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Your Wednesday Briefing: Russia’s Next Offensive

Good morning. We’re covering Russia’s new offensive in eastern Ukraine, Boris Johnson’s battle for his political survival and Twitter’s lawsuit against India.

With Luhansk Province firmly in its grasp, Russia set its sights on the next target in eastern Ukraine. Russian forces ramped up shelling on the outskirts of the city of Bakhmut as an apparent prelude to an offensive into the province of Donetsk.

The tactic drove out Ukrainian defenders from the last two cities standing in Luhansk, which along with Donetsk makes up the eastern Donbas region. President Vladimir Putin of Russia has made capturing the Donbas a crucial objective.

The city of Sloviansk is also likely to take the brunt of the Russian war machine, analysts said. But to capture all of Donetsk, Russian forces would most likely need to take Kramatorsk, the headquarters of Ukrainian military forces in the east.

Prime Minister Boris Johnson of Britain was battling for his political survival after two senior ministers in his Conservative government unexpectedly resigned from their cabinet posts in what appeared to be a coordinated move against their leader.

Rishi Sunak, the chancellor of the Exchequer, and Sajid Javid, the health secretary, announced their decisions shortly after Johnson apologized for having appointed a minister, Chris Pincher, who stepped down last week over accusations of inappropriate behavior.

The resignations thrust Johnson into the most perilous position of his three-year tenure as prime minister. He survived a no-confidence vote last month, but cabinet resignations could put pressure on him to resign.

What’s next: Johnson’s fate may rest on whether other members of his cabinet stand by him. There was doubt about the loyalty of other ministers, whose statements and actions will be watched closely.

Background: Pincher resigned as deputy chief whip last week after admitting to having been drunk at a private members’ club in London where, according to media reports, he groped two men. Downing Street acknowledged that Johnson had been told about previous accusations against Pincher.

Twitter said that it had sued the Indian government, challenging a recent order to remove content and block accounts within the country.

The company had been given a deadline of Monday to block dozens of accounts and posts from view within India, with a threat of criminal action against Twitter executives if they failed to comply.

Twitter has been told to remove content related to complaints about civil liberties, protests and the government’s response to the pandemic. Last week, it was ordered to block tweets from Freedom House, an American nonprofit organization that mentioned India as an example of a country where press freedom was on the decline.

Background: Prime Minister Narendra Modi and his ruling Bharatiya Janata Party have worked for several years to corral tech companies and strictly police what is said online, and they have used new information-technology laws to clamp down on dissent.

A new law lowered the minimum age for political office in South Korea to 18 from 25, and a record number of candidates under 40 ran in local elections this year. They faced skepticism, cultural hurdles and problems as old as politics itself.

Lives lived: Zhang Sizhi, a Chinese lawyer who defended politically contentious clients — Tiananmen-era dissidents, purged officials, victims of police frame-ups — died on June 24 in Beijing. He was 94.

The Fields Medals, given to young mathematicians every four years, honor not just past achievements but also the promise of future breakthroughs. This year, they went to four people.

Maryna Viazovska, from Ukraine, is the second woman to win the medal. She is known for proofs for higher-dimensional equivalents of the stacking of equal-sized spheres — a variation of a conjecture by Johannes Kepler involving the best way to stack cannonballs.

June Huh struggled with math in college and barely made it into a doctoral program. There, he came to prominence in the field of combinatorics: the number of ways things can be shuffled. At first glance, it looks like playing with Tinker Toys.

James Maynard has worked on a conjecture for years: For any pair of primes separated by 2, there will always be a larger pair. “It’s the tension between being somehow simple and fundamental but mysterious and poorly understood,” Maynard said of his interest in primes.

Hugo Duminil-Copin studies the mysteries of ferromagnetic phase transitions. There are mathematical models for the phenomenon in one and two dimensions, but he works in the intractable third: “The ability to produce exact formulas just collapses completely,” Duminil-Copin said.

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