2022 Fields Medals: a brief summary

If you didn’t have the opportunity to look into this yet, the 2022 Fields Medalists are: Hugo Duminil-Copin, June Huh, James Maynard, and Maryna Viazovska. Maybe "if all you have is a hammer, everything looks like a nail", but this year I'm excited to see a lot of combinatorics*.

Duminil-Copin worked on phase transitions in statistical physics. Roughly speaking, some of his major results are connected with “probability on graphs”. See, A new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model. The paper starts with "Let G = (V, E) be...", which for aficionados of Graph Theory is a treat.

June Huh's most well-known paper is Hodge Theory for Combinatorial Geometries. What is the paper about? Matroids! These are models for independence in vector spaces and graphs. "Most important for our purposes is the work of de Concini and Procesi on certain “wonderful” compactifications of hyperplane arrangement complements".

For James Maynard, see this gem in number theory: Small gaps between primes. Maybe not so combinatorial. I wish I could understand it though.

Maryna Viazovska's The sphere packing problem in dimension 8 has an essential abstract: "In this paper we prove that no packing of unit balls in Euclidean space R^8 has density greater than that of the E_8-lattice packing." The proof of the theorem is based on linear programming bounds, something that brings straight back to Error Correction or Discrete Optimization.

* My small personal hammer when I was actively enjoying scientific research.