Currently, some parts of the UI state are synchronized with the url via query parameters (like currently open panels etc.). Similarly, it would be great if the criteria the user inputs when performing a search could be synchronized with the query.

This way, by sharing the current url with another user, that second user would have the search criteria pre-filled and would see the same results as the first user.

This could apply to the /search page as well as to the filter boxes while browsing.