Live updates from the day session at Melbourne Park
Women’s and men’s No 1s on Rod Laver Arena
Any thoughts? Get in touch with an email

Elsewhere around Melbourne Park, defending women’s singles champion, Madison Keys, overcame a wobbly start to defeat Ukrainian Oleksandra Oliynykova, who was nearly successful in throwing off her opponent with her unusual style.

Tumaini Carayol took a closer look at that encounter:

Emmy award winner faces charges of inappropriately touching a minor while on set directing a TV series

A judge has ordered that actor Timothy Busfield be released from jail during a detention hearing on child sex abuse charges .

The order Tuesday by state district court judge David Murphy is linked to accusations that Busfield inappropriately touching a minor while working as a director on the set of the series The Cleaning Lady.

Close family friend says Nico Antic had ‘devastating injuries’ and was fighting for his life after more than 60 hours in hospital

• Follow our Australia news live blog for latest updates

• Get our breaking news email, free app or daily news podcast

The family of the 12-year-old who was attacked by a shark in Sydney Harbour are grieving as they contemplate “the worst possible outcome”.

The boy, named as Nico Antic in an online fundraiser, has been fighting for his life after being bitten on both legs on 18 January at a harbour beach in Vaucluse, in Sydney’s east.

Mark Ruffalo, Brian Eno and Abigail Disney sign letter timed for WEF in Davos saying wealthy are buying political influence

Nearly 400 millionaires and billionaires from 24 countries are calling on global leaders to increase taxes on the super-rich, amid growing concern that the wealthiest in society are buying political influence.

An open letter, released to coincide with the World Economic Forum in Davos, calls on global leaders attending this week’s conference to close the widening gap between the super-rich and everyone else.

Actor says it is ‘more important than ever’ to safeguard city’s parks as report finds more than 50 are at risk

Dame Judi Dench has called for greater protections for London’s parks and green spaces, as research finds more than 50 of the city’s parks are at risk from development.

The Oscar-winning actor has long loved trees, and in 2017 fronted a BBC documentary about her love for them. She plants a tree every time a close friend or relative dies, including for her late husband, Michael Williams, who died in 2001, and the actor Natasha Richardson, who was killed in a skiing accident in 2009, and one for her brother Jeffery Dench, who died in 2014.

The number of small venues shrank by just nine in 2025, but more than half of them reported making no profit, while employment in the sector dropped almost 22%

The number of grassroots music venues (GMV) in the UK shrank in effect by just nine in 2025, the lowest rate of annual decline since 2018.

Thirty venues closed permanently between July 2024 and 2025 and 48 ceased functioning as GMVs, citing financial viability, change in ownership and eviction or redevelopment. However, 69 spaces that had previously ceased operating as GMVs returned to the sector.

European countries now reliant on US liquified natural gas shipments, creating risk of higher bills amid recent tensions

Donald Trump has a stranglehold over EU and UK energy supply as a result of Europe swapping its dependency on Russia for reliance on the US, analysis has shown.

In part due to the war in Ukraine and the imposition of sanctions on Russian pipeline gas, European countries have become dependent on shipments of US liquified natural gas (LNG), according to a paper co-authored by the Clingendael Institute, in The Hague, the Ecologic Institute, in Berlin, and the Norwegian Institute of International Affairs.

‘Cost-cutting’ announcement comes amid uncertainty over deal struck with Saudi Arabia to perform in Riyadh

New York’s Metropolitan Opera has announced a round of layoffs, pay cuts and program reductions as it grapples with financial strain.

The organization cited problems left over from the Covid pandemic, which drastically affected performing arts shows across the US and internationally.

The scars remain and there is much to be fixed still but this was a step towards reconciliation. It was something of a statement too, and not just in the goals scored but the reaction to them. Nine days after Xabi Alonso’s sacking, six after their captain said they had hit rock bottom with Copa del Rey elimination and three after the protest of a generation, white hankies and whistles greeting the players and even the president, there were songs and support at last as Real Madrid defeated Monaco 6-1.

Kylian Mbappé, Franco Mastantuono and Jude Bellingham all scored, while there was an own goal from Monaco’s Thilo Kehrer. More significantly still, the man who had been at the centre of the storm made three of the six goals and smashed in a superb strike of his own. And if Vinícius Júnior, who had stood accused before the game and stood with the MVP trophy at the end of it, wasn’t entirely ready to share his moment with fans yet, his first goal here since October saw teammates come to his side. He then hugged his new coach, Álvaro Arbeloa, who claimed that was the embrace of the whole of Madrid.

• 29-year-old had stimulants and kratom in system

• Death investigated as possible overdose or suicide

American chess grandmaster Daniel Naroditsky had a combination of stimulant and psychoactive substances in his system when he died last year, according to a toxicology report released by North Carolina authorities.

Naroditsky, 29, was found dead at his home in Charlotte in October 2025, a loss that sent shockwaves through the global chess community. At the time, police said his death was being investigated as a possible overdose or suicide. No official cause was announced.

In the US, you can call or text the National Suicide Prevention Lifeline on 988, chat on 988lifeline.org, or text HOME to 741741 to connect with a crisis counselor. In the UK and Ireland, Samaritans can be contacted on freephone 116 123, or email jo@samaritans.org or jo@samaritans.ie. In Australia, the crisis support service Lifeline is 13 11 14. Other international helplines can be found at befrienders.org

• Ellis: ‘Careful not to throw stones in glass houses’

• Ex-USWNT coach criticises anti-LGBTQ+ legislation in US

• Qatar said to be in talks to stage 2028 Women’s Club World Cup

Fifa’s chief football officer and former USWNT coach Jill Ellis has criticised anti-LGBTQ+ legislation in the United States and spoken of not wanting to “throw stones in glass houses” when discussing the prospect of Qatar hosting the 2028 Women’s Club World Cup.

The Guardian revealed earlier this month that the world’s governing body is in discussions about Qatar potentially staging the new tournament, which will be held from 5 to 30 January 2028. While Ellis said she had not heard of any such talks personally, she appeared to be open to the tournament being played in the Middle East.

Mission accomplished for Arsenal. A seventh win out of seven ensured Mikel Arteta’s side will head straight into the last 16 of this competition as one of the two top seeds after Gabriel Jesus scored twice – including their 19th goal of the season from a corner – to see off last year’s beaten finalists.

It means that as well as getting one back over an Inter team that they lost to 14 months ago, Arsenal have surpassed their longest winning streak at this level. While Manchester City’s surprise defeat in Norway in the earlier kick-off had removed any jeopardy about them progressing, this was more evidence of the ruthless streak Arsenal have developed under Arteta. The only blot on the copybook in a fourth successive away game in four different competitions was Petar Sucic’s equaliser in the first half after Jesus had given Arsenal an early lead, although this was all about the Brazil striker even after the substitute Viktor Gyökeres sealed the points late on with a classy finish.

Prime minister puts faith in ‘pragmatic’ solutions, while US president drops one diplomatic bomb after another

In his account of Tony Blair’s years in power, The New Machiavelli, Jonathan Powell sets out two opposing strategies for any British prime minister in dealing with their counterpart in the White House.

The first, he says, is “cutting a bella figura” – parading for show – by openly criticising the US president, for which he gives the example of the French. The other, and the approach preferred by Powell, is to do diplomacy in private and build a close relationship, in the hope of having greater influence.

Authorities believe that in 2022 Austin Thompson, then 15, went on killing rampage, beginning with his older brother

An 18-year-old plans to plead guilty to a 2022 mass shooting in North Carolina that left five people dead – including his older brother – avoiding a trial in February, his attorneys have said.

A written notice filed in Wake county court by the lawyers for Austin Thompson said their client intends to plead guilty to all charges against him.

To channel Bjørge Lillelien and his famous commentary on Norway’s win against England in 1981: Pep Guardiola, your Manchester City boys took a heck of a beating here on the shores of the Norwegian Sea, below the skies of the aurora borealis, and on the Aspmyra Stadion’s ­artificial pitch graced by this immortal Bodø/Glimt victory which downed a ­continental superpower.

Jonas Gahr Støre was present to witness a win that came courtesy of Kasper Høgh’s two first-half goals plus Jens Petter Hauge’s curled peach after the interval, as Norway’s prime minister escaped Donald Trump’s curious obsession with the Nobel peace prize: another measure of how this result will never be forgotten.

• Annex attempt could bring about Uefa-led boycott

• Implications for World Cup alarming heads of FAs

European football leaders are increasingly concerned about Donald Trump’s wish to annex Greenland, and they have held initial discussions about how the sport could respond.

The Guardian understands the implications for the World Cup this summer were among the topics raised among about 20 football association heads in Budapest on Monday. Talks about the Greenland crisis were held informally on the sidelines of an event organised to celebrate the Hungarian football federation’s 125th anniversary, in the knowledge that a unified European response may be required should Trump seek to escalate the situation.

Minnesota governor Tim Walz and Minneapolis mayor Jacob Frey among officials who received subpoenas

The justice department subpoenaed several top officials in Minnesota on Tuesday as part of its investigation into whether Minneapolis officials have conspired to impede federal immigration efforts there.

A copy of a subpoena to the office of the Minneapolis mayor, Jacob Frey, obtained by the Guardian, requests guidance and policies related to immigration enforcement in Minnesota since last year. It also requests communication regarding those policies with other state agencies, as well as documents related to “hindering, doxxing, identifying, or surveilling immigration officers”.

Trump’s demand for Greenland is a throwback to the 1884 Berlin conference: a transaction of land and people driven by a might makes right worldview

The announcement on 17 January that Washington will impose punitive tariffs of 10% to 25% on eight European allies – unless they facilitate the “complete and total purchase” of Greenland – is likely to be the death knell of the post-1945 transatlantic order. By linking the territorial sovereignty of a Nato ally to trade access, the US has transitioned from Europe’s security guarantor to a 19th-century imperial rent-seeker.

This is a moment of profound rupture. For decades, the western world believed that raw imperialism had been relegated to the past among advanced industrial powers. Even China, for all its assertiveness, largely couches its ambitions in the language of revanchism – the “reclaiming” of lost territory. Washington’s current demand for Greenland, by contrast, is a throwback to the age of the 1884 Berlin conference: a transaction of land and people driven by a might makes right worldview.

Christopher S Chivvis is a senior fellow at the Carnegie Endowment for International Peace and former US national intelligence officer for Europe

PM’s spokesperson insists government’s position is unchanged and that the US still supports the deal

The UK will press ahead with plans to hand the Chagos Islands back to Mauritius despite Donald Trump calling it an “act of great stupidity” and suggesting it was among the reasons he wants to take over Greenland.

The US president said ceding sovereignty of the British Indian Ocean Territory, which includes the Diego Garcia military base, was a sign of “total weakness” by the UK.

Ecosystem destruction will increase food shortages, disorder and mass migration, with effects already being felt

The global attack on nature is threatening the UK’s national security, government intelligence chiefs have warned, as the increasingly likely collapse of vitally important natural systems would bring mass migration, food shortages and price rises, and global disorder.

Food supplies are particularly at risk since “without significant increases” the UK would be unable to compete with other nations for scarce resources, a report to ministers says.

• Ceferin, as well as Fifa, intervened with the Israeli FA

• Aida facility was set to be removed by security forces

A football pitch used by refugees in the occupied West Bank has been saved from demolition after an intervention by the president of Uefa, Aleksander Ceferin.

A decision to stop plans to remove the pitch in the Aida refugee camp outside Bethlehem was taken by Israeli security forces on Tuesday after an international campaign for its preservation.

Leaders of EU, France and Canada stake out positions on Greenland ahead of US president’s speech to World Economic Forum

“There’s no diplomacy with Donald Trump: he’s a T rex. You mate with him or he devours you.” Debate at the World Economic Forum annual meetings high in the Swiss Alps is usually scrupulously polite, but as this year’s gathering got under way in Davos on Tuesday, California’s Democratic governor, Gavin Newsom, had this blunt advice for handling the week’s star speaker.

The US president was yet to arrive but throughout the blond wood congress centre the hottest topic among the global elite of business and politics – on and off conference stages – was Trump’s intemperate attack on European allies, threatening punitive tariffs if they fail to let him annex Greenland.

Child was on way home from a musical with parents, brother and cousin when trains collided, killing 42 people

A six-year-old girl who had travelled to Madrid to see a musical was the only member of her family to survive Sunday’s rail disaster in southern Spain, which killed 42 people, among them her parents, her brother and her cousin.

The girl, who has not been named, was found walking along the tracks after two trains collided near the town of Adamuz in the Córdoba province of Andalucía. She had emerged from the accident with only a minor head wound.