Dhruv Ranganathan: Algebraic Geometry

Welcome to Voices of Mathematics, a podcast from the Mathematics Faculty at the University of Cambridge. From number theory and geometry to cosmology and quantum physics, join us to explore topics across pure and applied mathematics, mathematical statistics and theoretical physics. In this episode we talk to Carola-Bibiane Schönlieb, Professor of Applied Mathematics in the Department of Applied Mathematics and Mathematical Physics (DAMTP). Carola's ground-breaking research covers areas including image analysis, image processing and inverse imaging problems, alongside developing innovative techniques in AI and machine learning. Her work has applications across a huge range of areas, ranging from healthcare to forest conservation and cultural heritage, and its impact has been recognised with multiple awards. In this episode, we sat down with Carola to talk about the power of inverse problems, different perspectives on AI, and the infectious inspiration of working with Cambridge's mathematical community.

Welcome to Voices of Mathematics, a podcast from the Mathematics Faculty at the University of Cambridge. From number theory and geometry to cosmology and quantum physics, join us to explore topics across pure and applied mathematics, mathematical statistics and theoretical physics. In this episode we talk to Hannah Fry, Professor of the Public Understanding of Mathematics in the Department of Applied Mathematics and Mathematical Physics (DAMTP). Hannah has just been awarded the Leelavati Prize at the International Congress of Mathematicians for outstanding contributions to raising the public awareness of mathematics. The prize citation calls her 'one of the foremost global ambassadors for mathematical thinking,' and outlines her extraordinary impact as 'a voice for mathematics that resonates far beyond the public audience normally interested in science communication': 'She has used outstanding creativity and originality to translate mathematics into a language of wonder and relevance for the public without diminishing its scope and importance.' We talked to Hannah to find out more about how it felt to win the Leelavati Prize, what fuels her passion for mathematics communication, and the key to connecting with people to spark their curiosity about maths.

Welcome to Voices of Mathematics, the podcast from the Mathematics Faculty at the University of Cambridge. From number theory and geometry to cosmology and quantum physics, join us to explore topics across pure and applied mathematics, mathematical statistics and theoretical physics. In this episode we talk to Julian Sahasrabudhe, Professor of Combinatorics in the Department of Pure Mathematics and Mathematical Statistics (DPMMS). Julian Sahasrabudhe and his collaborators have made headlines for a number of recent breakthroughs, including remarkable results in sphere packing, which you can imagine in terms of packing oranges into a very large, higher-dimensional box, and Ramsey theory, which involves finding order within systems which, at first sight, appear completely disordered. His outstanding research has been rewarded with several prizes, including a Whitehead Prize in 2024. Julian is also one of the invited speakers at the International Congress of Mathematicians (ICM) in July 2026. Taking place every four years, the ICM is one of the highlights of the mathematical calendar: it celebrates the diversity and excitement of modern mathematics, and also sees the award of some of the subject's most prestigious prizes, including the famous Fields Medals. We talked to Julian to learn more about his path into mathematics, a brief introduction to his work in the field of combinatorics and how it offers partnerships with other areas of maths, and the advice he'd give on how to make progress when wrestling with hard problems. And we also heard from Julian on what he's most looking forward to about attending this year's ICM.

Welcome to Voices of Mathematics, a podcast from the Mathematics Faculty at the University of Cambridge. From number theory and geometry to cosmology and quantum physics, join us to explore topics across pure and applied mathematics, mathematical statistics and theoretical physics. In this episode we talk to Richard Samworth, Professor of Statistical Science and Director of the Statistical Laboratory in the Department of Pure Mathematics and Mathematical Statistics (DPMMS). Richard Samworth's outstanding contributions to statistics have been recognised with numerous honours and awards. In 2025, he won two prestigious prizes in the space of 24 hours – the David Cox Medal for Statistics and the Guy Medal in Silver. He has also been invited to speak at the International Congress of Mathematicians (ICM) in July 2026. Held every four years, the ICM features the world's leaders in the field and celebrates the diversity of today’s mathematics. Only mathematicians whose work is of the highest international standard are invited to speak at the week-long event, which usually draws thousands of participants working in all areas of maths. The ICM also sees the award of some of the most prestigious prizes in mathematics, including the famous Fields Medals. In this episode, we talk to Richard to find out more about the work he will be speaking about at the ICM, how his field of statistics balances being simultaneously very theoretical and very applied, and what he most values about being part of the mathematical community in DPMMS.

Welcome to Voices of Mathematics, a podcast from the Mathematics Faculty at the University of Cambridge. From number theory and geometry to cosmology and quantum physics, join us to explore topics across pure and applied mathematics, mathematical statistics and theoretical physics. In this episode we talk to James Fergusson, Professor of Theoretical Cosmology in the Department of Applied Mathematics and Theoretical Physics. James is also the Executive Director of the University of Cambridge's innovative new Master's programme in Data Intensive Science, and the Director of the Infosys-Cambridge AI Centre. Fergusson's innovative collaboration with Infosys, a global consulting company and leader in next-generation digital services, is an outstanding example of how the University and industry can collaborate on cutting edge research with real impact and benefits for both sectors. "Out of our conversations with Infosys, we realised that a lot of the research challenges we have [in academia] are very similar to the challenges that large enterprises have," says Fergusson. "One of the really interesting things we are talking to companies about is how do you take these ideas from research and build them into robust, reliable systems that can be widely used." As well as exploring the potential of what AI can do in industry, Fergusson is also key in equipping the next generation of researchers through an innovative Master's programme: the University of Cambridge's MPhil in Data Intensive Science. Rather than a more traditional Master's course which focuses on one specific subject, Fergusson says the MPhil is intended to be more like vocational training, giving students the full package of skills that researchers in this field will need. "My hope is that people who come to us on this Master's take the great training they have from their undergraduate courses, and then use this vocational training on how to use these cutting-edge tools to drive the next round of exciting breakthroughs," he says. We talked to James to learn more about the potential of AI to drive forward scientific discovery, how industry and academia can work together, and training the researchers of the future through the MPhil in Data Intensive Science.