image: László Erdős (left) and Horng-Tzer Yau (right) are the winners of the 2017 AMS Leonard Eisenbud Prize for Mathematics and Physics. view more
Credit: László Erdős and Horng-Tzer Yau
László Erdős of the Institute of Science and Technology Austria and Horng-Tzer Yau (of Harvard University will receive the 2017 AMS Leonard Eisenbud Prize for Mathematics and Physics. The two are honored "for proving the universality of eigenvalue statistics of Wigner random matrices."
A matrix is a two-dimensional array of numbers. For example, data about the height and weight of members of a certain population could be arranged as entries in a matrix. Matrices are used across all areas science and engineering to represent quantitative information. Their spectrum, or eigenvalues, comprise the essential properties of these data.
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. Wigner's insight has turned out to be very useful and has been verified in many different experimental situations. Nevertheless, scientists still cannot prove exactly why it models physical reality so well.
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 Yau settled in their prize-winning work, an amazing feat that has received wide acclaim from scientists and mathematicians.
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, 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.
Born in Taiwan in 1959, Horng-Tzer Yau received his B.Sc. in 1981 from National Taiwan University and his PhD in 1987 from Princeton University. The following year, he joined the faculty of the Courant Institute of Mathematical Sciences at New York University. In 2003, he moved to Stanford University and then in 2005 assumed his present position as professor of mathematics at Harvard University. He was a member of the Institute for Advanced Study in Princeton in 1987-88, 1991-92, and 2003, and was an IAS Distinguished Visiting Professor in 2013-14. Yau was elected to the US National Academy of Sciences (2013) and received a MacArthur Foundation "genius" award (2000).
Presented every three years, the AMS Eisenbud Prize recognizes a work or group of works that brings mathematics and physics closer together. The prize will be awarded Thursday, January 5, 2017, at the Joint Mathematics Meetings in Atlanta.
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Find out more about AMS prizes and awards at http://www.ams.org/profession/prizes-awards/prizes.
Founded in 1888 to further mathematical research and scholarship, today the American Mathematical Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.