I know that's a weird question, but anyway :

I'm a research mathematician (well, officially still a student), doing mostly "abstract" algebra, geometry, number theory and other such "useless" things.

I would love to make myself useful in some way to Free Software. I'd like to contribute to some project in a way that would make use of some mathematics I know.

I know there's not much hope that someone has got work for me....
but just in case, here's what I'm relatively knowledgeable about.

Algebraic Geometry (Schemes, sheaves, curves, surfaces...)
Algebraic number theory,
Class Field theory
Elliptic Curves/Modular forms
Function fields, Drinfeld modules
Noncommutative Geometry (C*-algebras...)
Quantum Statistical Mechanics (mathematical point of view)
K-theory (both topological and C*-algebraic)
Differential geometry
Algebraic topology

And I should add that I'm not interested in writing another math library - there are just so many of them, and they are already quite good IMO. I'd like to apply my mathematics to something else that just mathematics... the problem being that my maths are theoretical/fundamental math, not traditional applied maths...

Don't hesitate to let me know if I can help for something.

Just an opinion: I think you could mostly help in some fields such as CAD/graphic applications (since you stated several types of Geometry among the math branches you've learnt). Maybe you can apply your knowledges even to gaming where some serious mathematics (with a high amount of geometry in some cases) is involved.
Whatever will it be, good luck!

"I would love to make myself useful in some way to Free Software. I'd like to contribute to some project in a way that would make use of some mathematics I know."

I have a degree in mathematics and have worked with computer software off and on for 40 years. The closest I ever came to using mathematical theory in computers was in performance analysis of an IBM operating system which I think is currently called MVS or perhaps OS 390.

An area where you can contribute is in developing a mathmatical model to analyze the kernel's performance. To be useful the model would have to have predicative value. In other words, people could run performance tests against the kernel under a half dozen sets of given conditions and then plug the results into your model to predict performance over a wide range of conditions.

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Steve Stites

Encryption projects, perhaps..?

thanks for your replies !

I had already considered computer graphics and cryptography, but it seems that these two fields have already been the subject of intense mathematical study... and I don't have any new idea to bring here.

For kernel performance analysis, that sounds very interesting, I will think about that. Thanks for the idea !