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Kemi Badenoch is kicking off Conservative party conference with a little bounce in her step and her personal poll ratings improved. But critics will say that as she embraces the nasty party accusations she is at risk of alienating some core Tory voters. Can she bring her party back to being the main opposition to the government?. Help support our independent journalism at theguardian.com/politicspod

Who is really in charge – the people or the markets? In the first episode of Radical Thinking, a new series from the Guardian, senior economics commentator Aditya Chakrabortty speaks to the former Greek finance minister Yanis Varoufakis. What was it like during the eurozone crisis when Varoufakis went head to head with those who wanted to stop his reforms?. Help support our independent journalism at theguardian.com/politicspod

Andy Burnham has delivered a powerful and emotional speech to the Labour conference. He announced policies on pensions, social care and electoral reform. He said he was willing to talk about the things politicians usually avoided. But without a big budget, can he deliver his big dreams for the country?. Help support our independent journalism at theguardian.com/politicspod

Speaking to Pippa Crerar and Kiran Stacey at the Labour party conference in Liverpool, Miatta Fahnbulleh, the energy secretary, said a mark of her success or failure would be whether she could get bills down and said she would do so. She also challenged Reform UK and the Tories on their climate inaction, saying they would eventually ‘bow’ because they were on the ‘wrong side of history’. Help support our independent journalism at theguardian.com/politicspod

Andy Burnham will make his first speech at Labour conference as prime minister on Tuesday. Ahead of that, he has been talking to Pippa Crerar about why he is in the job and what changes he wants to make. Pippa and Kiran Stacey discuss his comments and the feeling behind the scenes at this year’s conference. Help support our independent journalism at theguardian.com/politicspod

Pippa Crerar had a front row seat for the PM’s first meeting with Donald Trump. What really happened during that 12-minute press conference? And as the Labour conference kicks off this weekend, she and Kiran Stacey discuss the ethics of journalist-politician karaoke. Help support our independent journalism at theguardian.com/politicspod

The UK prime minister will meet the US president for the first time in New York on Tuesday. With Trump at his weakest in the polls, could this be a perfect moment for Burnham to charm the president and avoid a very public political spat? Pippa and Kiran discuss what the two leaders might discuss in policy terms, and some of the potential high-risk issues. Help support our independent journalism at theguardian.com/politicspod

Former Bank of England economist Andy Haldane said the markets regarded this government as ‘a pretty traditional tax and spend socialist government with better TikTok videos’. Harsh criticism or truth? As pressure mounts on the chancellor, John Healey, to rule out tax rises, what options do they have left? Plus, what can the government do to tackle AI warnings?. Help support our independent journalism at theguardian.com/politicspod

There’s been a huge backlash against Reform UK after the party received £72m from two crypto billionaires over the weekend. Paul Nowak, the TUC leader, said the money showed democracy was ‘in crisis’. Labour is pushing for tighter restrictions on political donations which could be retrospective, but Reform is confident this will not affect its new war chest. How much does this money change the political landscape? And with Labour receiving millions from unions, will its new rules backfire?. Help support our independent journalism at theguardian.com/politicspod

It has been a huge week for Labour as Ed Miliband shifted the party’s stance on Israel by announcing sanctions on the illegal settlements in the West Bank and describing what is happening as ethnic cleansing. What is behind this shift, and will it make any difference on the ground?. Help support our independent journalism at theguardian.com/politicspod

Alternative für Deutschland has claimed a historic win in Germany, continuing the pattern of populist far-right parties gaining power across Europe. In the UK, balaclava-clad far-right protesters have marched on Dover, and then Portsmouth, trying to intimidate asylum seekers. Meanwhile, Reform UK’s conference ended with a beleaguered Nigel Farage dealing with protesters and allegations following an undercover investigation into party donors. Will far-right sentiment in Europe and the UK be a boost for Farage or a burden?. Help support our independent journalism at theguardian.com/politicspod

New from the Guardian Investigates team: Across the world, hundreds of people have come to believe they have made extraordinary scientific discoveries with AI chatbots such as ChatGPT, Claude and Gemini. Others say their AI has ‘awakened’, or is leading them to a higher spiritual realm. The Guardian journalist Michael Safi begins investigating a phenomenon labelled ‘AI psychosis’, travelling to the US to meet two people who have been on weird journeys with their chatbots. Help support our independent journalism at theguardian.com/politicspod

The Green party leader, Zack Polanski, has confirmed he will stand in the Holborn and St Pancras byelection, which was triggered when Keir Starmer announced he was quitting as an MP. It’s going to be a tough race to win, so can he do it? Plus, Reform UK’s conference starts today but it’s been a rough couple of months for the party and Nigel Farage – can he hold it all together?. Help support our independent journalism at theguardian.com/politicspod

Will the UK ever rejoin the EU? Who is funding Andy Burnham? And will the bedroom tax be scrapped? In a special episode, Kiran Stacey and Peter Walker answer some of your questions. Help support our independent journalism at theguardian.com/politicspod

It’s been a month since Andy Burnham became prime minister. And while polls have shown a ‘Burnham bounce’, the coming months will force the new PM into making some tough – and potentially unpopular – decisions that will reveal how serious he is about delivering the changes he believes the country needs. Kiran Stacey and Peter Walker look at the choices facing Burnham. Help support our independent journalism at theguardian.com/politicspod