Uploaded September 2026 | Updated September 2026, 2 weeks ago
Siqi Liu (Duke University)
https://simons.berkeley.edu/talks/siqi-liu-duke-university-2026-09-03
Joint Boot Camp: Spectral Theory Beyond Graphs + Pseudorandomness and High-Dimensional Expansion
In this series of talks, we introduce coboundary expansion, a generalization of graph expansion to higher-dimensional complexes. Coboundary expansion can be understood both as a high-dimensional isoperimetric inequality and as a local testability property of codes arising from these complexes. We will first present the coding-theoretic definition of coboundary expansion. We will then introduce Gromov’s cone method, a fundamental technique for proving coboundary expansion. Finally, we will dive into an application of coboundary expansion: the Evra–Kaufman result that local spectral expanders with coboundary-expanding links give rise to locally testable codes.
Siqi Liu (Duke University)
https://simons.berkeley.edu/talks/siqi-liu-duke-university-2026-09-03
Joint Boot Camp: Spectral Theory Beyond Graphs + Pseudorandomness and High-Dimensional Expansion
In this series of talks, we introduce coboundary expansion, a generalization of graph expansion to higher-dimensional complexes. Coboundary expansion can be understood both as a high-dimensional isoperimetric inequality and as a local testability property of codes arising from these complexes. We will first present the coding-theoretic definition of coboundary expansion. We will then introduce Gromov’s cone method, a fundamental technique for proving coboundary expansion. Finally, we will dive into an application of coboundary expansion: the Evra–Kaufman result that local spectral expanders with coboundary-expanding links give rise to locally testable codes.
