engineering, management, agriculture and art, 9 first-class doctoral programs, 9 postdoctoral mobile stations, 32 first-class master programs, and 18 professional degree categories. The school has 1 national key disciplines; 1 1 Shanghai Key Discipline; 1 1 discipline entered the discipline of Gao Feng Plateau; Ministry of Education and Shanghai Undergraduate Major Comprehensive Reform Pilot Major1; Four characteristic specialty construction points in the institutions of higher learning of the Ministry of Education: three reform projects of the "Excellent Teacher Training Program" of the Ministry of Education: 1 National New Engineering Research and Practice Project; Eight pilot professional construction projects of applied undergraduate courses in Shanghai municipal universities; 18 Shanghai undergraduate education highland construction project. Five subjects entered 1% subjects before ESI. There are nearly 9000 graduate students in the school.
The school attaches great importance to international education and has extensive exchanges and cooperation with foreign countries. It has been listed in China Government Scholarship College for Foreign Students and Shanghai Foreign Student Reserve Base. The school has established exchanges and cooperation with nearly 400 universities and organizations in more than 40 countries and regions on six continents.
2, "Basic Mathematics" discipline, professional introduction (tutor, research direction and characteristics, academic status, research results, research projects, curriculum, employment, etc. ):
The mathematics discipline of Shanghai Normal University began to recruit postgraduates in the early 1980s from 1980, and was awarded the first-class doctoral degree in mathematics on 201/. There are 23 teachers majoring in basic mathematics, including 7 professors and 0 associate professors/kloc-0. They are engaged in academic research in more than ten research fields of mathematics, with strong overall research strength and dynamic research team. Some teachers enjoy a high academic reputation at home and abroad. In recent years, he has published more than 0/00 academic papers/KLOC in various SCI/SCIE magazines, and undertaken more than 30 projects such as National Natural Science Foundation, Doctoral Program Special Fund of Ministry of Education, Shanghai Science and Technology Commission and Education Commission. Basic mathematics majors recruit doctoral students in functional analysis, harmonic analysis and function approximation, algebra, rings and algebra, combinatorial mathematics and its application, and master students in functional analysis, harmonic analysis and function approximation, commutative algebra and algebraic geometry, Lie algebra and linear groups, general algebra, combinatorial mathematics, algebra and coding, partial differential equations, convex geometric analysis and geometric analysis. This major mainly studies analysis (real analysis, functional analysis, C*- algebra, operator algebra, harmonic analysis, function approximation theory, convex geometric analysis, etc. ), algebra (algebra foundation, algebra, Lie algebra and algebraic group, ring and algebra, commutative algebra, semigroup theory, algebra and coding, etc. ), differential equations ((linear) partial differential equations, nonlinear partial differential equations and so on. Graduates of this major should have a solid foundation in mathematics and be broad. After graduation, either pursue doctoral degrees and engage in research and teaching related to mathematics, or use mathematics and computers to solve practical problems in engineering, technology, economy, finance and other departments, so as to train qualified professionals for universities, secondary schools and colleges and related fields.
Brief introduction of research direction:
Functional analysis direction: This direction mainly studies the theory and application of Hilbert C*- modules, operators and generalized inverses of matrices. In recent ten years, we have mainly studied the polar decomposition of * * * yoke operator and its application, the Halmos decomposition of two projection operators and its application, the generalized Douglas range inclusion theorem and its application, the generalized parallel sum of * * * yoke operator, the representation and perturbation of the generalized inverse of operator and matrix, etc. The main results were published in SIAM J.Numer.Anal, Siam J. Matrix. Anal. Appl, J.Math.Anal.Appl, linear algebra Appl, linear multi-linear algebra Appl, Appl.Math.Comput presided over 3 projects of the National Natural Science Foundation, and several projects of Shanghai Science and Technology Commission and Education Commission.
Harmonic analysis and function approximation direction: The research fields involved in this direction include harmonic analysis, Dunkl theory, function approximation and Radon transform, with special emphasis on the intersection between these fields. For more than half a century, modern harmonic analysis based on real methods has formed a complete theoretical system, which has got rid of the strong dependence of classical harmonic analysis on complex methods and promoted the development of partial differential equations, probability theory and other fields. Dunkl theory is a new field to study analytical problems related to reflection symmetry and root system, involving many branches of mathematics. For example, the Calogero-Sutherland model describing quantum multibody systems is essentially a dunkel operator about symmetric groups; Function approximation and Radon transform are mathematical methods to study reconstruction problems, and they are also important topics in function theory and integral geometry respectively. This research direction has published systematic and influential research results in internationally renowned academic journals, and has presided over 5 national natural science foundation projects and 7 provincial and ministerial-level projects such as doctoral programs fund of the Ministry of Education.
Commutative algebra and algebraic geometric direction: In commutative algebra, we mainly study some problems related to homology, including complex of free contact, free decomposition of modules, local homology modules, consistency of Noether rings, etc. In algebraic geometry, we mainly study the classification theory of algebraic surfaces, the birational geometry of high-dimensional algebraic clusters, and the stability theory in algebraic geometry. The research results in this field have been published in internationally renowned academic journals such as trans. Amer. Math.SOC., J.Algebra, Int.Math.Res.Not. and Math. Z, undertaking key projects of NSFC and presiding over 4 NSFC projects.
Lie Algebra and Algebra Group Direction: In Lie Algebra, we mainly study the structure and representation of infinite-dimensional algebra, including Kac-Moody algebra and Virasoro algebra, and the corresponding vertex algebra and quantum algebra. These algebraic structures and representations have important applications in many branches of mathematics and physics. Relevant research results have been published in international important academic journals such as J. Algebra, J. Lie Theory, J. Geometry and Physics, J. Mathematics, etc. Physics, J.Phys.A, and Science China Mathematics. , and was supported by the National Natural Science Foundation of China, Shanghai Municipal Education Commission and Shanghai Natural Science Foundation. In the aspect of algebraic groups, we mainly study the structure and representation theory of real reflection groups (Coxeter groups), complex reflection groups and their Hecke algebras, as well as the combination problems related to the representation of reflection groups. Relevant research results are published in international journals such as Proc. Edinburgh Mathematics Football, Science China Mathematics. Austria J. mathmatics SOC。 And was supported by the National Natural Science Foundation of China.
Direction of general algebra: In the aspect of ring theory, we mainly study derivations, automorphisms and their related mappings, and functional identities on rings. In semigroup algebra, we mainly study the properties and structure of completely regular semigroups, discuss the interaction between different semilattice classes, and study the subclasses of completely regular semigroups by using congruences and idempotents. As a generalization of completely regular semigroups in the scope of regular semigroups, the structure and properties of GV- semigroups are also one of the main research contents in this direction. Relevant research results have been published in Israel J.Math, Algebra Communication, Linear Algebra and Its Applications and other important international academic journals.
Combinatorial mathematics and its application: this direction mainly studies combinatorics, word combination, graph theory and the application of combinatorics in life sciences on finite sets and finite posets. He has published more than 80 articles in various SCI/SCI magazines, participated in many key projects of the National Natural Science Foundation, and presided over the completion of 2 general projects, many base projects and many provincial and ministerial projects of the National Natural Science Foundation. In recent years, he has also studied the application of combinatorial mathematics in computational biology, and published more than 30 papers in genomics, bioinformatics and PLOS computational biology.
Algebra and coding direction: coding originated from studying the stability and reliability of binary sequence transmission in symmetric channels, and later developed into coding over general finite fields and finite rings, which are widely used in computers and communications. Because of the profound application of tools such as algebraic thinking method and combinatorial technology, algebraic coding and algorithm are important research directions of coding theory. Cryptography studies the protection methods and technologies of data security, which protects data information from being stolen, forged, tampered with, destroyed and denied in the process of generation, storage, processing, transmission and display, and ensures the confidentiality, authenticity, integrity, availability and non-repudiation of information. This major mainly studies the properties and construction of cryptographic functions in symmetric cryptography, and the properties and construction of linear codes over finite fields. At present, more than 0 SCI papers 10 have been published, and academic monographs 1 have been published, among which the main achievements have been published in important international magazines in this field, such as IEEE Trans Inf Theory, Fine Fields Applications, SCI China Math, Cryptography, Communications, etc.
Direction of partial differential equations: mainly study nonlinear elliptic equations, reaction-diffusion equations and equations, and some nonlocal diffusion equations, with emphasis on some practical models in ecology and biomathematics that are of international concern at present; In this paper, we study the weak solutions of classical solutions of quasilinear hyperbolic equations and equations, nonlinear wave equations, and the regularity singularity analysis of solutions of Euler equations and Naville-Stokes equations. The main results were published in J.Diff. Equality. J. math Anal. Application, mathematics. Methamphetamine. Applied science. And J. Math in Asia. Discrete and continuous dynamic systems. mathmatics Quart. Chin. Ann. mathmatics B and other important international magazines in this field. He presided over a number of provincial and municipal scientific research projects and won and participated in the second prize of provincial and municipal scientific research achievements.
Convex geometric analysis: Geometric analysis mainly studies geometric structures and invariants on convex sets in Euclidean space, represented by isoperimetric inequality, Brunn-Minkowski inequality, Minkowski problem and Hadwiger assignment characterization. It is an active branch of modern geometric analysis, which intersects with functional analysis, probability statistics, information theory and partial differential equations. The achievements in this direction have been published in Journal of Functional Analysis and Transactions of the American Mathematical Society. He has successively presided over the Youth Project of the National Natural Science Foundation of China and the Sailing Plan for Young Scientific and Technological Talents in Shanghai, and won the Oriental Young Scholars in Shanghai universities.
Geometric analysis: We mainly study quasilinear, completely nonlinear elliptic and parabolic partial differential equations on differential manifolds, mainly involving mean curvature equation, Monge-Ampere equation and k-Hessian equation. The research focuses on the existence and regularity of classical solutions of Dirichlet boundary value, Neumann boundary value and oblique Wechat business boundary value conditions, curvature flow problem and completely nonlinear k-Yamabe problem in * * geometry. The main results are published in Adv.Math, Pacific J.Math, Internat. Mathematics magazine, mathematics handbook. Contemporary mathematics and other important international journals in this field. The scientific research projects under study include the National Natural Science Foundation Youth Project.
Tutor for graduate students majoring in basic mathematics:
Functional analysis: Professor Qingxiang Xu.
Harmonic Analysis and Function Approximation: Professor Li
Commutative Algebra and Algebraic Geometry: Professor Zhou and Associate Professor Sun Hao.
Lie Algebra and Algebra Array: Associate Professor Pei Yufeng and Associate Professor Wang Li.
General Algebra: Professor Wang Yu, Associate Professor.
Combinatorial Mathematics and Its Application: Professor Wang Jun.
Algebra and Coding: Associate Professor Peng Jie.
Professor Xu and Associate Professor Dai.
Convex Geometry Analysis: Associate Professor Ma Dan
Geometric analysis: Associate Professor Xu Jinju
Is the postgraduate entrance examination policy unclear? Is Shen Shuo confused with the same academic level? Is it difficult to choose a college major? Click on official website below, and a professional teacher will answer your questions. 2 1 1/985 postgraduate master/doctor open network application name: /yjs2/