Date/Time
28 February 2027 - 5 March 2027
Organized by
Asaf Shapira (Tel Aviv U.) and Benjamin Sudakov (ETH Zurich)
Event page & registration
https://indico.global/event/16539/
Description
Extremal and Probabilistic Combinatorics explores the relations between different parameters of various discrete structures, such as graphs, set systems, permutations, and boolean functions. While this area emerged as a collection of unrelated problems around a century ago, it has since been structured into well-defined subareas, each with its own established sets of tools and techniques. The past 2 decades in particular have seen tremendous growth, and this has borne fruit recently in an exciting series of generational breakthroughs. Our workshop aims to sustain and further this momentum.
Tools from other areas of mathematics have always been used to solve problems in combinatorics. More recently, in a hugely important trend, the ideas from combinatorics have been applied to solve several fundamental problems in other areas of mathematics. This meeting aims to explore several recent developments that exchange ideas in each direction, under the following four main topics.
- Expanders: Expanders are remarkable constructs that have been used in various areas of mathematics. Several surprising recent applications show that they still have much to offer.
- Extremal graph theory: The study of problems in this area has recently led to significant progress on problems in number theory.
- Ramsey theory: The past 2-3 years have seen extraordinary breakthroughs on some nearly century-old problems.
- Latin squares: Despite being studied since Euler’s work in the 18th century, the last few years have seen tremendous progress, including the resolution of several long-standing conjectures.
Location
SwissMAP Research Station, Les Diablerets, Switzerland
