The László Fejes Tóth Medal will be awarded on November 10 in the Main Lecture Hall of the Rényi Institute. This year's recipient is Maryna Viazovska, professor at the École Polytechnique Fédérale de Lausanne and winner of numerous prestigious mathematics awards, including the Fields Medal.
Programme:
14:15 Lecture by Maryna Viazovska
15:15 Presentation of the László Fejes Tóth Medal
Title: Polynomial Freiman-Ruzsa, Reed-Muller codes and Shannon capacity
Abstract: In 1948, Shannon used a probabilistic argument to show the existence of codes achieving a maximal rate defined by the channel capacity. In 1954, Muller and Reed introduced a simple deterministic code construction, based on polynomial evaluations, conjectured shortly thereafter to achieve capacity. The conjecture led to decades of activity involving various areas of mathematics and was finally settled in 2023 by Emmanuel Abbe and Colin Sandorn. In this talk, I will present an alternative proof of the weak form of the capacity result, i.e., that RM codes have a vanishing local error at any rate below capacity. Our proof puts forward a connection with the recent proof of the Polynomial Freiman-Ruzsa conjecture and an entropy extraction approach. Further, a new additive combinatorics conjecture is put forward, with potentially broader applications to coding theory and, in particular, the stronger result of a vanishing global error for RM codes. This is joint work with Emmanuel Abbe, Colin Sandon, and Vladyslav Shashkov.
The László Fejes Tóth Award and the accompanying medal were established by the HUN-REN Rényi Institute in 2023. This initiative by the Institute pays tribute to both the world-class geometer and the second director of the Rényi Institute, who held this position for 13 years from 1970 to 1983. With this award, the Institute aims to recognize significant mathematical achievements in the field of geometry (in the broadest sense) on an international scale each year.
Former laureates:
- László Lovász (2024)
- Endre Szemerédi (2025)
László Fejes Tóth was born in Szeged in 1915, graduated from Pázmány Péter University (now ELTE) in 1938 under the supervision of Lipót Fejér, and published his first paper in 1935 in the proceedings of the French Academy of Sciences on an analytic problem. He joined the faculty of the University of Kolozsvár in Transylvania, and returned to Budapest in 1944 to teach mathematics at the Árpád Gimnazium. From 1949 he became a professor at the University of Veszprém (now Pannon Egyetem) for 15 years, and joined the faculty of the Rényi Institute (then Mathematical Institute of the Hungarian Academy of Sciences) afterwards. He was the director of the Institute for more than a decade in the 1970's. He became member of the Hungarian Academy of Sciences in 1962. Professor Fejes Tóth received numerous distinctions, among others the Kossuth Prize, the State Award and the Gold Medal of the Hungarian Academy of Sciences in 2002. He passed away shortly after his 90th birthday, in 2005. He left a profound mathematical legacy not only through his papers, results and theorems, but through a still blossoming mathematical school of discrete geometry at the Rényi Institute.
A recording of János Pach’s lecture on the life and legacy of László Fejes Tóth is available at this link.