Combinatorics

Abstract

Combinatorics is a thriving branch of Mathematics with strong links to other areas of Mathematics and the sciences. Many of the modern techniques employed in Combinatorics draw on diverse ideas from Probability, Analysis, Geometry, Topology, and conversely, combinatorial approaches often lead to new insights in these other areas, and in the broader scientific arena (particularly Theoretical Computer Science). The most recent years in Combinatorics have been particularly exciting with spectacular solutions of many longstanding open problems, via an array of new ideas that promise to have many future applications. Leading experts and new talents came together to share and further develop these exciting ideas. Talks emphasized recent breakthroughs in discrete geometry, graph theory, combinatorial applications in Fourier analysis, group theory, combinatorial probability, Ramsey theory, nonabelian additive combinatorics, and design theory.