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