Abstract

As you all know, a tree is a graph that is connected and acyclic. From a topological perspective a graph is a 1-dimensional simplicial complex. Both notions of connectedness and acyclicity can be defined for higher dimensional simplicial complexes as well. This prompted Kalai (1983) to define the notion of a d-dimensional hypertree. There are still many things that we do not know about these fascinating objects. In this talk I will try to give you a glimpse of this domain of research. My lecture is based on papers with several collaborators: Roy Meshulam, Yuval Peled, Yuri Rabinovich, Tomasz Luczak and students: Lior Aronshtam, Mishael Rosenthal, and Amir Dahari

Speaker Intro

Nati Linial is a Professor of Computer Science and Mathematics at the Hebrew University of Jerusalem. He works in Combinatorics, Theory of Algorithms, Applications of Geometry and Analysis to these fields and Computational Molecular Biology. He gave an invited talk in the Combinatorics section at the International Congress of Mathematicians (ICM) in 2002 and is a fellow of the American Mathematical Society (AMS). Professor Linial is a recipient of the Inaugural FOCS ”Test of time” Award, the Rothschild Prize in Mathematics and Computer Science, the Dijkstra Prize and the Conant Prize of the American Mathematical Society. He has co-authored more than 150 research papers.