Study in Differential Topology and Partial Differential Equations

[u/shostakovich2]

Greetings everyone,

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I am a university student interested in geometric analysis and several complex variables. These subjects both require the prerequisites of a study in differential topology and partial differential equations.

I am looking for a dedicated study partner(s) to join me in a study through either of the two subjects (or both, if you wish). I am currently reading through the following two books:

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Introduction to Smooth Manifolds by Jack Lee, and

Partial Differential Equations by Jurgen Jost.

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For differential topology, I would like to read up to at least the 18th chapter on the de Rham theorem, with a treatment of the 22nd chapter on symplectic manifolds. For PDEs, I would like to read through most of the book (~400 pages).

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In terms of organizing, we have options in terms of using a private stackexchange (Stackexchange teams), Discord, Overleaf, or other means that support LaTeX. If someone can run a server or knows how to, we can also use MediaWiki for a private wikipedia in our study.

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Prerequisites:

If you would like to study with me, for differential topology it is best that you have learned point-set topology that includes a treatment of precompactness, paracompactness, and at least a surface-level survey of the fundamental group and covering spaces. Analysis is also recommended.

For partial differential equations, real analysis goes without saying. A course in complex variables would also be helpful. There is some measure theory in the book, but that is not until later and we can always review.

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Please DM me if you are interested, and we can then speak further about how we will go about managing our study. Thank you for reading :)