# Fields Medal for two SwissMAP members: Hugo Duminil-Copin & Maryna Viazovska

### 22 Jul 2022

The Fields Medal is the most prestigious award for mathematicians. It is awarded every four years at the International Congress of Mathematicians to two to four researchers under the age of 40 for their «*existing work and for the promise of future achievement»*

###### (mathunion.org)

The four laureates were announced today Tuesday 5 of July, during the IMU Award Ceremony in Helsinki. We congratulate our members Hugo Duminil-Copin (UNIGE) and Maryna Viazovska (EPFL) who earned the highest recognition in mathematics for their outstanding contributions to the field. Hugo has been recognised for the exceptional quality of his work in statistical physics and Maryna for her solution to the centuries-old problem of sphere-packing in dimensions 8 and 24.

Their impressive careers have captivated the attention of the scientific community for some time now. Listed amongst the currently most brilliant mathematicians, they are both recipients of numerous prestigious international awards and distinctions. Amongst them, Hugo was recipient of the 2017 Breakthrough Foundation’s New Horizons in Mathematics Award and Maryna of the 2020 Latsis prize.

**Outstanding scientists **

Hugo completed his PhD at the University of Geneva in 2011 and was promoted three years later to professor at the age of 29, "*becoming one of the youngest researchers to be promoted to professor in the history of the University of Geneva*."

###### (UNIGE)

Since 2016 Hugo splits his time between the UNIGE’s Faculty of Science and the Institut des Hautes Etudes Scientifiques (IHES).

Maryna obtained her doctoral degree in Max Planck Institute of Bonn in 2013, followed by postdoctoral positions at the IHES and the Humboldt-Universität Berlin. She joined EPFL as a tenure-track assistant professor in 2017 and was appointed full professor in 2018. Today, Maryna became the second woman to receive the Fields Medal.

“*I am delighted… and I also hope that the prize will help to inspire young girls to go into mathematics” Latsis Prize Acceptance Remarks from Maryna Viazovska. *

###### (EPFL)

#### A passion for physics and probability theory

*Hugo’s work focuses on the mathematical branch of statistical physics. He studies phase transitions – sudden changes in the properties of matter, such as the transition of water from the gaseous to the liquid state – using probability theory. In particular, he uses probability theory to analyse mathematical models that describe three distinct phenomena: material porosity (via percolation theory), ferromagnetism (via the Ising model) and polymers (via the study of self-avoiding walks).*

*The first seeks to understand the mechanisms at work in porous materials such as pumice or coffee: what path does water take when it passes through such a material, for example? The second attempts to determine the behaviour of magnets, and in particular the progressive loss of their magnetism, when they are subjected to high temperatures. The third seeks to determine the positioning of polymers when they are immersed in a solvent.*

*By using new connections between these classical models, and by developing a theory of ‘dependent percolation’, Hugo Duminil-Copin has obtained transformative results that have improved our understanding of critical phenomena in statistical physics. ‘This is purely fundamental research with no direct application. Nevertheless, modelling phase transitions mathematically is very important: it allows us to better understand the behaviour of matter. It gives us solid foundations that can be used for applied research with a view to industrial developments that are still impossible to foresee,’ Hugo explained.*

###### (UNIGE)

#### Ground-breaking progress on long-standing sphere-packing problem

*The mathematical derivation of the densest possible arrangement of spheres in a given space goes back to a problem posed by the explorer Sir Walter Raleigh in the 16th century. He raised the question of how cannonballs should be stacked in the densest possible way on a ship. For centuries, luminaries of mathematics made assumptions about the sphere-packing problem in multidimensional space, which could only be proven three-dimensionally in 1998 through huge computer calculations.*

*Maryna caused a sensation in the world of modern mathematics with her original and amazingly simple calculation of the densest sphere packing in the much more complex 8th and 24th dimensions – the latter in cooperation with a research group. *

*The way spheres are packed in these particular dimensions is remarkably symmetrical, and uses the E8 and Leech lattices, respectively. *

###### (EPFL)

*The result in eight dimensions had been suggested by earlier work of Henry Cohn and Noam Elkies, who had conjectured the existence of a certain special function that would force the optimality of the E8 lattice. Maryna’s construction of the function involved the introduction of unexpected new techniques and establishes important connections with number theory and analysis.*

She subsequently adapted her method in collaboration with Cohn, Kumar, Miller and Radchenko to prove that the Leech lattice is similarly optimal in twenty-four dimensions.

###### (CMI)

*Research results on sphere packing in high-dimensional spaces also have practical applications in everyday technology. For example, in the analysis of crystal structures or in troubleshooting signal transmission of mobile phones, space probes or internet connections. While work on these two dimensions had previously been based on hypotheses, Maryna Viazovska’s exploit delivered the mathematical proof and is already being used in efforts to solve fundamental problems in applied mathematics*.

###### (EPFL)

#### SwissMAP

Both, Hugo and Maryna have been part of SwissMAP since the first phase of the project. Hugo joined our Statistical Mechanics project led by Stanislav Smirnov (UNIGE) at the very beginning of the program in 2014. Former master student to Wendelin Werner (ETH Zurich), former PhD student of Stanislav Smirnov (UNIGE) and a close collaborator of Ioan Manolescu (UniFR) and Vincent Tassion (ETH Zurich), Hugo has greatly contributed in our mission to promote collaborative research.

*Hugo is honoured and extremely proud to receive this Fieds Medal. “I want to share it with all my colleagues because mathematics is above all a collaborative process.”*

###### (UNIGE)

Furthermore, Hugo is also involved in the SwissMAP area of education and outreach. One recent example is the public talk he gave during the 2021 Colloque Wright: Does randomness really exist?

Upon her arrival at EPFL in 2017, Maryna joined SwissMAP as part of the Geometry, Topology and Physics project led by Rahul Pandharipande (ETH Zurich). Maryna has been colloquium speaker at the SwissMAP Annual General Meeting and contributed to our SwissMAP Perspectives Journal.

Furthermore, open questions regarding asymptotic sphere packing density will be one important collaborative research topic of SwissMAP's third phase, led by Maryna's group.

#### Six Fields Medalists

Hugo and Maryna’s recognition brings the number of Fields Medalists within the SwissMAP consortium to six: Hugo Duminil-Copin (UNIGE) & Maryna Viazovska (EPFL) 2022; Alessio Figalli (ETH Zurich) 2018; Artur Avila (UZH) 2014; Stanislav Smirnov (UNIGE) 2010; Wendelin Werner (ETH Zurich) 2006. These prizes further reinforce the excellence of SwissMAP’s research.

We rejoice today with Hugo and Maryna and look forward to their undoubtably many further contributions to mathematics.

### IMU Award Ceremony 2022

###### Photo: UNIGE

The talk by Hugo Duminil-Copin on 13th of July at UNIGE is available online in English and in French. Hugo spoke to us about his life, his research and also about the challenges he had to face.