On May 30th 2024 seminar goers at Princeton University witnessed a thrilling moment. The mathematician Zhouli Xu of the University of California, LA, announced that, together with colleagues he had sorted out the 126th dimension. Not in general, but in regards to a problem that has taunted mathematicians since the 1960s. The problem involves strange shapes and is called the Kervaire invariant problem, after the mathematician Michel Kervaire.
In this episode of Maths on the Move Zhouli takes us on a trip into higher dimensions, giving us a gist of what this long-standing problem is all about and retracing some of the long, and sometimes arduous, journey towards a proof. We met Zhouli when he visited our neighbours at the Isaac Newton institute for Mathematical Sciences (INI) in Cambridge to take part in a research programme called Equivariant homotopy theory in Context.
To find out more abut the topics discussed in this podcast see:
This content forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here.
The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.
Popular Podcasts
Stuff You Should Know
If you've ever wanted to know about champagne, satanism, the Stonewall Uprising, chaos theory, LSD, El Nino, true crime and Rosa Parks, then look no further. Josh and Chuck have you covered.
Dateline NBC
Current and classic episodes, featuring compelling true-crime mysteries, powerful documentaries and in-depth investigations. Follow now to get the latest episodes of Dateline NBC completely free, or subscribe to Dateline Premium for ad-free listening and exclusive bonus content: DatelinePremium.com
The Burden
The Burden is a documentary series that takes listeners into the hidden places where justice is done (and undone). It dives deep into the lives of heroes and villains. And it focuses a spotlight on those who triumph even when the odds are against them. Season 5 - The Burden: Death & Deceit in Alliance On April Fools Day 1999, 26-year-old Yvonne Layne was found murdered in her Alliance, Ohio home. David Thorne, her ex-boyfriend and father of one of her children, was instantly a suspect. Another young man admitted to the murder, and David breathed a sigh of relief, until the confessed murderer fingered David; “He paid me to do it.” David was sentenced to life without parole. Two decades later, Pulitzer winner and podcast host, Maggie Freleng (Bone Valley Season 3: Graves County, Wrongful Conviction, Suave) launched a “live” investigation into David's conviction alongside Jason Baldwin (himself wrongfully convicted as a member of the West Memphis Three). Maggie had come to believe that the entire investigation of David was botched by the tiny local police department, or worse, covered up the real killer. Was Maggie correct? Was David’s claim of innocence credible? In Death and Deceit in Alliance, Maggie recounts the case that launched her career, and ultimately, “broke” her.” The results will shock the listener and reduce Maggie to tears and self-doubt. This is not your typical wrongful conviction story. In fact, it turns the genre on its head. It asks the question: What if our champions are foolish? Season 4 - The Burden: Get the Money and Run “Trying to murder my father, this was the thing that put me on the path.” That’s Joe Loya and that path was bank robbery. Bank, bank, bank, bank, bank. In season 4 of The Burden: Get the Money and Run, we hear from Joe who was once the most prolific bank robber in Southern California, and beyond. He used disguises, body doubles, proxies. He leaped over counters, grabbed the money and ran. Even as the FBI was closing in. It was a showdown between a daring bank robber, and a patient FBI agent. Joe was no ordinary bank robber. He was bright, articulate, charismatic, and driven by a dark rage that he summoned up at will. In seven episodes, Joe tells all: the what, the how… and the why. Including why he tried to murder his father. Season 3 - The Burden: Avenger Miriam Lewin is one of Argentina’s leading journalists today. At 19 years old, she was kidnapped off the streets of Buenos Aires for her political activism and thrown into a concentration camp. Thousands of her fellow inmates were executed, tossed alive from a cargo plane into the ocean. Miriam, along with a handful of others, will survive the camp. Then as a journalist, she will wage a decades long campaign to bring her tormentors to justice. Avenger is about one woman’s triumphant battle against unbelievable odds to survive torture, claim justice for the crimes done against her and others like her, and change the future of her country. Season 2 - The Burden: Empire on Blood Empire on Blood is set in the Bronx, NY, in the early 90s, when two young drug dealers ruled an intersection known as “The Corner on Blood.” The boss, Calvin Buari, lived large. He and a protege swore they would build an empire on blood. Then the relationship frayed and the protege accused Calvin of a double homicide which he claimed he didn’t do. But did he? Award-winning journalist Steve Fishman spent seven years to answer that question. This is the story of one man’s last chance to overturn his life sentence. He may prevail, but someone’s gotta pay. The Burden: Empire on Blood is the director’s cut of the true crime classic which reached #1 on the charts when it was first released half a dozen years ago. Season 1 - The Burden In the 1990s, Detective Louis N. Scarcella was legendary. In a city overrun by violent crime, he cracked the toughest cases and put away the worst criminals. “The Hulk” was his nickname. Then the story changed. Scarcella ran into a group of convicted murderers who all say they are innocent. They turned themselves into jailhouse-lawyers and in prison founded a lway firm. When they realized Scarcella helped put many of them away, they set their sights on taking him down. And with the help of a NY Times reporter they have a chance. For years, Scarcella insisted he did nothing wrong. But that’s all he’d say. Until we tracked Scarcella to a sauna in a Russian bathhouse, where he started to talk..and talk and talk. “The guilty have gone free,” he whispered. And then agreed to take us into the belly of the beast. Welcome to The Burden.