Profile

British Professor David Thouless won this year's Nobel Prize for contributions to the field of topology. Two other British physicists, Professor J. Michael Kosterlitz and Professor Duncan Haldane shared the award. Of course the physics is rather complicated, you don't win a Nobel prize for discovering something obvious, but put simply, David Thouless worked out a way of predicting how a material will behave using maths.In this programme, though, we'll focus on the man himself. Who is David Thouless and how did he spend his time when he wasn't thinking about equations? We'll hear about the treats he liked as a school boy during the war, about family holidays from his son, Michael Thouless, himself a Professor of Engineering and we'll also hear that things in the real world didn't often go as smoothly as planned...Audio from the Hubbard Theory Consortium 50th Anniversary Lecture used, with thanks.Producer Smita Patel & Researcher Phoebe Keane.

When Theresa May became Prime Minister she appointed Fiona Hill and Nick Timothy as her joint Chiefs of Staff. It's a role first imported from the US by Tony Blair, when he brought in Jonathan Powell to help oversee the day-to-day running of government. The position puts Timothy and Hill at the heart of decision-making inside Number 10. So who are they? And how much influence do they really have? Mark Coles reports.Producer: Ben Crighton.

Emma Walmsley will be one of just seven female bosses in the country's top 100 companies when she takes the helm of GSK next year. The pharmaceutical giant is worth £80bn, making it the most valuable company with a woman CEO. But how did Emma Walmsley get to where she is today? Mark Coles looks back over her school days and her rise up the corporate career ladder at L'Oreal. We hear from her father, retired vice admiral Sir Robert Walmsley, her school friend and her business associate Sir Martin Sorrell, CEO of advertising firm WPP. Who is Emma Walmsley and what impact will she have on one of Britain's biggest companies?

The new President of the Philippines, Rodrigo Duterte, is in the news this week because he's threatening to send home some of America's troops and "re-orientate" his country's foreign policy away from its traditional ally, America. And last week he was reported to have called President Obama a "son of a whore". Not surprisingly, perhaps, he has caught the attention of the world's media. But human rights organisations have been paying close attention to Mr Duterte for other reasons: he is alleged to have been complicit in the killing of drug dealers and criminals by vigilante ‘death squads’. Presenter: Edward Stourton Producer: Phoebe Keane and Micaela Papa

Elon Musk is the billionaire owner of SpaceX and Tesla Motors, and the co-founder of Paypal. He plans to colonise Mars. Last week that dream might have been scuppered as his SpaceX rocket exploded on the Launchpad in Cape Canaveral, Florida. This is the first time a rocket has exploded at launch since 1960. It was carrying a satellite Facebook wanted to use to provide internet access to Africa. While investigations continue into what caused last week's explosion, this week Mark Coles explores the life of the man who also wants to make the travel time from London to Manchester 18 minutes and to counter global warming. Producers: Charlotte Pritchard and Phoebe Keane.

Amber Rudd has risen rapidly through British politics, becoming Home Secretary only six years after being elected an MP in 2010. It's a rise unmatched by any other politician since World War Two. Becky Milligan profiles the woman who has made this leap and stepped into Theresa May's shoes. In an exclusive interview for Profile her sister, Melissa Dunford Wood talks candidly about their childhood, parents and friends, and how her sister was "on the floor" after the unexpected and painful divorce from her ex husband AA Gill.

Last October Seumas Milne, a Winchester- and Oxford-educated left-winger, was granted unpaid leave from his position at The Guardian to enter the world of political spin as executive director of strategy and communications in Jeremy Corbyn's Labour Party.The appointment wasn't without controversy. Milne has been labelled a Stalinist by David Cameron and caused division at The Guardian for chairing an event with President Putin. Jeremy Corbyn has chosen a hard-left thinker as his right-hand man. As the Labour Party hustings come to a close this week, Adam Fleming speaks to friends and colleagues to find out about the man who's at the heart of the Corbyn project.Producer: Smita Patel.

Mark Coles speaks to family, friends and colleagues of cyclist Laura Trott - the first British woman to win four Olympic golds - to find out how, after winning her first bike race at the age of eight, she has carried on winning ever since.Producer: Smita Patel.

Poet, painter and virtuoso pianist, Stephen Hough has been described as a polymath. He learned to play on a piano that cost £5 from a local antique shop and went on to become a virtuoso to astonish the world. Becky Milligan speaks to lifelong friends and some of the world's leading names in classical music to profile a man who plays like a dream.Producers Smita Patel & Ed Davey.

You may not have heard of Sonia Friedman, but she's one of the most important people in British theatre. She's produced many of the biggest stage hits of the past 15 years - including Jerusalem and The Book of Mormon - and is a multiple award winner. This week, Harry Potter and the Cursed Child opened in London. It was produced by Sonia Friedman. Her first job interview was with Laurence Olivier and Joan Plowright in their kitchen. She got the job. She's a consummate deal-maker and is able to persuade writers and performers from JK Rowling to Mark Rylance and Benedict Cumberbatch to work with her. Mark Coles talks to family, friends and colleagues to discover more about her life and career.Producers: Charlotte Prichard and Sarah Shebbeare.