Prof. Irit Dinur

Department of Applied Mathematics and Computer Science, Weizman Institute of Science, Israel

Topic: Expanders in High Dimensions

Abstract:

Expander graphs have been studied in many areas of mathematics and in computer science with versatile applications, including coding theory, networking, computational complexity and geometry. High-dimensional expanders are a relatively new generalization to higher dimensions, namely to hypergraphs. These objects have already found new and exciting applications in the theory of Markov chains and in constructions of error-correcting codes with new properties.
In the sequence of talks we will start with an introduction to the topic and present the basic definitions of high dimensional expansion, including link-expansion, random-walk expansion, and coboundary / cosystolic expansion. We will talk about one of the key features of high dimensional expanders (HDXs): local-to-global. This feature often allows one to deduce global properties (such as expansion) from local behavior. We will present some of the beautiful constructions of sparse HDXs coming from group theory and number theory. Finally, we will discuss how the local-to-global properties are used for proving some of the main results in this area.

Bio:

Prof. Irit Dinur received her PhD in computer science in 2001 from Tel-Aviv University. She conducted postdoctoral research for three years, first at the Institute for Advanced Study in Princeton, then at NEC Research Institute, and finally at the Miller Institute at the University of California at Berkeley. From 2004 to 2007, she was a senior lecturer at the Hebrew University of Jerusalem. She joined the faculty of the Weizmann Institute in October 2007, where she now holds the Moross chair.
Prof. Dinur is interested in theoretical computer science, and especially in error-correcting and probabilistically checkable proofs, both of which capture a certain “robustness” in computation. Currently, she is interested in connecting these to so-called high-dimensional expansion—an analogue of expander graphs that draws on group theory, topology, and combinatorics.
Prof. Dinur was a plenary speaker at the International Congress of Mathematicians in 2010, and is the recipient of the Kannelakis Award (2022), Gödel Award (2019), the PODS Test-of-Time Award, the Erdős Prize in Mathematics (2012), the Yad Hanadiv Bruno Research Award (2007), and the Nessiyahu Prize in 2003 for the best PhD thesis in mathematics in Israel. She delivered the Hermann Weyl Lectures at the Institute for Advanced Studies in Princeton (2019) and was a visiting professor there from 2019-2020. She was the William Bentinck-Smith Fellow at Harvard University from 2012-2013.