Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: A higher dimensional analog of Margulis' construction of expanders
Speaker: Arghya Mondal, Chennai Mathematical Institute
Date: May 10, 2022
Time: 16:00:00 Hours
Venue: AG-77
Abstract: The first explicit example of a family of expander graphs was quotients of the Cayley graph of a group $G$, having Property $(T)$, by subgroups of finite index. This construction is due to Margulis, in a special case, and Alon-Milman in general. We will discuss a higher dimensional analog of this result that can be obtained by replacing 'expander graphs' by 'higher spectral expanders', 'group having Property $(T)'$ by 'strongly $n$-Kazhdan group' and and 'Cayley graph' by '$n$-skeleton of the universal cover of a $K(G,1)$ simplicial complex'. New examples of 2-dimensional spectral expanders are obtained using this construction.
Title of Talk: A higher dimensional analog of Margulis' construction of expanders
Speaker: Arghya Mondal, Chennai Mathematical Institute
Date: May 10, 2022
Time: 16:00:00 Hours
Venue: AG-77
Abstract: The first explicit example of a family of expander graphs was quotients of the Cayley graph of a group $G$, having Property $(T)$, by subgroups of finite index. This construction is due to Margulis, in a special case, and Alon-Milman in general. We will discuss a higher dimensional analog of this result that can be obtained by replacing 'expander graphs' by 'higher spectral expanders', 'group having Property $(T)'$ by 'strongly $n$-Kazhdan group' and and 'Cayley graph' by '$n$-skeleton of the universal cover of a $K(G,1)$ simplicial complex'. New examples of 2-dimensional spectral expanders are obtained using this construction.