Max Planck Institute for Mathematics

Geordie Williamson, advanced researcher at the Max Planck Institute for Mathematics, has received one of the this year's prestigious EMS prizes for outstanding young researchers. The prize was awarded „for his fundamental contributions to representation theory of Lie algebras and algebraic groups, for example, with the elegant proof of Soergel’s conjecture on bimodules associated to Coxeter groups and the counter-examples to expected bounds in Lusztig’s conjectured character for rational representations of algebraic groups.“ His results include proofs and re-proofs of some long-standing conjectures, as well as spectacular counterexamples to the expected bounds in others. The prize was awarded during the 7th European Congress of Mathematics last month in Berlin.

Maryna Viazovska and Danylo Radchenko, who both wrote their PhD thesis at the Max Planck Institute for Mathematics under the supervision of Don Zagier, were recently interviewed by the Ukranian branch of Deutsche Welle for their exciting new work on the centuries old Kepler problem. (Interview in Ukrainian language)

Danylo Radchenko, PhD student at the Max Planck Institute for Mathematics and the Bonn International Graduate School for Mathematics, on the famous sphere packing problem, his contribution to the proof in dimension 24, and on being a PhD student in Bonn.

You are co-author of a paper about the sphere packaging problem in dimension 24. Let’s start from the scratch: What’s the sphere packing problem about?

This problem goes way back to 1611 when Johannes Kepler discussed the question how to stack cannon balls most efficiently. He found the answer, but he couldn’t prove it. This is why it’s called the “Kepler conjecture”. Since then, physicists have been working with his solution. But for mathematicians it’s not enough to know the answer, we also have to find a way to deduce logically why it is indeed correct. The solution is actually pretty simple. Almost everyone will find it intuitively if you give them a bunch of balls and some time. But the mathematical proof of this is highly complex. Even for a normal three dimensional room, the proof was found only in 1998 by Thomas Hales.

Geordie Williamson, advanced researcher at the Max Planck Institute for Mathematics in Bonn will be awarded the 2016 Clay Research Award in recognition of his groundbreaking work in representation theory and related fields.

In particular, the award recognises two major breakthroughs. First, his proof, with Ben Elias, of Soergel’s conjecture on bimodules associated to Coxeter groups. This established the combinatorial result that the coefficients of the Kazhdan-Lusztig polynomials are non-negative, as well as yielding a new proof of Kazhdan and Lusztig’s conjectured character formula for representations of complex semi-simple Lie algebras.

The second is the construction (building on earlier work with Ben Elias and Xuhua He) of counterexamples to the expected bounds in Lusztig’s conjectured character formula for rational representations of algebraic groups in positive characteristics that grow exponentially with the rank of the group.

The awards will be presented at the 2016 Clay Research Conference at Oxford on Wednesday, 28 September.