Genghis Khan and his successors are reported to have forced millions of artisans/craftsmen as slaves back to Karakorum in Mongolia. How come the population there is largely homogeneous? Are there any residual effects of this forced migrations due to Mongol invasions.
Forced Migrations is a stretch, but there are a smattering of Mongol populations descended from the Mongol armies around Asia. The Hazara are beloved to have partial Mongol ancestry, with the Moghol language spoken in Herat until very recently. In China, there are the Khatso or Yunnan Mongols, the Dongxiang, the Bonan, among others, all believed to be partially descended from Yuan era troops. Since the Mongol army was itself multiethnic, Turkic groups such as the Tatars are also believed to be in part descended from Golden Horde era settlers and troops.
For present day Mongols, a recent genome analysis (https://academic.oup.com/gbe/article/6/12/3122/546344) showed 'found varying degrees of gene flows between Mongolians and populations living in Europe, South/Central Asia, and the Indian subcontinent. The analyses demonstrate that the genetic impacts of Mongolians likely resulted from the expansion of the Mongolian Empire in the 13th century.'