Research in Differential Geometry

In summary, the speaker is looking for information on leading researchers in differential geometry, specifically in Symplectic geometry, Kaehler geometry, Algebraic topology, and Geometric topology. They are seeking advice on how to find this information, such as asking a math advisor and researching recent math journals and the arxiv. This will help them identify schools with faculty who specialize in their interests.
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I am currently looking at grad schools, and I am wondering if anyone knew who are the leading researchers in differential geometry. I know that question is a little vague considering how diverse differential geometry is, but I was hoping that something could direct me in the right direction. Right now I am pretty interested in Symplectic geometry and Kaehler geometry. I also have some interest in Algebraic topology and Geometric topology.
 
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In addition to PF, you could ask your math advisor and research the most recent math journals and the arxiv for who's publishing on these geometries. From there you'll be able to see what schools have faculty that specialize in your interests.
 

FAQ: Research in Differential Geometry

What is differential geometry?

Differential geometry is a branch of mathematics that studies the properties of curves, surfaces, and higher-dimensional objects using techniques from calculus and linear algebra. It is a fundamental tool in many areas of physics and engineering, and has applications in fields such as computer graphics, robotics, and image processing.

What is the importance of research in differential geometry?

Research in differential geometry is crucial for understanding the geometric properties of objects and their relationship to other mathematical concepts. It also has important applications in areas such as Einstein's theory of general relativity, which uses differential geometry to describe the curvature of space-time.

What are some current areas of research in differential geometry?

Some current areas of research in differential geometry include minimal surfaces, geometric flows, geometric analysis, and symplectic geometry. These topics have applications in fields such as computer graphics, materials science, and mathematical physics.

What are some tools and techniques used in research in differential geometry?

Researchers in differential geometry use a variety of tools and techniques, including differential equations, variational methods, and geometric analysis. They also use computer simulations and numerical methods to study complex geometric objects.

What are some potential future developments in differential geometry research?

Some potential future developments in differential geometry research include the study of higher-dimensional objects and their relationships to other branches of mathematics such as algebraic geometry and topology. There is also ongoing research in the application of differential geometry to fields such as machine learning and data science.

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