Not long ago, they were calling each other names and raising fears of a nuclear war. Now, it is feasible they could together win the Nobel Peace Prize - if they can reach a deal. The mooted meeting between America’s Donald Trump and North Korea’s Kim Jong Un could go wrong in many ways. Mr Trump has already talked of walking out. But in a spirit of optimism, this week’s Inquiry hears from those who have brokered some of the world’s most unlikely pacts for advice on how to strike the deal of a lifetime. With Helena Merriman.

(Photo: President Trump, Credit: Zach Gibson/Getty Images; Photo: Kim Jong Un, Credit: Korea Summit Press Pool/Getty Images)

In late December 2017, one of the world’s leading neurobiologists died of pancreatic cancer. His name was Ben Barres. He was an extraordinary scientist, advancing our understanding of how the brain works, in particular how certain cells in the brain may contribute to degenerative brain diseases like Alzheimer’s and Parkinson’s.

He had also lived the last 20 years of his life as a transgender man. He used his unique perspective of having ‘lived in the shoes of a woman and…the shoes of a man’ to become an outspoken opponent of gender bias.

As the voice of the transgender community continues to grow in influence, what can wider society learn from people who’ve been in this rare position of living life as both a perceived man and woman? What does their experience tell us about the nature of gender bias? And does it help us fix it?

(Photo: People hold a giant transgender flag at a gay parade. Credit: Bulent Kilic/AFP/Getty Images)

Black infants in America are twice as likely to die in their first year as white infants. This stark disparity has long puzzled doctors and researchers. Why are so many African-American babies dying?

(Photo: A medical assistant measures the head of a newborn baby during a check-up in the USA. Credit: John Moore / Getty Images)

Syria, Salisbury, Malaysia Airport – all sites of nerve agent attacks carried out in the past couple of years. Yet hundreds of countries have supposedly destroyed their stockpiles of chemical weapons. It’s also illegal to produce and use them.

We look to four of the world’s most experienced chemists and researchers to tell us more about the nerve agents used in these recent attacks, how they are regulated and the ongoing problems of getting rid of them.

(Photo: Members of the emergency services in green biohazard encapsulated suits. Credit: Ben Stansall/AFP/Getty Images)

China’s ivory market is now closed for business. The country has long been one of the world's biggest consumers of ivory. But as of this year, buying and selling ivory in China is illegal. Carving factories, workshops and jewellers have all shut their doors. How did this happen? And will it be enough to save the African elephant?

(Photo: An African Elephant throws mud onto himself, Mpala Research Centre, Kenya. Credit: Simon Maina/Getty Images)

When Robert Mugabe was deposed last year, he had ruled Zimbabwe for nearly four decades. How do dictators and authoritarians stay in power? James Tilley, a professor of politics at Oxford University in the UK, finds out what's in the dictators' survival guide. How do they control ordinary people and stop revolts? How do they stop rivals from taking over? And why are elections often helpful to securing their rule?

Producer: Bob Howard.

(Photo: Zimbabwean President Robert Mugabe looks on during his inauguration and swearing-in ceremony on August 22, 2013 Credit: ALEXANDER JOE/AFP/Getty Images)

The tide of public opinion is turning on plastic.

The image of a whale with plastic stuck in its mouth on the BBC nature documentary Blue Planet 2 woke people up across the world to the reality of plastic pollution in our oceans. Experts think that by 2050, there could be more plastic than fish in the sea. Communities across the globe are saying that something must be done.

But does this change in public mood spell disaster for plastic? And if so, what would replace it? We go from Europe, to the US and Indonesia to examine the supply and demand of plastic.

Presenter: Michael Blastland

“Humans are the only species that willingly deprive themselves from sleep”. Ever since fire was discovered, we have traded off sleep time for other activities - from creating stone tools to partying. As our technology progressed, the list of things to do rather than sleep just got longer. But with sleep deprivation now a growing health problem, could we be reaching our limits? Or is tiredness part of our condition? In this week’s programme, an evolutionary biologist, a historian and a neuroscientist give us their take on whether we are now any more tired than our ancestors. We hear what makes human sleep unique and how it has evolved in surprising ways. And finally we hear from a woman with a dream – that we may never have to sleep again.

Presenter: James Fletcher

This programme was first broadcast in July 2017.

(Photo: A woman shows signs of tiredness as she counts ballot cards. Credit: Leon Neal/Getty Images)

From courtrooms and prisons to rehab centres and martial arts training. We look to Europe, Iraq, Central Asia and Saudi Arabia to investigate how they are dealing with Islamic State militants.

The defeat of Islamic State in Iraq and Syria has raised a new, global challenge. While Iraq is funnelling huge numbers of Islamic State suspects through its courts, thousands of foreign fighters are returning to their home countries. What is happening to former IS fighters?

(Photo: A man takes down a poster of the IS militant group's flag. Credit: Getty Images)

It is one of the largest, most profitable companies in the world, with billions of users, but more and more questions are being asked of Facebook. Accused of allowing the spread of fake news and hate speech, and of turning a blind eye to election meddling by Russia, Facebook is in the spotlight for the wrong reasons. Facebook’s founder and CEO, Mark Zuckerberg has committed himself to “fixing Facebook.”

With the help of experts in the field, in the US, India and Germany, we ask if Facebook really is in trouble.

Presenter: Helena Merriman

(Photo: Indian demonstrators protest against Facebook's Free Basics initiative in Bangalore on 2 January, 2016. Credit: Manjunath Kiran/Getty Images)