Date/Time
26 January 2025 - 31 January 2025
Organized by
Asaf Shapira (Tel Aviv University), Benjamin Sudakov (ETH Zurich).
Event page & registration
https://indico.cern.ch/event/1369791/
Description
Problems in Extremal and Probabilistic Combinatorics seek to understand the maximum/minimum value attainable by one parameter of a discrete structure assuming only the value of another parameter of that structure. The discrete structure can be either deterministic, or drawn from some distribution. For example, the discrete structure can be a graph, and the question can be: what is the maximum number of edges assuming the graph is triangle free. It can also be a uniformly random matrix and the question is the probability of it being singular. This field experienced a recent Decennium Mirabilis with the solution of several long standing open problems. In addition to being fundamental in its own right, the subject is an essential component of many other branches of mathematics and the part of mathematics most relevant to theoretical computer science. The main goal of this workshop is to provide a survey of the most recent advances in this area. The workshop will pivot on the following main topics.
• Ramsey Theory: This area has seen tremendous recent progress, especially the new bounds for diagonal and off-diagonal Ramsey numbers.
• Random Graphs: One of the most important advances in this area is the resolution of the Khan-Kallai conjecture, which led to several other landmark results.
• Tiling Problems: Several old conjectures in this area have been resolved in the past decade, most notably the existence of designs. The tools developed in this area, such as variants of the absorption method, have and will have major ramifications.
Location
SwissMAP Research Station, Les Diablerets, Switzerland
