Once every four years, the highest award of mathematics is announced!

Author:Institute of Physics of the Ch Time:2022.07.06

The Phils Award is one of the highest prizes in the field of mathematics. It is often called the Nobel Prize in the mathematical world and is awarded every four years. Just now, the Phils Award in 2022 was announced, and 4 young mathematicians were awarded 4 outstanding contributions to the field of mathematics (under 40 years of age).

(Photo / IHES)

Hugo Dimini-Copan changed the mathematical theory related to phase changes in statistical physics. He solved several long-term open problems, especially in the three-dimensional peace and four-dimensional and the unbearable situation in two dimensions. Down. His work has opened up several new research directions. Here we only list a small part of his many achievements in this field.

The most significant result of Dimini-Copan is the three-dimensional and four-dimensional Issin-shaped model. He established the continuity and sharpness of three -dimensional phase changes with the collaborators, which have been hanging and unjust since the 1980s. In the four -dimensional space, he and Aizenman proved the average critical behavior of the Issin model and proved the ordinaryness of the quantum field theory of four -dimensional Europe. Scholars' open conjecture.

Similarly, in the two-dimensional Futuyin Castrin infiltration, Dimini Kopan and the collaborators have proved the continuity or discontinuousness of all parameter values, as well as the radiation chart at the equal angle point Popularity of the critical Futuyin-Castorin model. In addition, by proved the large-scale rotation of the critical Futu-Castorin model, he took an important step towards the establishment of their large-scale common shape, which in turn can strictly and two for them to two. The world of Victoria's Field Theory provides important missing parts.

(Figure / Princeton University)

Using Hodg's theory, tropical geometry, and magical point theory, Xu Yan and his collaborators changed the field of geometric combination. Xu Yan and Wang Boyi used the tools of algebraic geometry and intersection theory to prove that the Daolin Wilson conjecture that can be used to realize.

Karim Adiprasito, Xu Jie and Eric Katz discovered the combination of Hodg theory, and proved the Leff Schind theorem and any of the arbitrarily arracks. Qi-Riemann Relationship. They used these results to solve the concave Heron Rota Welsh guesses of the characteristic polynomial polynomial.

Petter Brändén and Xu Yan developed the theory of Lorentz polynomial, which connected continuous and discrete convex analysis through tropical geometry. They proved the array of Johnson's conjecture and discovered a series of applications in different mathematical fields such as the Pots model from the shooting algebra to the statistical mechanics.

(Photo / Academia Europaea)

James Menard made amazing contributions in analytical theory. He often brings amazing breakthroughs on important issues that seem to be unable to use existing technology.

Some of the most famous issues in the theory are related to the distribution of prime numbers. Although the large -scale distribution of prime numbers is dominated by the element theorem (or more accurately, it is speculated by Riemann's conjecture), many natural problems are treated on the sparse scale. On such issues, Monad has achieved many significant results. For example, when he proves that when the prime sequence becomes more and more sparse, there will be "prime clusters" with an unlimited size M. In the boundary, this is a significant improvement of the results of the famous when M = 2. Menard's method is elegant and powerful, and it promotes the boundary of the sieve theory in a surprising way. Monad continued to prove in a seemingly opposite direction that sometimes the prime number is much more sparse than the average, which is an Eldsh issue that has not made any qualitative progress in decades.

Monad also did a basic work in the approach of throwing a picture. He and Koukoulopoulos resolved Dufen Shefver's conjecture. This conjecture was proposed in 1941 that it was considered to describe the ultimate promotion of Xin Qin's theorem that described a typical real number.

(Figure / EPFL)

A long -term problem in mathematics is to find the most dense way to fill the same sphere in a given dimension. People already know that the round hexagon filling is the densely densely complicated space. In 1998, Thomas Callister Hales proved Cairple's conjecture with a computer, that is, the filling of the face -to -face cube is the most dense in three -dimensional space.

Any other dimensions in any dimension have been in an unknown state. Until 2016, Viazovska proved that the E₈ grid has the most dense filling in the 8 -dimensional space. Soon after, she, with Cohn, Kumar, Miller, and Radchenko, proved that Lichig had the most densely filled in 24 dimensional spaces.

Viazovska's method is based on the work of Cohen and Elkies. They use Posonic and formulas to give any possible upper bounds of the sphere to fill in the sphere. Their work shows that in the 8 -dimensional and 24 -dimensional space, there may be a very special radial Schwaz function with a very special nature, which can give an upper boundary equal to the lower boundary of the known grid. Viazovska invented a new method of generating such functions based on pattern theory. Viazovska developed these ideas in other directions. She and Radqinko have proved an unexpected result that any Schwaz function disappeared at the square roots of each non -negative integage at the ingenuity of the Fourier, which must be zero. In fact, they prove that for some special functions AN and BN, any occasional Schwaz function can be written:

Together with Cohen, Kumar, Miller, and Radqinko, she proved that E₈ and Lichig not only gave up the best sphere to fill in the 8 -dimensional and 24 -dimensional, but also minimized each in the square distance. Energy of a monotonous potential function.