Computer Science/Discrete Mathematics

High-dimensional expanders (HDX) are a generalization of expander graphs which have seen various applications in coding theory, PCPs, pseudorandomness, derandomization, approximate sampling, and beyond. One technique for proving a complex is an HDX...

The study of Turán numbers of graphs and hypergraphs is a rich problem in extremal combinatorics. The Turán problem asks, given a fixed forbidden (hyper)graph F, what is the maximum number of edges in an F-free (hyper)graph in terms of the number of...

In this talk, I will discuss the solution to several problems in two closely related settings: set families in 2^[n] with many disjoint pairs, and low-rank matrices with many zero entries.

Highlights include a resolution of an old question of Daykin...