Russian and Syrian government officials have declared their intent to extend a "regime of calm" over some of the country's most embattled hotspots. Kerry is pushing for a truce to halt the violence over Aleppo, which last week saw a deadly airstrike on a civilian hospital by regime forces.

"We're getting closer to a place of understanding, but we have some work to do, and that's why we're here," Kerry told reporters ahead of a meeting with Saudi Arabia's foreign minister.

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Yet there is one key constituency in Syria that has so far been excluded from the Geneva process.

The Syrian Kurds, led on the battlefield most prominently by a militia known as the People's Protection Units, or YPG, are not represented at the talks. This is despite the fact that the YPG and its political parent, the Democratic Union Party (PYD), have de facto control over a broad sweep of territory in the north of the country and have been on the front lines against the ravages of the Islamic State.

The areas "liberated" by YPG forces and their allies have been loosely grouped into a region known by the Kurds as Rojava. In March, senior PYD officials signaled their intent to make Rojava into its own federal region within an already fracturing political landscape. The declaration was rejected by Damascus and received coolly by the United States, which has to awkwardly balance its interests in fighting the Islamic State with mollifying an ally in Turkey that cannot stomach a Kurdish breakaway state on the other side of its border.

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Others, though, believe that rather than a stumbling block, the advances of the Syrian Kurds ought to present the basis of a solution. Selahattin Demirtas, the leader of the main pro-Kurdish political party in Turkey, argued as such during a visit to the United States last week.

"For the sake of stability, it is important that [the Americans] do accept the reality of Rojava. It is an oasis within a morass of instability," Demirtas told WorldViews at a hotel in Washington last Thursday. "Only by taking it as your starting point can you get a solution and stability in Syria."

Demirtas, a charismatic politician who heads the Peoples' Democratic Party (HDP), one of the main opposition parties in Turkey's parliament, believes that a PYD-led autonomous region would embody the politics needed to fix the rest of war-torn Syria.

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"They are building a pluralist democracy over there," he said. "They are preventing the partition of Syria and they're preventing a new dictatorship from emerging. It's also a blow to the ideology of ISIS, because they believe in a secular system." ISIS is another name for the Islamic State.

This position is anathema to Turkey's ruling government and its president, Recep Tayyip Erdogan. During a visit to Washington at the end of March, Erdogan urged the West to see the violence of Kurdish separatist groups in Turkey in the same light as the terrorism of the Islamic State. Pro-Ankara propaganda posters have gone up around the American capital in recent weeks, saying the outlawed Kurdistan Workers' Party, PKK, was no different from the YPG or even Islamist extremists.

That is a view not shared by Washington, which has provided logistical and military support to the YPG in its battles against the Islamic State.

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"YPG is not a designated foreign terrorist organization," said State Department spokesman John Kirby when questioned at a news briefing last week. "PKK is. Nothing has changed about that."

A slow-moving peace process between Ankara and the PKK collapsed last year. The resumption of hostilities has led to curfews in major towns in southeast Turkey, the heartland of the country's minority Kurdish population, and to hundreds of casualties. Splinter groups of the PKK have claimed responsibility for a number of deadly terror attacks in Ankara.

The violence has been a disaster for Demirtas and his party, which sees itself caught between the strong Turkish nationalism of the state and the excesses of its erstwhile brothers in the mountains.

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"We are not the legal arm of the PKK, we are an entirely independent political party. But there is certainly a lot of overlap between the people who vote for us and the people who support the PKK," Demirtas said. He described the HDP, which combines a strain of Kurdish nationalism with broader leftist, pluralist politics, as an "alternative to violence" in the country.

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"The Kurds are a reality, and in every country in the Middle East, in Iraq, Turkey, Syria, they are on the front lines for the struggle of democracy," Demirtas said. But he argued that Erdogan, instead of seeing Kurdish aspirations as an opportunity, viewed them as a threat.

"There's a fundamental ideological conflict between the Kurds and Erdogan, who has a Turkish Islamist ideology," Demirtas said. "He wants Muslim Kurds under his hegemony. But Kurds won't accept that."

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In parliamentary elections in November, many conservative religious Kurds did choose to vote for Erdogan's Justice and Development Party, rather than the HDP. Intra-Kurdish rivalries between various factions shape the ethnic group's political status quo across borders in Turkey, Syria and Iraq.

Currently, Turkish authorities have initiated a process to lift the legal immunity guaranteed to a number of HDP members in parliament, including Demirtas. The politicians are accused of inciting violence against the state and being members of the outlawed PKK.

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It's a move that Demirtas rejects. In a written statement circulated last week, he decried "the totalitarian turn that the Turkish political system has recently taken, wherein anybody critical of Erdogan [and his allies] is labeled a 'terrorist' or 'supporter of terrorism'" and warned that the prosecution of opposition parliamentarians "will render Kurds and other marginalized peoples of Turkey even more vulnerable to grave forms of state violence and repression."

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In Washington, Demirtas said U.S. officials need "to play a much more encouraging role" not only to help establish better relations between Ankara and the Syrian Kurds, but also to help push for peace within Turkey.

"Turkey is sliding toward instability step-by-step and not enough is being done to stop that," Demirtas said.