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My name is Sean Raleigh. I am a mathematician with specific interests in the fields of symplectic and contact topology and geometry, and more generally, geometric and low-dimensional topology. I am also capable in topics of music (especially classical music and music theory) and Mormonism.
I'm pretty busy working on my Ph.D. dissertation, teaching part-time, and being a dad, so I haven't done much major editing yet. I try to stay active in the Wikipedia:WikiProject Mathematics community and I try to make small fixes whenever I come across them.
Feel free to visit my homepage: VectorPosse.com
[edit] Pages to work on (someday):
- Algebraic link. A fellow editor asked me to take a look at this page, and I intend to help out when I can. There's not too much to say here, but I'm sure we can find something to expand this article at least a little.
- Clutching construction. Most of the problems with this page have been fixed, but an example might be good to add.
- Contact geometry. Needs section on tight vs. overtwisted, among other things.
- Contact topology. This is different from Contact geometry and so it could use an article. (Probably, the tight/overtwisted stuff would go here and not in Contact geometry.)
- Ends of a space. A stub that needs expansion.
- Deformation retract. I can fix this one up pretty easily. Add some examples, add discussion on absolute neighborhood retracts, add a reference or two (Hatcher's book does a good job on this stuff).
- Heegaard diagram. Maybe I'll finally learn how to create images and upload them.
- Floer homology. This page is a great summary, but each type of homology could use to have its own fleshed-out article. This article would then be more clearly an intuitive idea as to why all these theories are modeled on the same basic idea.
- Legendrian knot. This page is only the tiniest of stubs at the moment. A proper treatment will also spawn the creation/expansion of even more pages (like Thurston-Bennequin number, for example).
- Maslov index. This could use its own page. (Currently it redirects to a section in Lagrangian Grassmannian.) Perhaps Maslov class is better. Well, I'm not sure. One needs to redirect to the other. And then Conley-Zehnder index could have a page as well (albeit a smaller one).
- Nassi. A last name that needs a bit of disambiguation.
- Surgery theory. This poor article is stuck half-done. (Quite literally, in fact. There is an incomplete sentence in the middle of it.)
- Symplectic filling. If referred to in Contact geometry—or maybe Contact topology (can be linked from the yet-unborn section on tight vs. overtwisted)—maybe the "Orphaned articles" tag can be removed.
- Symplectic geometry. Currently redirects to Symplectic topology, but this should be its own article with a completely different focus from Symplectic topology.
- Symplectic topology. This needs to be a major, comprehensive article, along with Symplectic geometry.
- Symplectization. Then redirect Symplectification to it.
- Transverse knot. Needs a treatment like the one I propose for Legendrian knot (spawning Self-linking number, for example).
- Well-behaved. Kind of an odd, only-sporadically-edited article. But it does describe an incredibly important idea in mathematics. Beyond the good stuff that is there already, which deals more with the "intuitive" idea of how mathematicians use the term, the article could use some category theory to explain it more precisely.
[edit] Useful Links:
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Pages I've started:
Pages I've substantially edited:
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