Speaker: Alex Lubotzky (Weizmann Institute & the Hebrew University, Simons Distinguished Visiting Professor, MIT)

Title: High Dimensional Expanders (HDX) and their applications in pure math and computer science

Abstract: 

Expander graphs have been an intensive topic of research in math and CS during the last six decades. In the last two decades a high dimensional theory has emerged with (very different) applications in math & CS.

In this series of 8 independent (but related) lectures we present some aspects of the theory of HDX and its applications, a number of open problems and suggestions for further research.

A more detailed plan:

1. Thursday 2/20/25, 4:30pm, 2-190 (Math Colloquium); refreshments served at 4pm in 2-290

  Introduction: three main problems

(a) Gromov overlapping property

(b) Locally testable codes

(c) Are all groups sofic?

2. Tuesday 2/25/25, 4:15-5:15pm, 32-G449 (Theory of Computing Colloquium), refreshments served at 4pm

Good Locally testable codes

3. Wednesday 2/26/25, 9:30-11am, 2-449

Expander graphs: combinatorics, spectral gap, representation theory

(Kazhdan property (T), property (\tau) and more) and property testing

4. Wednesday 3/5/25, 9:30-11am, 2-449

Geometric & topological expanders, Coboundary expanders, Random simplicial complexes and Property testing

5. Wednesday 3/12/25, 9:30-11am, 2-449

From Ramanujan graphs to Ramanujan complexes

6. Wednesday 3/19/25, 9:30-11am, 2-449

Stability and group approximation, Garland Theorem and the p-adic Deligne central extensions

Wednesday 3/26/25 - Spring vacation

7. Wednesday 4/2/26, 9:30-11am, 2-449

Some more CS: Agreement tests, direct product test; PCP

8. Wednesday 4/9/25, 9:30-11am, 2-449

Are there non-sofic groups? The Aldous-Lyons conjecture and more