We prove new cell-probe lower bounds for data structures that maintain a subset of $\{1,2,...,n\}$, and compute the median of the set. The data structure is said to handle insertions non-adaptively if the locations of memory accessed depend only on the element being inserted, and not on the contents of ... more >>>

A locally decodable code (LDC) C:{0,1}^k -> {0,1}^n is an error correcting code wherein individual bits of the message can be recovered by only querying a few bits of a noisy codeword. LDCs found a myriad of applications both in theory and in practice, ranging from probabilistically checkable proofs to ... more >>>

A sunflower with $r$ petals is a collection of $r$ sets so that the
intersection of each pair is equal to the intersection of all. Erd\H{o}s and Rado proved the sunflower lemma: for any fixed $r$, any family of sets of size $w$, with at least about $w^w$ sets, must ... more >>>

Lifting theorems are a generic way to lift lower bounds in query complexity to lower bounds in communication complexity, with applications in diverse areas, such as combinatorial optimization, proof complexity, game theory. Lifting theorems rely on a gadget, where smaller gadgets give stronger lower bounds. However, existing proof techniques are ... more >>>