Programs
- Fundamental Algebra and Analysis I
- Fundamental Algebra and Analysis II
- Geometry and Topology
- Abstract Algebra I
- Abstract Algebra II
- Ordinary Differential Equations
- Measure Theory and Real Analysis
- Probability Theory
- Functions of One Complex Variable
- Functional Analysis
- Numerical Analysis
- Category Theory
- Number Theory
- Algebraic Topology
- Representation Theory
- Differential Geometry and Differential Manifolds
- Partial Differential Equations
- Stochastic Processes
- Mathematical Modeling
- Numerical Algebra and Optimization
- Numerical Simulation
- Regression and Generalized Linear Models
- Scheme Theory
- Sheaf Theory and Cohomology
- Riemannian Geometry
- Elliptic Curves
- Topics in Several Complex Variables
- Geometric Measure Theory
- Harmonic Analysis
- Analytic Theory of Biological Dynamics
Topics in Several Complex Variables
Prerequisites:
Real analysis, Complex analysis
Course description:
This course is designed for students interested in pursuing research in several complex variables or complex geometry. The teaching objectives are to equip students with the foundational language and fundamental methods in complex analysis of multi-variables, preparing them for advanced studies in several complex variables and complex geometry. Additionally, the course aims to cultivate students' innovative thinking and stimulate their interest in mathematics and mathematical research.
Learning objectives:
By the end of this semester-long course, students should achieve the following learning outcomes:
(1) Understand the basic concepts in several complex variables, such as pseudoconvexity, domain of holomorphy.
(2) Solve the Cauchy-Riemann equation under various conditions using L2 techniques.
(3) Understand the L2 division problem and the L2 extension problem and their applications.
(4) Study the singularity of the plurisubharmonic functions through Lelong numbers
(5) Read and understand foundational results and current research directions in several complex variables.
Detailed topics covered:
L2 estimates of Cauchy-Riemann equation and applications
References:
Lars Hormander, An introduction to complex analysis in several variables; Takeo Ohsawa, L² approaches in several complex variables: towards the Oka–Cartan theory with precise bounds.