[{"_id":{"$oid":"628f739398580cae9c21b44f"},"place":"Amsterdam","events":[{"eventName":"Event one","eventText":"Event","eventDate":"010101","host":"Bob"},{"eventName":"E2","eventText":"e2","eventDate":"020202","host":"John"}]},{"_id":{"$oid":"628f739298580cae9c21b44f"},"place":"London","events":[{"eventName":"e3","eventText":"e3","eventDate":"010101","host":"Bob"}]}]

db.collection.aggregate([{"$match":{"events.host":"Bob"}},{"$project":{"e":{"$filter":{"input":"$events","as":"event","cond":{"$eq":["$$event.host","Bob"]}}}}}])