User:David Schwein

Welcome to my user page! As a Wikipedia editor, I focus on pages about mathematics, my primary area of technical knowledge. Wikipedia has helped me learn about many mathematical subjects and I hope to pay back this generous gift by sharing my own knowledge, especially the subjects I study as a working mathematician.

Why should mathematicians edit Wikipedia?

Fellow mathematicians: Wikipedia

1. Reaches more people than you can. Consistently ranked among the top-ten most-visited websites, Wikipedia is the first place (or second, after a search engine) where we go to look up a new idea. This makes the potential impact of your expository work here much greater than any blog, technical article, textbook, or lecture. (Though such work can feed into Wikipedia articles.)
2. Complements other communication methods. We have many ways to communicate mathematical knowledge, among them research articles, textooks, scientific journals, lectures, and personal discussions. Wikipedia is none of these things. I hope to convince you that nonetheless there is a place for Wikipedia in mathematical discourse.
3. Organizes the literature. The mathematical literature is massive and has a long shelf-life. Sites like MathSciNet and zbMATH are an invaluable tool for searching this literature, but they do little to organize it systematically. As a tertiary source whose scope is the sum of human knowledge, Wikipedia aims for systematic organization of the research literature.
4. Encourages collaboration. Mathematicians understand the benefits of lumping our efforts together, from a humble pair of coauthors to a Bourbaki group or Stacks project. Wikipedia fits solidly in this collaborative tradition.
5. Aggregates information. This point is subtly different from the previous one. Although excellent summary and overview articles do exist, it is rare for all the important facts about a topic to be collected in one place. Wikipedia can be such a place, though not at a technical level.
6. Allows edits. Knowledge evolves over time. Published mathematical literature is static, a trait that aids in record keeping but not in tracking this evolution of knowledge. Wikipedia is much more flexible and can change with the times.
7. Needs your help. Many mathematics articles, especially on topics beyond the undergraduate curriculum, are shallow or nonexistent. Only those of us with technical knowledge can write them.

Articles

Here is a list of articles I hope to create or polish.

Reductive groups

• Levi subgroup (currently redirects to Levi decomposition)
• quasi-split group
• relative root system
• list of irreducible Tits indices
• Chevalley involution
• Table of nilpotent orbits

p-adic groups and their representations

• p-adic group (currently redirects to p-adic number)
• idempotented algebra
• locally profinite group
• Moy-Prasad filtration
• Bernstein decomposition
• Langlands classification (currently only covers the real case)
• supercuspidal representation
• affine root system
• Steinberg representation

Langlands program

• local Langlands correspondence for GL(2)
• Aubert duality

$e^{i\pi \ }$This user is a mathematician.

This user thinks you can learn a lot by editing an Encyclopedia.