Fields Medal: Hugo Duminil-Copin

so [Music] [Music] smartness is not that relevant for being creative in math it's more about your experience and your sensibility these things are going to shape your vision of the world and it's going to make you think about something that somebody else would never think about it is important that everybody finds what he likes in life i'm very lucky i'm doing a job that i enjoy my work and my passion are the same thing so i hope i can show how beautiful math is and how amazing being a mathematician is [Music] i'm currently a professor

at the university of geneva for me math is really something that i share with people when learning mathematics we are told not to make mistakes but that doesn't match my experience as a mathematician i cannot tell you the number of wrong arguments i describe to my collaborators but often they just bounce on it and realize that this is saying something else they say you know no your thing is wrong but look if you modify it then it's saying something interesting making mistakes is just an important component of the creative process and you have to teach

younger people how to accept that once they start to get it must become more joyful statistical physics is about deriving global properties of a huge system by analyzing the interactions between its tiny constituents when you try to do so you realize that these systems are extremely complex think of a fountain if there is wind everybody knows that the water is pushed in its direction but there is no way you can track the behavior of each drop of water so what do you do instead of trying to understand the behavior of each drop you look at

the probability of how the drops behave and by forgetting this hopeless quest of understanding the entire system you can do something simpler which is to look at what is the typical behavior of the system what is true for fountains is also true for other phenomena and the one that is dear to me is a question of magnetism magnets are made of tiny constituents we call dipoles and their interaction is extremely complex so again you use probability to construct a system and this is called the easing model now there have been thousands of papers on this

model but most of them were not dealing with the dimension of real magnets my co-authors and i developed a new probabilistic insight based on what is called percolation theory its aim is to understand the phenomenon of a liquid moving through something like water over rocks it turns out that these properties are linked to the dipoles in the easing model imagine you put a bottle of water in your freezer when it reaches zero degrees the volume changes and the bottle explodes this is a discontinuous phase transition for magnetization things are different imagine you pick a magnet

on your fridge and you hate it the strength will decrease continuously until it reaches zero at what we call the critical temperature your magnet won't stick to the fridge anymore it's an example of a continuous phase transition it's what you see in your everyday life but it's very difficult to prove mathematically but using percolation theory we did finally answer this question in this three-dimensionalism the most beautiful thing is that you can apply percolation to very general statistical physics systems of course it comes at a cost which is that the percolation models are more and more

complicated that's why it's very important to me to keep trying to discover new mechanisms in percolation in order to build the most general and robust theory possible i'm also a permanent professor at the institute the authentic scientific i was raised in bursurivet where the institute is so it's a little bit like getting back home the institute has been one of the most important places for the development of algebraic geometry being the first professor in probability means that i should also make this place an important place for probability itself after i arrived at the institute we

put blackboards outside in the park when you work in nature part of your body is just not really with you it's in the place where you are and the other part which is the one doing math is somehow doing it better as a young mathematician i was super enthusiastic always doing research sometimes not managing to find sleep i was just too much into it but then my wife severine and my daughter anna came and they showed me how to you know sometimes step back and enjoy these other things that are outside of math it changed

me as a mathematician [Music] i had less time but it was better time [Music] seven teaches philosophy and french in high school we have been living in france next to geneva for many years [Music] my work is crucial i love my work i live for my work but i also live for the rest of my life and i never want that to change [Music] you