Conversation so far:
Where did the Ashkenazi Jews migrate to?
By the 11th century Jewish settlers, moving from southern European and Middle Eastern centers, appear to have begun to settle in the north, especially along the Rhine
Was there any reason for Ashkenazi Jews moving from southern European and Middle Eastern centers to settle in the north, especially along the Rhine?
often in response to new economic opportunities and at the invitation of local Christian rulers
Did the Ashkenazi Jews stay in the nort, especially along the Rhine, or migrate more?
Expulsions from England (1290), France (1394), and parts of Germany (15th century), gradually pushed Ashkenazi Jewry eastward, to Poland (10th century), Lithuania (10th century), and Russia (12th century).

Question: When did they move there?
Self-contained rewrite: When did the Ashkenazi Jews move to Poland, Lithuania, and Russia?