Division of Pure Mathematics

The division of pure mathematics is one of five departments making up the School of Mathematical Sciences of Fudan University. Led by a number of distinguished mathematicians, for instance, the CAS Members HU Hesheng, LI Ta-Tsien, HONG Jiaxing, CHEN Shuxing, the division grows to be a major participant in current developments in many major areas of mathematics. Currently, the division consists of approximately 40 members in the academic staff, of whom 27 are professors, with research interests in various areas of mathematics: differential geometry, mathematical physics, partial differential equations, functional analysis, algebra, algebraic geometry, function theory, harmonic analysis, dynamical system, topology, number theory, and etc. As a national key discipline, it has an international reputation as an outstanding center for mathematical education, scholarship and research. Scholars interested in mathematics are welcome to join us!

Research areas and academic staff
Head of division: ZHANG Yongqian (Professor)
Deputy head of division: YANG Ling (Professor), YAO Yijun (Professor)

Differential geometry
Differential geometry is such a discipline that enjoys a long history. With connections having been formed among analysis, algebra and other subdisciplines of mathematics, differential geometry is a vivid key discipline of the core of mathematics, which is also closely related to physics. This area examines issues in geometric variation such as harmonic map and minimal submanifold, the relationship between geometric invariants and topological invariants, the eigenvalue problems of the Laplace operator on manifolds, and how the above-mentioned issues are applied in physics.
       Academic staff (role):
       HU Hesheng (CAS member, professor, advisor)
       DONG Yuxin (Professor, advisor)
       DING Qing (Professor, advisor)
       FU Jixiang (Professor, advisor)
       JI Qingchun (Professor, advisor)
       YANG Ling (Professor, advisor)
       WANG Zhizhang (Professor)
       LIU Xusheng (lecturer, doctor)

Mathematical physics
By utilizing the modern differential geometry, partial differential equations, global analysis, and the representation of Lie groups, researchers in this area study the gauge field (Yang-Mills gauge field), the gravitational field, soliton theory, and non-linear sigma model. They also study the existence and nonexistence of the solution of the field equation, and find the solution of physical significance, establishing new powerful instruments so as to solve the problems in mathematical physics.
       Academic staff (role):
       HU Hesheng (CAS member, professor, advisor)
       ZHOU Zixiang (Professor, advisor)
       FAN Engui (Professor, advisor)
       XIE Naqing (Professor, advisor)
       QIN Zhenyun (Associate professor).
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Partial differential equations
As an important discipline in mathematics, partial differential equations enjoy a long history, closely related to analysis, geometry, algebra and other subdisciplines of mathematics, and widely applied in many areas of physics, mechanics, chemistry, biology and engineering technology. This area includes nonlinear evolution equations , mixed type equations, general theories of partial differential equations, mathematical physics, geometric analysis, etc.
       Academic staff (role):
       LI Ta-Tsien (CAS member, professor, advisor)
       CHEN Shuxing (CAS member, professor, advisor)
       HONG Jiaxing (CAS member, professor, advisor)
       LIU Xiangao (Professor, advisor)
       ZHANG Yongqian (Professor, advisor)
       HUA Bobo (Associate research fellow, advisor)
       HUANG Genggeng (Associate professor)

Functional analysis
Developed from 1930s, functional analysis is an indispensable part of disciplines of analysis, studying various problems of noncommutative mathematical objects in infinite dimensional spaces, which tends to be a fundamental and crucial aspect of mathematical research and application. The main research direction includes operator theory, operator algebras, noncommutative geometry and its application, etc.
       Academic staff (role):
       CHEN Xiaoman (Professor, advisor)
       GUO Kunyu (Professor, advisor)
       WANG Kai (Professor, advisor)
       YAO Yijun (Professor, advisor)
       HUANG Zhaobo (Associate professor)
       XU Shengzhi (Associate professor)

Algebra
Algebra is a vivid discipline with a long history, closely connected to almost all subdisciplines of mathematics. Researchers in this area mainly study the structure of noncommutative algebra and homology theory, especially the cohomology, noncommutative algebraic geometry, the Hopf algebras, and quantum group theory and its application, etc.
       Academic staff (role):
       WU Quanshui (Professor, advisor)
       ZHU Shenglin (Professor, advisor)

Algebraic geometry
It focuses on the general properties of algebraic variety, mainly the algebraic surfaces and the birational classification of algebraic varieties of higher dimension (especially the canonical classification of general algebraic varieties). It also covers the properties of moduli spaces of algebraic varieties of lower dimension, and properties of the transcendental method in complex geometry.
       Academic staff (role):
       CHEN Meng (Professor, advisor)
       Li Jun (Professor, advisor)
       XIE Qihong (Professor, advisor)
       WANG Qingxue (Associate professor)

Complex function theory
It mainly studies the complex dynamical system, the fractal geometry, quasiconformal mapping, the Teichmüller space, function theory of several complex variables, and deformation of complex structures, etc.
       Academic staff (role):
       QIU Weiyuan (Professor, advisor)
       JIN Lu (Professor, advisor)
       CHEN Boyong (Professor, advisor)
       WANG Jun (Associate professor)
       SU Weixu (Associate research fellow)

Dynamical system
This area focuses on qualitative properties, limit sets, periodic solutions and strange attractor of the nonlinear dynamical system, the dynamical behavior of the dynamical systems defined by ordinal differential equations and evolution partial differential equations which includes the KAM Theory, Arnold diffusion, Nekhoroshev estimation and Aubry-Mather set.
       Academic staff (role):
       YUAN Xiaoping (Professor, advisor)
       SHEN Weixiao (Professor, advisor)
       ZHANG Guohua (Professor, advisor)
       TIAN Xueting (Professor, advisor)
       LIANG Zhenguo (Associate professor)

Topology
Researchers in this area study the topological geometric properties and variational problems of the topological space (especially the differential manifolds) with the group action, the geometry and combination theory of the transformation group of the closed manifolds, and geometry and topology of regular graphs.
       Academic staff (role):
       LV Zhi (Professor, advisor)
       MA Jiming (Associate professor)

Number theory
Research interests in this area are modular forms theory and automorphic forms theory, especially the Jacobi form and the Siegel modular form. Modular forms and the analytic properties and arithmetic properties of L- functions are also involved.
       Academic staff (role):

Harmonic analysis
Modern harmonic analysis has a close connection with partial differential equations, geometric analysis, functional analysis, probability analysis and the other subdisciplines of mathematics. This area covers harmonic analysis on manifolds, including maximal functions, Riesz transform, multipliers, estimation for the heat kernel, gradient estimates for the heat semigroup, and the application of harmonic analysis in partial differential equations.
       Academic staff (role):
       LI Hongquan (professor, advisor)
       He Danqing (Associate Young-Fellowship)

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