Living proof: Hunting through higher dimensions with Zhouli Xu
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:
Maths in a minute: Topology
The hypersphere in four dimensions
Telescope topology
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.
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Brainstorming AI with Maths4DL
The capabilities of artificial intelligence may appear to be galloping ahead, but there are still many challenges that need to be solved. Last month we joined members of the Maths4DL research project for a hackathon — an intensive two-day brainstorming session designed to figure out how one might teach machine learning techniques for solving differential equations and how best to test those techniques.
In this episode of Maths on the Move, Maths4DL members Yolanne Lee from University College London, Georg Maierhofer from the University of Cambridge, and Chris Budd OBE from the University of Bath tell us all about the hackathon, the science behind it, and what it was like to participate in those ambitious but exciting 48 hours.
For a brief introduction to machine learning see Maths in a minute: Machine learning and neural networks and for a brief introduction to differential equations see Maths in a minute: Differential equations. You might also like:
Our podcast featuring Yolanne Lee talking about her work as a Maths4DL researcher,
Our podcast featuring Georg Maierhofer talking about physics informed neural networks, as well as the accompanying article,
Our article AI and GoPro physics featuring the work of Nathan Kutz who is mentioned in this podcast.
This content is part of our collaboration with the Mathematics for Deep Learning (Maths4DL) research programme, which brings together researchers from the universities of Bath and Cambridge, and University College London. Maths4DL aims to combine theory, modelling, data and computation to unlock the next generation of deep learning. You can see more content produced with Maths4DL here.
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Meet your digital twin
Imagine we could have a digital version of our entire body which could help us, and our doctors, decide what life style is good for us, predict which diseases we might get, and how to best treat them? In short, what if we could all have our very own digital twin?
The idea isn't quite as sci-fi as it sounds. A gigantic scientific effort called the Physiome Project is about piecing together a mathematical description of the entire physiology of the human body. Once this has been achieved to a sufficient level digital twins will be a spin-off.
In this podcast we revisit an interview we did back in 2019 with Steven Niederer, who was then Professor of Biomedical Engineering at King's College London but has since moved to a new position at Imperial College London as Chair of Biomedical Engineering. Niederer told us about the physiome project, about how the fitbits many of us own are a very first step towards a digital twin, and about how you can model individual human organs such as the heart. We also challenge ourselves to explain differential equations in one minute.
You can find out more about maths and medicine, differential equations and mathematical modelling on Plus.
We met Niederer in 2019 when he helped to organise a research programme at the Isaac Newton Institute for Mathematical Sciences in Cambridge.
The music in this podcast comes from the artist Oli Freke. The track is called Space Power Facility.
This podcast 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.
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Living proof: The meaning is in the arrows with Adina Goldberg
In this podcast we hope to give you some interesting information. This information is encoded in terms of 0s and 1s – the classical bits in your computer or phone. But what if instead we were using a quantum computer? Then we'd be dealing with quantum bits, or qubits, opening up exciting new possibilities. And quantum information theory is the area of mathematics that explores how we can do that.
Adina Goldberg was one of the participants at a recent research programme in this area at the Isaac Newton Institute for Mathematical Sciences (INI). In this episode of Living proof, our podcast produced in collaboration with the INI, we speak to Adina about her work and how her intriguing motto – "the meaning is in the arrows" – applies to her research, her career path, and the way she looks at life.
You can find out more about quantum information in this short introduction and delve into the details of information theory in this collection of content.
Make sure you visit Adina's website to find out more about her work and her fascinating career. Since we recorded this podcast Adina has finished her PhD – congratulations Dr Goldberg!
This podcast 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.
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Postcard from Oslo: Masaki Kashiwara and the 2025 Abel Prize
From sunny parks to banquets in castles – come with us on an exciting adventure in Oslo as we join the celebrations for the 2025 Abel Prize! We meet Masaki Kashiwara, winner of this year's prize, who tells us about the importance of collaborations and creating new things. Ragni Piene, previous chair of the Abel Prize Committee, gives us a look behind the scenes. And Andrea D'Agnolo, one of Masaki Kashiwara's most recent collaborators, celebrates his friend and fellow bridge-builder between mathematical worlds.
You can read more about Masaki Kashiwara's work in our article, and you can listen to a recent podcast where we spoke to Helge Holden, Chair of the Abel Prize committee, about the Abel Prize and about Masaki Kashiwara's work. And can you see all our reporting on every Abel Prize since it was first awarded in 2003 here.
Thanks to the musicians Peter Baden, Astrid Garmo and Liv Lande for playing such wonderful music in the Abel Prize ceremony which you'll hear a little taste of in this podcast. And thank you to all the Abel Prize team, including Unni Irmelin Kvam, Pål Petterson, Marina Tofting and Anne Lise Stranden for inviting us to Abel Week and for such a fantastic celebration!
Photo of Masaki Kashiwara is copyright Thomas B. Eckhoff/DNVA and used with permission
Maths on the Move, the podcast from plus.maths.org, will bring you the latest news from the world of maths, plus interviews and discussions with leading mathematicians and scientists about the maths that is changing our lives. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.
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