High-dimensional Expanders in Pure Mathematics and in Computer Science
Lecture 1 on January 13, 2026 at 11:00: Between group stability and CS testability
We will discuss how problems in group stability can be thought of as property testing problems. In particular, this suggests a non-commutative version of locally testable error correcting codes. We will survey a few methods to prove such stability/testability results.
On 13/1/26 at 14:00 in our seminar room on the 6th floor of the Science and Education building there will be a colloquium talk by Chen Meiri of the Technion.
Lecture 2 on January 14, 2026 at 11:00: Group approximation
In this talk, we will show how high-dimensional expanders are employed to prove various non-approximation results in group theory via group stability.
Lecture 3 on January 15, 2026 at 11:00: Topological expanders
Gromov's overlapping problems led to the notions of geometric and topological expanders. These problems have been solved by using the high-dimensional expanders ( a.k.a. Ramanujan complexes). We will survey these developments.
Then we will point out how the methods developed there MAY be useful to tackle the holy grail open problem of group approximation theory: are all groups sofic?