January 9, 2017

# László Erdős receives Leonard Eisenbud Prize

## Together with Horng-Tzer Yau (Harvard University), László Erdős (IST Austria) is honored by the American Mathematical Society "for proving the universality of eigenvalue statistics of Wigner random matrices." · Price awarded on January 5, 2017

In the 1950s, physicist Eugene Wigner, who would go on to win the Nobel Prize, was studying energy levels in atomic nuclei. Because it was not possible at that time to predict these energy levels based on fundamental physical principles, Wigner represented their statistical behavior by the eigenvalues of a matrix in which the entries were chosen at random. This was an extraordinary leap of intuition. Since that time, random matrices have been used across many areas of physics and, more recently, in such areas as statistical analysis, finance, wireless communications, and materials science. These developments, together with mysterious connections observed between random matrices and prime numbers, have led to the burgeoning of random matrix theory as a major subject within mathematics.

There are many different ways of randomly choosing the entries in a random matrix. In simulations of large random matrices, researchers observed the same statistical patterns emerging from the matrices, regardless of which way was used for the random choice of the entries. These patterns seemed to be “universal,” and the question of whether the observations could be nailed down in a mathematical proof became known as the “universality conjecture.” It is this conjecture that Erdős and his former postdoctoral advisor and long term collaborator Yau settled in their prize-winning work, an amazing feat that has received wide acclaim from mathematicians and other scientists.

Born in Budapest in 1966, László Erdős completed university education in mathematics at the Lorand Eötvös University in 1990 and a PhD at Princeton University in 1994. After postdoctoral positions in Zurich and New York, he joined the faculty at the Georgia Institute of Technology. In 2003, he was appointed to a chair professorship at the Ludwig-Maximilian University in Munich. Since 2013 he has been a professor at the Institute of Science and Technology Austria (IST Austria), near Vienna. He was an invited speaker at the International Congress of Mathematicians (2014), and is a corresponding member of the Austrian Academy of Sciences, an external member of the Hungarian Academy of Sciences, and a member of the Academia Europaea. “It is a great pleasure and honor to be selected as a co-recipient of the 2017 Leonard Eisenbud prize. I am grateful to the committee for this recognition of our work,” he says.

Presented every three years, the AMS Eisenbud Prize recognizes a work or group of works that brings mathematics and physics closer together. The story of the Wigner conjecture is a textbook example of synergies between the two fields: “Wigner posed a question from physics, in this case the statistics of energy levels of nuclei, had the ingenuity to raise it to a high level of abstraction and formulated a conjecture that actually made very much sense in pure mathematics as well. This is because he had the intellectual courage, he valued mathematics as well and he was looking for unifying principles in physics,” explains Erdős. About 20 years later, Freeman Dyson, an outstanding visionaire of mathematical physics, had the insight that Wigner’s conjecture may be proven in a dynamical way — a new approach. But the mathematical tools were missing and hence practically no progress was made for almost 50 years until Erdős and Yau settled the problem.

The prize was awarded Thursday, January 5, 2017, at the Joint Mathematics Meetings in Atlanta.