Dr. Maryna Viazovska from Humboldt Universität Zu Berlin recently published two papers in which she puts an end to a nearly 400 year old mathematics conjecture. The Sphere Packing Problem in Dimensions 8 and 24 were released just two weeks apart from each other in March 2016 after years of hard work and a particular obsession by number theorist Maryna Viazovska, who couldn’t let go of the final solution for this conjecture, at first posed by Johannes Kepler in 1611.
The sphere packing problem in dimension 8 – A brief explanation
In mathematical language: we know what 8th dimensional space is and we know how many 8th dimensional spheres there are. So, now we want to fill the space with as many spheres as possible.
For a long time, it was believed that the best way to do that was to arrange the spheres in order to match the center with nods of E8 lattices. And because this is such a symmetric and dense construction, everyone believed that no other model could be better. However, the problem with 8th dimension is that you have infinite spheres and 8th dimensional space with an infinite amount of different possibilities, making it difficult to exclude all of them.
But what Elkies and Cohn discovered in 2003 is that this problem can be translated into a language of free analysis and if you find the magic function that has certain special properties, it will sort every packing problem. So what I did in my research was look for this function explicitly and I was able to find it. Therefore, what we know now is that the best way to pack spheres is to do it in this E8 Lattices Packing.
What was the starting point for your research?
Some years ago, a collaborator showed me the Elkies and Cohn paper and it occurred to me that the solution was just a function away. Unfortunately, our first attempts didn’t work out and my collaborator decided to move on to another project. But as a Number Theorist, who likes special numbers and functions, not finding this one really bugged me. The problem wouldn’t let me go so after a couple of years I fashioned a way to find it and, luckily for me, it worked out well.
From May 12th to May 14th you will be attending Moduli and Automorphic Forms:
a Meeting for Women in Mathematics. What do you expect from it?
I will attend as a listener but not as a speaker. Mostly, I hope to meet my friends as it gets hard to find the time to see colleagues with whom I have formed close ties with over the years. The atmosphere there is friendly. Furthermore, the organizer of this event is a friend of mine who I met when we coincided in Berlin but now she works in Darmstadt, so it will be nice to spend time with her and some friends from Ukraine who are attending as well.
This event calls attention to equal rights, not unlike the European Women in Mathematics
organization. Do you find your field of study to be misogynist?[1]
I was talking to a friend of mine recently and she made me realize that the number of female mathematicians in European countries tends to vary. The reason for that can’t be that mathematics is a masculine discipline because it is a universal science. I think that it is possible that the existence of a stereotype is one of the roots of the problem for having less women in mathematics. The only way to change it is through education as it is not a problem exclusive to mathematics but a universal issue.
[1] According to EWM in 2005 only 14,6% of mathematicians were women in Germany : source http://www.europeanwomeninmaths.org/sites/default/files/documents/history_d/womeninmathineurope.pdf
