A blast from the (recent) past: the open problems from the Workshop on Data Summarization held in March 2018 in the University of Warwick have been posted online, and are available here.
Fast-forward to this summer: the recently concluded 3rd Workshop on Local Algorithms, which took place last month at ETH Zurich, featured an open problems session. The list of open problems can be found in this link, or here for a PDF version.