Hello

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and welcome to my wiki page! Here I will discuss plans for where I want to see wikipedia (specifically the maths pages) go in the future. My core belief about mathematics is that it should be absolutely democratized. By this, I mean anyone should be able to look up a topic, read the gist of what it is about, get a sense of examples, and be guided through the literature. Unfortunately, the mathematics community has largely failed on this front and I think it is somewhat deliberate. For example, consider this blog post https://web.archive.org/web/20170929060614/https://alexandercoward.com/writing/2017/4/17/blowing-the-whistle-on-the-uc-berkeley-mathematics-department

Even Grothendieck admitted later on in his life that the lack of examples and guiding intuition in mathematics is oppressive (although I cannot find the page where he said this, I think it was one hosted by Ronnie Brown).

The moral of the story is that I want to see more mathematics openly explained on this site which includes a plethora of examples.

Pages I Have Worked On

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Here are some pages that I've worked on

If you see todo lists, or examples needed sections on the talk pages for a math wikipage there is a good chance that I put it up there. These notes are both there to remind myself of things I want to put on wikipedia while giving an open invitation to others for improve wikipedia in a directed manner.

Pages Needing Help

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There are several pages on wikipedia which need attention. This includes

Wish List

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I have a wish list of topics which I would like to see discussed on this site including

  • equivariant cohomology with applications to computing the cohomology of orbifolds/DM-stacks
  • motivic spectral sequences
  • derived stacks
  • spectral schemes
  • chromatic homotopy theory (including the motivic version)
  • brown peterson homology
  • moduli of curves
  • computations with characteristic classes and GRR
  • mixed hodge modules/mixed hodge structures
  • more perverse sheaves
  • resolutions of singularities and using them to compute intersection cohomology
  • computations with adams operations both on topological k-theory and algebraic k-theory
  • rational homotopy theory

Papers, Notes, Etc.

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This is a section I will keep for organizing notes in different topics. Hopefully it will help guide others to learning material and improving wikipedia

Etale Cohomology

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Homotopy Theory

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Constructible Sheaves/Hodge Theory

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String Theory

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Intersection Theory

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