Special Year on Expansion and Computation

During the 2027-28 academic year the School will have a special program on Expansion and Computation. The program will be led by Irit Dinur, IAS, School of Math, Betsey Lombard Overdeck Theory of Computing Professor and Co-organizer Dor Minzer from MIT. 

Expander graphs have been a central object of study for decades, with profound connections to many mathematical areas such as group theory, number theory, geometry, combinatorics, and theoretical computer science. High-dimensional expanders (HDX) are hypergraph analogues of expander graphs, that display remarkable local-to-global phenomena. These structures have already given rise to a variety of new applications including the mixing of Markov chains, group stability, quantum error-correcting codes, pseudorandomness, analysis of Boolean functions, PCPs, and hardness of approximation. 

A distinctive feature of HDX is that, unlike expander graphs, there are several natural non-equivalent notions of expansion arising from topology, geometry, spectral theory and combinatorics. Each of these has proved important in different mathematical and computational settings.

The goals of the special year include deepening and broadening the connections between HDX and neighboring fields, developing new constructions, and extending the theory beyond simplicial complexes to more general posets such as the Grassmann complex. 

Other senior participants include: Shai Evra, Alex Lubotzky, Shayan Oveis-Gharan