The main purpose is to gather, promote and produce material on research topics (mainly mathematical physics) which are as accessible and pedagogical as possible (see Criteria below) in an open access way.

In our researchers life, we encounter constantly concepts outside of our expertise for which we wish to understand the main ideas. Why does the concept exist? For what is it used? It is worth looking deeper into it? In this library, you should get approximate answers to these questions.

In addition, we try to give for every concept a very short overview, a picture to have in mind, a slogan to remember.

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The material we want to gather here should meet as many of the following criteria as possible:

• pleasant to read or watch
• conceptual, clear and concise (can be imprecise to gain clarity)
• use of visual items (figures, pictures, animations, …)
• addressed to researchers
• gives motivation, overview and applications of a concept
• uses heuristics, analogies and metaphors
• no technical details
• gives concrete examples
• gives sparse, but precise references
• open access

This wiki is at its very beginning. If your favorite pedagogical introduction to a topic is missing, please feel free to add it in the library! All you have to do is to create an account!

See the Howto to get a quick guide to use DokuWiki for Pharos Library, or the more general Dokuwiki entry. To edit a page, go to the page and click either on a button “Edit” (to edit a section) or on the pencil on the right hand side (to edit the whole page). To create a new page, write the name of the concept in the search field (in the top right corner), and click on the proposed link to create the page.

Ideally for a new concept, you add a document together with a short “slogan”, a short description, a picture or scheme, a joke, … If you don't have time, then feel free to put only the document. You can add comments later or others will do.

Here are examples of concepts:

• Soergel bimodules
• Punctual Hilbert scheme

And here are examples of entries in our Library:

• Nicolas Libedinsky: Gentle introduction to Soergel bimodules I: The basics, arXiv https://arxiv.org/abs/1702.00039
• Alexander Thomas, Punctual Hilbert Scheme of the Plane, https://www.youtube.com/watch?v=lBLHEn2Dvkw

If you want to get an overview over a concept, here are some general ideas how to find quickly information.

1. Historical papers: It might be a good idea to look at the first paper where the concept arises. There you should find the motivation for introducing the concept, often without abstract considerations. But it may lack of conceptual clarity and links to other areas.
2. Lecture notes: Find a course on the subject. Often the first paragraphs give an overview over the concept.
3. Papers “Introduction to…”: Often these are modern treatments of concepts in a conceptual unified way.

To find a specific item, some hints:

• Use Google Scholar, it often provides the pdf files if available
• To search inside a website, enter “site:www.website.com search term” into the search box of Google. For Example site:https://johncarlosbaez.wordpress.com/ dykin diagram

Some sources of pedagogical explanations:

• for mathematical physics: the blogs of John Baez, This Week's Finds in Mathematical Physics (old one) and Azimuth (new one)
• for mathematics: the book The Princeton Companion to Mathematics, edited by Timothy Gowers
• for physics: the Physics Travel Guide
• for mathematics: the blog of Terence Tao
• for mathematics: Snapshots in Mathematics

For questions, suggestions and remarks, feel free to write an email to contact at pharos-library.com.

The Pharos Library is supported by the Basic Research Community for Physics.