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MAT 535: Nonlinear Wave Equations
0.00 - 4.00 Credits
Princeton University
This will be a seminar on topics related to nonlinear wave equations, general relativity, etc. The seminar will consist of two parts. At the beginning, introductory lectures on wave equations and general relativity will be given. It is aimed to give the participants, especially the new-comers, a familiarity with the basic ideas and techniques of the fields. Then in the second part of the seminar, participants will be asked to give talks on topics of their choice.
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MAT 535 - Nonlinear Wave Equations
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MAT 537: Topics in Analysis - Linear and Non-Linear Functional Analysis
0.00 - 4.00 Credits
Princeton University
The course will cover basic topics in linear and nonlinear functional analysis, including theory of self-adjoint operators, Leray-Schauder theory, Lyapunov-Schmidt reduction, general implicit function theorem, and applications to nonlinear equations of mathematical physics.
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MAT 537 - Topics in Analysis - Linear and Non-Linear Functional Analysis
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MAT 539: Topics in Harmonic Analysis
0.00 - 4.00 Credits
Princeton University
The class will focus on applications of harmonic analysis methods to the study of certain nonlinear evolution equations. The work in this area started in the mid 80's and led to partial or complete solutions of most subcritical evolution equations. This is still a very active research area, mostly in the case of critical or supercritical models. The goal of the class is to explain the main techniques developed in this area, and applications of these techniques to relevant examples. A different topic will be covered every semester.
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MAT 539 - Topics in Harmonic Analysis
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MAT 549: Differential Geometry
0.00 - 4.00 Credits
Princeton University
In this course, I will discuss my program with J. Song etc. on the Kahler-Ricci flow. I will start with some basics on Kahler geometry and the Kahler-Ricci flow. A sharp local existence theorem will be presented. Next, I will explain how the flow forms a finite-time singularity and how to extend the flow across such a singularity. Finally, I will give a more detailed discussion on the Kahler-Ricci flow on complex surfaces and its asymptotic limits. Some related problems will be also discussed.
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MAT 549 - Differential Geometry
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MAT 554: Algebraic Geometry
0.00 - 4.00 Credits
Princeton University
TBA
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MAT 554 - Algebraic Geometry
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MAT 555: Analytical Methods in Algebraic Geometry
0.00 - 4.00 Credits
Princeton University
TBA
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MAT 555 - Analytical Methods in Algebraic Geometry
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MAT 558: Topics in Geometry - CR Geometry
0.00 - 4.00 Credits
Princeton University
TBA
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MAT 558 - Topics in Geometry - CR Geometry
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MAT 563: Dynamical Systems
0.00 - 4.00 Credits
Princeton University
TBA
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MAT 563 - Dynamical Systems
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MAT 565: Algebraic Methods in Topology
0.00 - 4.00 Credits
Princeton University
The development of algebraic topological approaches to problems in topology, utilizing ordinary and extraordinary cohomology theories (such as K-theory) and applied to geometric problems (such as classification problems for manifolds and surgery theory) is the focus of this course. The course content varies from year to year.
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MAT 565 - Algebraic Methods in Topology
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MAT 569: Gauge Theory & Low Dimensional Topology
0.00 - 4.00 Credits
Princeton University
TBA
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MAT 569 - Gauge Theory & Low Dimensional Topology
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