Geometry and Topology Seminar
Wednesday, 15 March 2023, 2.30 pm
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Venue: Ramanujan Hall
Host: Sandip Singh
Speaker: Arghya Mondal
Affiliation: CMI, Chennai
Title: A higher dimensional generalization of Margulis' construction of expander graphs
Abstract: Expanders are a family of finite graphs whose vertex sizes go to infinity but edge sizes grow at most linearly in vertex sizes, while still remaining highly connected. The first explicit construction of such graphs was by Margulis using discrete groups having Property (T), a rigidity property defined in terms of unitary representations. In recent years various higher dimensional generalizations of expanders, replacing graphs by simplicial complexes of a fixed dimension, have been considered. We will discuss a group theoretic construction of one such generalization, which is an extension of Margulis' construction to higher dimensions.