Sarnak's research reached its peak in 1999, in his foundational work together with N. Katz, on the statistical properties of "low-lying" zeros of families of functions - L.
The Wolff Prize Committee in Mathematics for the year 2014 - XNUMX unanimously decided to award the prize to Prof. Peter Sarnak, Princeton University, New Jersey, USA, for his profound contributions in analysis, number theory, geometry and combinatorics.
Dr. Liat Ben David, Executive Director of the Wolf Foundation, said that when she called Prof. Sarnak to inform him of his selection, it turned out that he was staying for his research at the Hebrew University, and for the first time in the history of the Wolf Prize, the winner was also invited to the announcement event and not just to the prize distribution event.
Prof. Sarnak is a mathematician with a far-reaching vision of a very broad spectrum of mathematical topics. He influenced the development of several fields in mathematics, often by revealing deep connections, which no one suspected existed. In analysis, he studied in a series of fundamental papers, eigenfunctions of quantum-mechanical Hamiltonians, corresponding to classical, chaotic dynamical systems. Sarnak formulated and provided evidence supporting the quantum ergodic unit hypothesis, which states that all eigenfunctions of the Laplacian on sheets of negative curvature are uniformly distributed in phase space. He introduced tools from number theory in this field, and these helped him achieve results, which until then were considered out of reach, and paved the way for many more advances, especially in the recent works of Alon Lindenstrauss and N. Anantharaman.
In Sarnak's work (together with Z. Rudnik) on L-functions, the connection between the current research in automorphic patterns and the theory of random matrices and the Riemann hypothesis was raised to a new level by calculations of high-order correlation functions of the Riemannian zeros. This is a major step forward in the study of the connection between the theory of random matrices and the statistical properties of the zeros of the Riemann zeta function, a connection as already pointed out by Montgomery and A. Odlitzko.
Sarnak's research reached its peak in 1999, in his foundational work together with N. Katz, on the statistical properties of "low-lying" zeros of families of functions - L.
Sarnak's work (together with A. Lubotsky and R. Phillips) on Graffi Ramanujan had a huge impact on combinatorics and computer science. Here, he again used profound results from number theory to achieve new and surprising advances in another mathematical field.
With his insights and willingness to share his ideas with others, Sarnak has inspired students and fellow researchers in many areas of mathematics.
About Prof. Sarnak in the Hebrew Wikipedia
The winners of the 2014 Wolf Prize in Arts and Sciences have been announced
12 תגובות
Eigenfunctions are the solutions of quantum problems formulated by quantum equations of the particle/problem.
The eigenfunctions were also suitable as solutions to deterministic quantum problems. The Hamiltonian is an energy expression that expresses the dynamics of the problem in the quantum equation. There is another type of problem where the problem is chaotic. The first time it is probabilistic in the sense of quantum uncertainty. The second time the dynamics are non-linear and then a small shift completely changes the probabilistic solution. A set of random matrices (the Hamiltonians) is obtained.
Ergodicity is that a system of particles passes in a very short time in all its possible states, for example in space or energy values, angular momentum, momentum. An ergodic system is a system that goes through all its possible Hamiltonians, so that the different dynamics can be described as a statistical distribution.
Laplacean is a motion operator that has an energetic expression of the quantum problem. Sheets with negative curvature: in the space of possible energy solutions for the same particle for example. If, as the energy increases, the momentum decreases, for example.
The phase space - instead of (x,y,z,t) space, it is energy space, momentum. In multi-particle systems it is more natural to describe particles as occupying values of energy, momentum and not space-time. The statistical distribution of the particles is in the energy space, momentum = phase. The innovation of the problem is that Sarnak offers a treatment of a multi-particle system that can accept many states - the choice between them is chaotic. If their choice happens too quickly for us to notice the system is ergodic and it is possible to give a known statistical distribution (called Poisson) to all situations, and calculate the behavior of the space of all possibilities.
Can you clarify the sentence:
"Research in a series of fundamental papers, eigenfunctions of quantum-mechanical Hamiltonians, suitable for classical, chaotic dynamical systems. Sarnak formulated and provided evidence supporting the quantum ergodic unit hypothesis, which states that all eigenfunctions of the Laplacian on sheets of negative curvature are uniformly distributed in the phase space.
??
The average person (also with an academic mathematical education) has more unclear words than clear ones...
I entered their book. Every day looks more exciting. Physical mathematics and probability theory. Just look up the basic concepts there in Wikipedia. Even things that Dr. Nachmani sometimes talks about such as (statistical physics) in graphene, etc. make use of it.
More research on the world of low zeros..
http://www.youtube.com/watch?v=v-KwnV9lXO8
And the obvious question is where in Israeli society can you find those low-lying zeroes.
And how high is this low?
I blushed when he published the work on the low-lying zeros. came up on me
This work was done with Nick Katz. Before them, in random matrix theory, they discovered empirically the distribution of the zeros of the Riemann zeta function. They analytically prove the distribution and also generalize it to a considerable group of holomorphic functions (I don't know what it is, but it's a term from abstract algebra that indicates a property that characterizes a group of objects. Their work seems to me, and maybe I'm wrong, to have an application in quantum field theory. I do this based on an interview article with Sarnak, based on an article of his from the present time and based on an abbreviation he used in a book that apparently does not mean quantum electrodynamics but QED.
Here is a link to their book that is a bit obscure so we can buy it
https://web.math.princeton.edu/~nmk/RMFEM.pdf
I found his works. looks serious The Wolf Prize usually precedes the Fields Medal for people under the age of 40. Why do you think you're a clown? Hash is editor-in-chief and faculty member at Princeton.
The comment above is puzzling. The award-winning man, member of academic committees and editor of 2 newspapers. Please give me a link to his work.
Unfortunately his theory does not hold water.
He is considered a clown in the scientific world