## Five researchers from the Department of Pure Mathematics and Mathematical Statistics were invited speakers at the 2022 International Congress of Mathematicians (ICM).

The Congress is held every four years and represents the largest regular gathering of mathematicians across all subjects and from all nations — the 2018 Congress in Rio de Janeiro, Brazil, attracted over 3000 delegates from 114 countries. Invited speakers at the ICM can be counted among the best mathematical minds around the world, so it's a great honour for so many Faculty members to be chosen.

"We are proud and encouraged to have again a good number of members of the Department of Pure Mathematics and Mathematical Statistics speaking at the ICM," said Head of Department James Norris.

### Famous prizes

The ICM sees the award of some of the most important prizes in mathematics. The famous Fields medal recognises mathematicians up to the age of 40 for "outstanding mathematical achievement for existing work and for the promise of future achievement". In 2018 one of the recipients of this prestigious prize was the Cambridge mathematician Caucher Birkar for his work on algebraic topology. You can find out more about Birkar's work in this article, and watch an interview with Birkar here.

Alongside the Fields Medals, the ICM also sees the award of the Chern Medal, a lifetime achievement award in mathematics, the Carl Freidrich Gauss prize for mathematical research that has had an impact outside mathematics, the Abacus Medal (formally the Rolf Nevanlinna Prize) for contributions in mathematical aspects of information sciences, and the Leelavati Prize for contributions to increasing public awareness of mathematics.

### Twenty-nine and counting

The origin of the ICM can be traced back to the late nineteenth century. In 1893 a small gathering, sometimes called the zeroeth ICM, was held in Chicago. The first true ICM was held in Zürich in 1893, followed by a 1900 edition in Paris, held alongside many other events and exhibitions that marked the new century.

It was at the Paris ICM that the respected mathematician David Hilbert gave a now famous lecture outlining a series of problems he thought mathematicians should address in the new century (see here for an example of one of the problems). The problems have defined a lot of twentieth-century mathematical research, with some still providing active research areas even today. Their announcement in Paris cemented the role of the ICM as the heavy weight among mathematical conferences. (You can find out more about the history of the ICM here.)

Since then, 29 ICMs have taken place at various locations around the world. The previous three ICMs were held outside of Europe: in Brazil in 2018, South Korea in 2014, and India in 2010. The 2022 ICM was held virtually from July 6 to July 14, with all lectures recorded and made available straight after the Congress on the YouTube channel of the International Mathematical Union. The award ceremony for the prizes was held as a live event in Helsinki, Finland, and streamed here.

### DPMMS at the ICM

The Department of Pure Mathematics and Mathematical Statistics (DPMMS) is proud that five of its members were chosen to speak at the 2022 Congress.

**Roland Bauerschmidt**

Roland Bauerschmidt is a Professor in Probability at DPMMS who investigates problems that are motivated by physics. In particular, he works on systems that involve a very large number of particles that interact with each other, as happens in fluids or gases that consist of many atoms and molecules. Starting from a simple microscopic description of these systems, Bauerschmidt is interested in understanding the collective macroscopic behaviour. And because the number of particles in such systems is typically very large, he uses statistics and probability theory to understand them.

Bauerschmidt's work has already been recognised by a number of awards, including the IUPAP Young Scientist Award in Mathematical Physics and the Rollo Davidson Prize.

You can read more about Bauerschmidt's work in this article.

**Richard Nickl**

Richard Nickl is a Professor of Mathematical Statistics at DPMMS. He is interested in the mathematical theory of high-dimensional (or even infinite-dimensional) statistics. Such a theory is needed when you have data sets that are not only large, but also have a large number of features you’d like to understand statistically. His work provides theoretical foundations for problems that are encountered in modern data science.

"I am very happy about [being an invited speaker], as this supports the standing of mathematical statistics within the mathematical sciences, particularly in the UK," says Nickl.

His monograph *Mathematical foundations of infinite-dimensional statistical models*, co-authored with Evarist Giné, won the 2017 PROSE Award in Mathematics. Other prizes he has won include the 2017 Ethel Newbold Prize and a 2015 ERC consolidator grant. In 2020 he was an invited speaker at the European Congress of Mathematicians.

**Oscar Randal-Williams**

Oscar Randal-Williams is a Professor of Mathematics at DPMMS who is interested in geometry and topology. The latter studies geometric objects without paying attention to exact measurements of length, angles, areas, and so on. In topology, two objects are considered the same if one can be deformed into the other by stretching, bending and squeezing, but without cutting or tearing. A particular interest of Randal-Willimas are moduli spaces, which provide a way of considering a whole class of mathematical objects at the same time. Moduli spaces can be considered as topological objects in their own right, and their overall shape can be studied. You can find out more in this article.

Randal-Williams has previously been awarded the Whitehead Prize, the Philip Leverhulme Prize, the Dannie Heineman Prize, and the Oberwolfach Prize.

**Jacob Rasmussen**

Jacob Rasmussen is a Professor in Pure Mathematics at DPMMS who also works on topology. A particular interest of his are knots. These tricky objects, which we are all too familiar with from real life, lend themselves particularly well to topological study because their complexity depends on the way they are tangled up rather than their exact lay-out in space. Rasmussen is known for developing powerful tools for studying knots, as well as three and four dimensional shapes called manifolds.

**Peter Varju**

Peter Varju is a Professor of Pure Mathematics at DPMMS. His interests lie at the interface of analysis, combinatorics and number theory. A particular field of interest is the geometry of fractals: infinitely complex shapes that often display some self-similarity. An example is the famous Mandelbrot set. Fractals can be thought of as existing "between dimensions". A fractal that at first sight appears to be a curve can be so complex that it can no longer be thought of as one-dimensional, but not extensive enough to be thought of as two-dimensional. Varju talked about recent advances in our understanding of the dimension theory of self-similar fractals.

"[Being invited to speak at the ICM] is a great honour, and a wonderful opportunity to talk about my field of research in front of a broad audience," he says.

Varju's work has previously been honoured by the Paul Erdös Prize, the EMS Prize, and the Whitehead Prize.

*To find out more about the 2022 ICM, and read about the prizes, visit https://plus.maths.org.*