A rundown of stories from Tuesday 1 October.
Insight, analysis and expert debate as key policy makers are challenged on the latest news stories.
In today's programme
With Sarah Montague and John Humphrys.
ShungaHere are some of the images of Japanese erotic art known as Shunga we discussed at the end of the programme:
PapersHere's a round-up of this morning's newspaper headlines:
Today's running order
Subject to change
Business with Simon Jack including news that the US government has begun a partial shutdown after the Republican-led House of Representatives refused to approve a budget for next year. Plus the most significant rule changes to directors pay to happen in a decade have been introduced later.
The United States government has been partially shut down - unable to pay hundreds of thousands of employees - after Congress failed to approve a federal budget by last night's deadline. The BBC's North America correspondent Jonny Dymond reports.
Business news with Simon Jack.
Doctors in the US and Japan say a woman who went through a very early menopause has had a baby - with the help of a pioneering medical technique. The BBC's James Gallagher reports.
A new law that takes effect today should make it harder for anyone to sell stolen metal. The Today programme's Tom Bateman reports from a scrap yard in south London, and Paul Crowther, deputy chief constable of British Transport Police, outlines how the law will operate.
If the Conservatives are to get an outright majority at the next election they need to win in places like Bolton West, a constituency that Labour only just held onto in the last general election. The Today programme's Sarah Montague hears how the Conservatives hoping to win it next time round.
The paper review.
Dr Singh, an ex-Cern physicist and number one bestselling author of Fermat's Last Theorem, will be lifting the lid on the hidden maths behind the most successful show in TV history: The Simpsons. Simon Singh, science writer and author of The Simpsons and their Mathematical Secrets, and Sian Mainwaring, head of maths at Pontllanfraith Comprehensive, discuss the mathematics behind the cartoon.
Thought for the Day with Mona Siddiqui, professor of Islamic studies, New College at the University of Edinburgh.
The Mayor of London Boris Johnson will taking to the stage today here at the conservative party conference in Manchester. The BBC's political editor Nick Robinson gives his analysis.
The US government has begun a partial shutdown after the Republican-led House of Representatives refused to approve a budget for next year. Bill Huizenga, US representative for Michigan's 2nd congressional district, reflects on the gravity of the situation.
The Prime Minister David Cameron speaks to the Today programme on the penultimate day of the Conservative Party's annual conference in Manchester.
The US government has begun a partial shutdown after the Republican-led House of Representatives refused to approve a budget for next year. The BBC's business editor Robert Peston gives his analysis of the partial closure.
Four MPs from Greece's far-right Golden Dawn party are to appear in court. Achilleas Topas, a news reporter for the SKAI TV network in Athens, and Nantia Valavani, a Greek MP from the Left-wing Syriza party, discuss how deep the group's influence extends into the Greek state institutions.
Business news with Simon Jack on news that the rules will change surrounding the amount of business rates that is payable for new build commercial premises that are still empty, from Tuesday.
Pope Francis convenes his shadow cabinet this week for a first round of talks on reforming the Catholic Church. Professor Hans Kung, honorary president of the Foundation for a Global Ethic and author of Can the Catholic Church be Saved? outlines the importance of the shake-up.
The British Museum is daring to exhibit the most comprehensive exhibition of Japanese Shunga, explicit and erotic paintings, prints and books used historically for education and entertainment. The Today programme's Nicola Stanbridge reports form the exhibition.
Are the Conservative messages this week resonating as much as Labour's cost of living themes? Matthew d'Ancona, political columnist with the Sunday Telegraph, and Isabel Oakeshott, political editor of the Sunday Times, examine the Conservative's strength of message at the conference.