Uploaded July 2026 | Updated September 2026, 3 days ago
The 25th Midrasha Mathematicae on Groups, Expanders and Codes -- Celebrating Alex Lubotzky's 70th birthday.
Day 5, Session 3
Speaker: Irit Dinur (IAS)
Title: High Dimensional Expansion and Local Testability
Abstract: High-dimensional expanders form a rich meeting point between group theory, topology, combinatorics, and theoretical computer science. They arise from highly structured geometric objects, such as Bruhat–Tits buildings and their finite quotients, while at the same time providing combinatorial models for robust local-to-global behavior. I will discuss this local-to-global philosophy through the lens of cocycle expansion: A foundational work of Kaufman Kazhdan and Lubotzky shows that under suitable expansion assumptions on the (local) links of a complex, one can deduce global cocycle expansion. I will describe how closely related ideas appear in the study of locally testable codes, where global errors are detected by local checks, and in agreement testing, where one asks whether many locally consistent pieces must come from a single global object. The goal of the talk is to highlight the common mechanism behind these notions.
The 25th Midrasha Mathematicae on Groups, Expanders and Codes -- Celebrating Alex Lubotzky's 70th birthday.
Day 5, Session 3
Speaker: Irit Dinur (IAS)
Title: High Dimensional Expansion and Local Testability
Abstract: High-dimensional expanders form a rich meeting point between group theory, topology, combinatorics, and theoretical computer science. They arise from highly structured geometric objects, such as Bruhat–Tits buildings and their finite quotients, while at the same time providing combinatorial models for robust local-to-global behavior. I will discuss this local-to-global philosophy through the lens of cocycle expansion: A foundational work of Kaufman Kazhdan and Lubotzky shows that under suitable expansion assumptions on the (local) links of a complex, one can deduce global cocycle expansion. I will describe how closely related ideas appear in the study of locally testable codes, where global errors are detected by local checks, and in agreement testing, where one asks whether many locally consistent pieces must come from a single global object. The goal of the talk is to highlight the common mechanism behind these notions.
