Avner Magen Memorial Lecture Day

The geometric point of view has been one of the most interesting and fruitful perspectives of combinatorics in recent years. This was also a major theme in Avner Magen's work. When viewed this way, many of the fundamental objects we study in combinatorics turn out to be "one-dimensional". Moreover, they often have interesting high-dimensional counterparts which are much less understood. The study of these high-dimensional objects is challenging and fascinating. Thus, two of the main pillars of modern combinatorics are extremal graph theory and the theory of random graphs. This suggests the study of analogous questions on higher-dimensional simplicial complexes. The various definitions of a tree have high-dimensional counterparts, which are, however, no longer equivalent. In the main technical part of this talk I will explain recent work with Zur Lurias about higher-dimensional permutations and their enumeration.