User:Username6330

Hello
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
Here are some pages that I've worked on


 * Chern class
 * Discrete valuation ring
 * Stable curve
 * Deligne–Mumford stack
 * Regular sequence
 * Serre duality
 * Constructible sheaf
 * Primary decomposition
 * Hilbert series and Hilbert polynomial
 * Derived scheme
 * Borel–Moore homology
 * Atiyah–Hirzebruch spectral sequence
 * Deformation theory
 * Algebraic K-theory

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
There are several pages on wikipedia which need attention. This includes
 * Vanishing cycle (https://www.math.u-psud.fr/~illusie/Illusie-Grothendieck-nearby-cycles5.pdf)
 * Lefschetz pencil
 * Abelian variety
 * Semistable abelian variety
 * Serre duality
 * Derived functor
 * Sheaf cohomology
 * Spinor bundle
 * Clifford module bundle
 * Heat kernel
 * Dirac operator

Wish List
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.
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

 * Etale cohomology of number fields - http://www.numdam.org/article/ASENS_1973_4_6_4_521_0.pdf

Homotopy Theory

 * Sheaves and homotopy theory - http://math.mit.edu/~dspivak/files/cech.pdf

Constructible Sheaves/Hodge Theory

 * https://web.archive.org/web/20170921213130/https://www.ma.utexas.edu/users/rhughes/TopicsInD-modules.pdf

String Theory

 * D-Braines, Sheaves and Categories - http://www.ulb.ac.be/sciences/ptm/pmif/Rencontres/lectures_sheaves.pdf

Intersection Theory

 * GRR - https://www.math.leidenuniv.nl/scripties/MasterJavanpeykar.pdf
 * Hilbert Series + Chern Polynomials - http://www-personal.umich.edu/~takumim/HilbertandChernPolynomials.pdf
 * Steenrod operations and quadratic forms (contains nice overview of intersection theoretic machinery using homological approach) - http://www.mathematik.uni-muenchen.de/~haution/these.pdf