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Ankara and Washington agreed on a roadmap in June amid Turkish demands for the withdrawal of the US-backed Kurdish militia that freed Manbij from the Islamic State group in 2016.
They are now reportedly fighting to take the last few villages Islamic State holds along the Euphrates River in Syria, close to the border with Iraq, and has detained more foreign fighters.
The Fields medal recognizes the outstanding mathematical achievements of candidates who were under 40 years old at the start of the year.
Alexanda Kotey and El Shafee Elsheikh, from west London, are believed to be two terror suspects out of a foursome that had joined the terrorist network after being radicalised in the UK.
Kurdish fighters from the Syrian Democratic Forces, a Kurdish-Arab alliance backed by the US-led coalition, are also stationed at the base.
Turkish warplanes have often bombed PKK hideouts in the mountainous northern Iraq while the security forces have sporadically launched cross-border incursions in pursuit of rebel fighters.
Assad also said that a confrontation between Russia and US forces over Syria was narrowly avoided.
Polling stations were being moved from villages where the party has a strong backing to nearby villages with more support for President Tayyip Erdogan's AK Party, they alleged.
The Peoples' Democratic Party (HDP) had agreed Demirtas as its candidate and his campaign would be launched in simultaneous rallies in Istanbul and the majority Kurdish city of Diyarbakir.
The conflict has left more than 350,000 people dead, according to the Britain-based Syrian Observatory for Human Rights.
Turkey's state-run news agency said the United States is setting up two military bases and has increased its presence in the Manbij region of northern Syria.
The PKK has been waging an insurgency in the southeast since 1984 and is proscribed as a terror organisation by Ankara and its Western allies.
French President Emmanuel Macron on Thursday said he hoped "a dialogue" could be established between the two sides with help from Paris and the international community.
The French leader reaffirmed the priority of this battle against "the terrorist threat" and assured the SDF of France's support, in particular in stabilising the security zone in northeast Syria.
Turkey considers the YPG "terrorists" allied with the outlawed Kurdistan Workers' Party (PKK) which has waged a three-decade insurgency inside Turkey.