How do we post our publications there?
You should make a PR to this repo:
Will any scientific paper do?
According to the publications page:
The following is a list of publications about the Julia language, its standard library, Julia packages, and technical computing applications using code written in Julia.
Maybe someone with better inside knowledge can help you more than I can. I have put one of my own papers on the page, even though I am not a package author. In the paper, we described some numerical techniques, which we implemented in Julia. We provided the code as supplemental material and cited the Julia paper, the DiffEq paper and the JuMP paper. I think that if you just make a PR with your publications and briefly describe what you did, then someone will be able to let you know if your publications can be put on the page.