Department of Mathematics colloquium - Sibe Mardešić presents a sequence of lectures given by leading experts in the fields of theoretical and applied mathematics. The lectures take place at the Department of Mathematics, Faculty of Science, Bijenička cesta 30, Zagreb.

### Lecture announcement

**Time:**May 9, 2024 at 12:15PM

**Lecture room:**A102

**About the lecturer**: Benny Sudakov received Ph.D. in 1999 from Tel Aviv University under the supervision of Noga Alon. He was an instructor and an assistant professor at Princeton University and a professor at University of California, Los Angeles. He is currently a Professor of Mathematics at ETH in Zürich. He has versatile mathematical interests, solving open problems and publishing papers in extremal combinatorics, graph and hypergraph theory, Ramsey theory, random structures, and applications of combinatorics in computer science. He received many awards and distinctions for his work. He was an invited speaker at the International Congress of Mathematicians in Hyderabad in 2010. He is a Fellow of the AMS (since 2012) and a member of the Academia Europaea (since 2019). He will also be a plenary speaker at the European Congress of Mathematics in Sevilla this year. The arXiv server hosts 275 of his research papers and preprints, his Google scholar page counts more than 10,000 citations, while Math genealogy list 16 of his finished graduate students, several of them born in Croatia.

**Lecture abstract**: Every large system, chaotic as it may be, contains a well-organized subsystem. This phenomenon is truly ubiquitous and manifests itself in different mathematical areas. One of the central problems in extremal combinatorics, which was extensively studied in the last hundred years, is to estimate how large a graph/hypergraph needs to be to guarantee the emergence of such well-organized substructures.
In the first part of this talk we will give an introduction to this topic, mentioning some classical results as well as a few applications to other areas of mathematics. Then we discuss the recent solution (with Oliver Janzer) of the following fundamental problem, posed by Erdős and Sauer about 50 years ago: How many edges on n vertices force the existence of an r-regular subgraph (r>2)? Our proof uses algebraic and probabilistic tools, building on earlier works by Alon, Friedland, Kalai, Pyber, Rödl and Szemerédi.