In any case, Alexander's toppling of the Achaemenid Empire, after his victories at the battles of the Granicus, Issus and Gaugamela, and his advance as far as modern-day Pakistan and Tajikistan, provided an important outlet for Greek culture, via the creation of colonies and trade routes along the way. While the Alexandrian empire did not survive its creator's death intact, the cultural implications of the spread of Hellenism across much of the Middle East and Asia were to prove long lived as Greek became the "lingua franca", a position it retained even in Roman times. Many Greeks settled in Hellenistic cities like Alexandria, Antioch and Seleucia. Two thousand years later, there are still communities in Pakistan and Afghanistan, like the Kalash, who claim to be descended from Greek settlers.