Fields Medal: Maryna Viazovska

[Music] nothing in life comes for free we are all very adaptable we can manage a lot but it all somehow has its price i am from kiev ukraine and in february my life changed forever and not only for me but for everyone in the world and especially the people in my country whenever we have something good in our life often we take that for granted and peaceful is what i always took for granted [Music] now i understand how wrong i was about that i'm a professor of mathematics at epfl a ecole polytechnique federal dollars i'm

a chair of number theory what we are doing of course is shaping the future but maybe it will be used at 100 years from now but it's still important what we like about students is that they are young they are still enthusiastic they have a lot of energy and they believe in what is ahead of them i can tell them what my opinion is and a student would say like you know professor does not know what you're thinking about so maybe one advice for phd students is to okay at least give your advice or this

privilege of a doubt and i think this is advice which is good both for professors and for students i work on geometric optimization problems so sphere packing is a very natural geometric problem you have a big box and you have an infinite collection of equal balls and you're trying to put as many balls into the box as you can legend is that people are interested in is how many cannon balls can they pack into the ship so the answer for the cannonballs is as you see in a supermarket the orange is stuck in this pyramidal

shape so essentially this is the best possible packing but now we could also go to other dimensions and maybe here is a time to explain what are other dimensions if we are on the plane we would need only two coordinates to describe every point and on the line we need one number that if we are moving in a three-dimensional space we need three coordinates to describe every point like gps coordinates but as mathematicians we can go farther nothing stops us for introducing one more coordinate or 24 different coordinates for many years people thought about this

fair packing problem and developed many methods how to address it either you have to construct some object which is optimal or you have to show that nothing better can be done so in each dimension they found some bound however in dimensions 8 and 24 the bound came very very close to the actual density of known backings e8 packing in dimension 8 and leech lattice in dimension 24. so they realized there exists this magic function which is supposed to actually prove the optimality of specking my contribution was to give an explicit formula for the magic function

and this is what took from 2003 to 2016 like 13 years to find [Music] my parents and my two sisters normally live in kiev so when the war started i could not think about anything else including mathematics during those first days i realized how much i love teaching because on the very first day i had my first class here in the pfl of course when i'm in front of class i have to forget about everything else because i have to be very focused this made me to forget about this fear and pain inside myself [Music]

recently i dedicated a lecture to julius dinovska a young mathematician and computer scientist from harkef my teachers from kiev university were also her teachers julia was a person filled with light and her big dream was teaching mathematics to kids in ukraine during the first days of war she was killed in a missile attack on hercules when young people die you think okay what's the point of my work as teacher if young talented people are just wasted in this terrible war when someone like her dies it's like the future dies right now ukrainians repaying the highest

price for our beliefs and for our freedom i'm very happy that my sisters tanya and natasha vacated from kiev and are staying with my family as the war continues tanya has to separate with her husband and i know it is extremely difficult for her my niece and my nephew miss their dad a lot they understand what is happening now in ukraine and it is a lot to process for them my husband daniel is a physicist at the pfl daniel has a passion for photography thanks to his pictures we have a wonderful way to remember important

and happy moments of our lives [Music] the thing i like about kiev the most are the green parks and quiet places and the asian churches i understand that now there will be marks of war there and this is a scary thought but kiev is one of the eternal cities one day soon i hope to return [Music] you