Nvidia, OpenAI and Microsoft announce investments as part of multibillion-dollar package alongside Trump visit

Donald Trump’s arrival in the UK on Tuesday night was accompanied by a multibillion-dollar transatlantic tech agreement.

The announcement features some of the biggest names from Silicon Valley: the chipmaker Nvidia; the ChatGPT developer, OpenAI; and Microsoft. Big numbers were involved, with Microsoft hailing its $30bn (£22bn) investment as a major commitment to the UK – and adding, in an apparent swipe at its rivals, that it was not making “empty tech promises”.

Anderson updates Thomas Pynchon for the era of Ice roundups, pitting shaggy revolutionary Leonardo DiCaprio against cartoonish forces of reaction

One of the great creative bromances has flowered again: Paul Thomas Anderson and Thomas Pynchon. Having adapted Pynchon’s Inherent Vice for the screen in 2015, Anderson has now taken a freer rein with his 1990 novel Vineland, creating a bizarre action thriller driven by pulpy comic-book energy and transformed political indignation, keeping his pedal at all times welded to the metal.

It’s a riff on the now recognisable Anderson-Pynchonian idea of counterculture and counter-revolution, absorbing the paranoid style of American politics into a screwball farcical resistance, with a jolting, jangling, nerve-shredding score by Jonny Greenwood. It’s partly a freaky-Freudian diagnosis of father-daughter dysfunction – juxtaposed with the separation of migrant children and parents at the US-Mexico border – and a very serious, relevant response to the US’s secretive ruling class and its insidiously normalised Immigration and Customs Enforcement (Ice) roundups: the toxic new Vichyite Trump enthusiasm.

The choice for governments around the world is clear: engage, or fall beneath the US president’s wheel. For now, Britain must do the former

Has any visiting leader ever seen so little of Britain or the British as Donald Trump is doing this week? The absurdly unrepresentative version of the country offered up to the US president on his second state visit on Wednesday was a Windsor parody, a Potemkin version of this country, glistening with protocol and polish, amid a lavish reenactment of the British monarchy’s invented traditions. Just about the only thing that was authentic was the rain.

But here’s the unalterable and underlying thing. None of that really matters. What matters is that Trump is the most powerful leader in the world. Despite all the Trumpian shocks, the US and Britain remain allies. Business can and should be done between them. So the opportunity for face-time with Trump, in circumstances designed to soften him up with flattery and engage him over this country’s own priorities, is to be seized. Not to do this would be perverse.

Martin Kettle is a Guardian columnist

Donald Trump is back on UK soil for his ‘unprecedented’ second state visit. Will the US president’s trip help to distract from Keir Starmer’s challenges at home? Or could it leave the prime minister even more exposed? Kiran Stacey asks the columnist and Politics Weekly America host, Jonathan Freedland

• Send your thoughts and questions to politicsweeklyuk@theguardian.com

She had a zest for life that propelled her to the heights of stage and screen – but behind all this lay a shocking story of violence, grooming and abuse. From her bed, flanked by pills and cigarettes, Ireland’s grande dame looks back

Brenda Fricker is sitting up in a bed plumped with pillows, wearing a sapphire blue blouse and a head of grey-golden ringlets. One bedside table has her medication, 25 pills a day. Another has a cup of water, an ashtray and her cigarettes. Above and on either side of her are shelves jammed with an eclectic hoard of books: Salman Rushdie, Edna O’Brien, Brian Aldiss, Alex Ferguson. Meanwhile, gazing out from framed black and white photographs on the walls, are writers, producers and actors from another era, plus a young, luminous Fricker herself.

The current version of Fricker is 80 and not so well, happy to be interviewed but only from the bed of her Dublin home – not exactly a common setup with stars, but then she is no ordinary star. “I’m out of breath just talking,” she says. “I’ve never known tiredness ever in my life. Weary. Will I ever get up again?” She will, but the question is not entirely rhetorical. “I’m having a dreadful death,” she says. “I’m just dying, every day in pain.” This is said in a matter of fact tone, only to be undercut by a rueful prediction: “I’ll probably live to be 100.”

An American football fan called in sick so he could attend a game – and was rumbled after being caught on camera, his face projected up on the stadium’s giant screens

Name: Getting Coldplayed.

Age: The original incident happened on 16 July this year.

Prime minister seeks to make best of difficult state visit by US president with package of commitments by US firms

Keir Starmer has sought to navigate a politically treacherous state visit by Donald Trump with an announcement of £150bn of US investment in the UK, as the president was kept safely within the confines of Windsor Castle.

As thousands of protesters voiced their anger in London at a Stop Trump Coalition protest, the US president was escorted by the king and queen through a first day that ended in a state banquet but kept him out of reach of his critics.

Other nations including France, Australia and Canada plan to take the same step at next week’s UN summit

Keir Starmer will reportedly recognise a Palestinian state over the weekend after Donald Trump concludes his state visit to the UK.

The prime minister has previously said he plans to recognise Palestinian statehood before the UN general assembly in New York this month if Israel does not meet a series of conditions to improve the humanitarian situation in Gaza.

Those in top roles are five times as likely to have been to private school than general population, study finds

The privately educated are tightening their “vice-like grip” on some of the most powerful and influential roles in British society, such as FTSE 100 chairs, newspaper columnists and BBC executives, a report has found.

Those in the most important positions are five times as likely to have attended private school than the general population, showing it is still possible to “buy advantage”, according to the Sutton Trust.

Home Office says it will review modern slavery laws to save PM’s ‘one in, one out’ returns deal with France

Shabana Mahmood has accused asylum seekers of making “vexatious, last-minute claims” to avoid removal to France as the Home Office said it would review modern slavery laws to save Keir Starmer’s returns deal.

After an 11th-hour injunction that scuppered Labour’s “one in, one out” scheme, the home secretary said she would stop claimants “suddenly deciding that they are a modern slave on the eve of their removal”, adding that it made a “mockery of our laws and this country’s generosity”.