The Institute of Science and Technology Austria (IST Austria) has been informed by the European Research Council that Professor Laszlo Erdös has been awarded an ERC Advanced Grant. The grant for Erdös who works on the mathematics of disordered quantum systems and matrices is funded with € 1.75 mio for the duration of five years. This is the 13th ERC grant for the IST Austria faculty of 29 professors.

President Thomas Henzinger expressed his appreciation: “The ERC grants are an undisputed benchmark for excellent research in Europe. This distinction highlights the attraction that IST Austria presents for such outstanding scientists as Laszlo Erdös. I congratulate him on this success and look forward to his future contributions.” IST Austria professors have so far acquired € 33.4 mio in research grants, 85% coming from sources outside of Austria.

Mathematician Laszlo Erdös will tackle the universality of the random matrix theory (RMT). RMT reaches back to a ground-breaking vision of the Nobel-prize winning physicist Eugene Wigner in the 1950s. Trying to calculate the spacings of energy levels of the nuclei in heavy atoms, Wigner proposed to replace the several hundred dimensional quantum model, leading to an intractable calculation, by a much simpler matrix, in which numbers are filled in at random – a so-called random matrix. Surprisingly, this much simpler model had the same qualitative and quantitative properties, and allowed Wigner to reproduce the statistics of the energy level spacings in uranium. Although experimental data leave no doubt that Wigner’s substitution is correct, the reason for why it works is still not fully understood. Nevertheless, RMT has since been used to find patterns in huge amounts of data, even in stock market trends.

In his ERC-funded project, Laszlo Erdös asks whether the reduction by Wigner is justified not just by experimental evidence or physics arguments, but also with mathematical rigour. Extending RMT to other physical systems and looking for universality in them, Laszlo Erdös intends to move the simplified random matrix model back towards the original object of research from physics. At the same time, he asks whether the random matrix model is also underlying other physical models, and whether the “intermediate” approaches he develops may be used to mathematically solve other long-standing questions in physics, such as the metal-insulator transition in the Anderson model. The mathematical ideas and tools developed as part of Erdös’ work will extend RMT, and are likely to be used in its many applications, such as network analysis, information theory and other fields of physics.

Laszlo Erdös** **studied mathematics at the Loránd Eötvös University in Budapest, and earned his PhD at Princeton University in 1994 under the supervision of Elliott H. Lieb. After holding junior positions at ETH Zurich and the Courant Institute (NYU), he stayed at the Georgia Institute of Technology, Atlanta, for five years, moving through the ranks from Assistant to Full Professor. Laszlo Erdos took up a Chair in Applied Mathematics at the Ludwig Maximilian University, Munich in 2003 and joined IST Austria in 2013.

ERC Advanced Grants allow exceptional established research leaders of any nationality and any age to pursue ground-breaking, high-risk projects that open new directions in their respective research fields or other domains. The ERC Advanced Grant targets researchers who have already established themselves as independent research leaders in their own right.

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