The Turkish president, Recep Tayyip Erdoğan, may receive a warm welcome from Donald Trump when he arrives in Washington on Wednesday, but his reception elsewhere is likely to be extremely frosty.

US-Turkish relations are perhaps at their lowest in the last 40 years, reaching a new crisis point after Ankara’s decision to invade Kurdish-held parts of Syria last month. Just this week, a new crisis has erupted after Turkey tried to deport a US citizen believed to be a member of Islamic State to Greece, leaving him in a legal and physical no man’s land between the two countries.

It is also widely feared the trip could once again be marked by violence. Erdoğan’s previous state visit in 2017 went down in infamy after phone footage captured the president looking on calmly as members of his security detail attacked unarmed protesters outside the Turkish ambassador’s residence, putting 11 people in hospital.

Despite recent pointed US moves against Turkey – including criminal charges against one of Turkey’s biggest banks for its part in a scheme to evade sanctions against Iran, and Congress’s vote in favour of a resolution recognising the Armenian genocide – the rapport between the countries’ two leaders has endured.

Indeed, the strength of Erdoğan and Trump’s personal relationship is regarded by many as the only reason relations have not yet completely collapsed. Instinctively, Trump is closer to Erdoğan on Syria than to much of his administration. The Turkish president will seek to persuade Trump to go with his gut and ignore the advice of his own officials.

Ankara has described this week’s meetings as “critical” for setting the shape of future ties with the US, and Turkish policymakers appear willing to bet on Trump being the only decision-maker in Washington who really matters.

A White House official said that Trump was determined to take the long view on Turkish relations and will be looking for areas of common ground.

“The alliance has seen both our countries through very dark times. We are not going to throw it away lightly if there is a way forward,” one senior administration official said.

Here’s what’s at stake:

Syria

One of the Trump administration’s main goals this week is to get Turkey to agree to a permanent ceasefire in Syria. The 9 October offensive triggered bipartisan outrage in the US over the attack on the Kurdish-led Syrian Democratic Forces (SDF), the US’s ground partner in the five-year-long fight to defeat Isis.

Erdoğan is seeking to persuade Trump to finally sever US ties with the SDF and leave north-eastern Syria to Turkey and Russia. He thought he had won the argument in the infamous 6 October phone call when the US president appeared to give the green light for the Turkish incursion. Since then, the Pentagon and state department have pushed back, convincing Trump to leave a residual force in eastern Syria, with the ostensible mission of “securing the oil”, but which is also intended to maintain the SDF partnership.

“There’s no intention for our cooperation to end,” a senior administration official said in advance of the meeting.

The Turkish president will seek to drive a wedge between the president and his own officials on Syria. He has done it before but it has become evident that Trump has little support in his own party for his position. Congress last month passed a sanctions package to punish Turkey over its Syria operation while key members of the Senate, including Trump ally Lindsey Graham, have vowed to advance it if Ankara encroaches further into Kurdish-held territory.

Human rights

The human rights abuses being committed by Turkish-backed militias in north-eastern Syria are a big issue for the administration. They are bringing congressional sanctions closer, angering evangelical Christians and driving a wedge between the US and its Kurdish allies.

Senior administration officials have said the issue will be raised with Erdoğan. Ankara has blamed the Syrian militias for the abuses, but one senior US official said on the eve of the presidential visit: “As far we’re concerned, our interlocutor on these things is Turkey because Turkey has been supporting these people, and Turkey took the initiative to cross the border.”

Russia, jets and missile defence systems

This summer, Ankara pushed ahead with the first deliveries of the Russian-made S-400 missile defence system, an unprecedented move by a Nato ally.

Turkey says it was forced to buy the sophisticated Russian equipment in 2017 after the US refused to supply the alternative Patriot missile defence system.

The US subsequently kicked Turkish pilots out of the F-35 fighter jet training programme over worries that if Turkey integrates the S-400 into its defences, sensitive data about the F-35, a new generation multi-role stealth fighter, could be accessed by Moscow.

“This is one of those very tough problems that the president will be trying to address head on,” a senior US administration official said on Tuesday.

Despite the threat of sanctions, which could significantly weaken Turkey’s already fragile economy, Ankara – which is establishing ever closer ties with Russia – has so far refused to bow to the pressure from Washington, calling it a matter of national sovereignty.

No sanctions have materalised yet but last week White House national security adviser Robert O’Brien reiterated that the threat was real. “If Turkey doesn’t get rid of the S-400, I mean, there will likely be sanctions … Turkey will feel the impact of those sanctions,” he told CBS News.

The Halkbank scandal

Halkbank, one of Turkey’s biggest state-owned banks, was finally charged last month with violating US sanctions against Iran over the transfer of approximately $20bn in gold and funding through a complex web of shell companies and sham transactions that involved high-ranking Turkish officials, discovered in 2013.

The indictment was met with deep anger across Turkey, and helped strain relations between the Nato allies to their current breaking point. Erdoğan labelled the charges “an unlawful, ugly step” designed to punish Turkey over its recent Syria operation.

Fetullah Gülen and Turkish detainees

Turkey has long been frustrated by the US refusal to extradite the cleric Fetullah Gülen, whom Ankara alleges is responsible for a failed 2016 coup attempt against Erdoğan but has not produced sufficient evidence to convince US courts.

While Washington has largely stayed quiet in the face of increasingly authoritarian measures enacted in Turkey cracking down on political opposition and freedom of speech, it has dug its heels in over the detention and prosecution of Turkish US consular employees who are accused of spying and links to Gülen.

Sanctions threats

Congress and the Senate have been keen to distance themselves from the White House’s policy towards Turkey, although sanctions slapped on Turkish ministries and senior government officials in response to Ankara’s Syria offensive were widely viewed as not as harsh as expected and quickly lifted after Erdoğan agreed to a pause in fighting after meeting with Pence and Pompeo.

However, if Turkey refuses to step away from Russia’s S-400s more punitive measures are possible. The memory of crippling US sanctions and increased tariffs on Turkish steel and aluminium in 2018 related to the detention of US pastor Andrew Brunson which sent the Turkish lira into freefall is still fresh.