Computer Science and Discrete Mathematics (CSDM)

Given a family of m matchings in a graph G (where each matching can be thought of as a color class), a rainbow matching is a choice of edges of distinct colors that forms a matching. How many matchings of size n are needed to guarantee the existence...

The tasks of finding and randomly sampling solutions of constraint satisfaction problems over discrete variable sets arise naturally in a wide variety of areas, among them artificial intelligence, bioinformatics and combinatorics, and further have...

In this talk, I'll illustrate how to lift a "small" locally testable code via a high dimensional expander (HDX) to a "large" locally testable code. Given a D-left regular bipartite graph G = ([n], [m], E) and a "small" code C \in {0,1}^D, the Tanner...

The tasks of finding and randomly sampling solutions of constraint satisfaction problems over discrete variable sets arise naturally in a wide variety of areas, among them artificial intelligence, bioinformatics and combinatorics, and further have...

I will introduce an isoperimetric inequality for the Hamming cube and some of its applications. The applications include a “stability” version of Harper’s edge-isoperimetric inequality, which was first proved by Friedgut, Kalai and Naor for half...

Extremal set theory typically asks for the largest collection of sets satisfying certain constraints. In the first talk of these series, I'll cover some of the classical results and methods in extremal set theory. In particular, I'll cover the...

In this work, we exploit the ill-posedness of linear inverse
problems to design algoithms to release differentially private data or
measurements of the physical system. We discuss the spectral
requirements on a matrix such that only a small amount of...

Extremal set theory typically asks for the largest collection of sets satisfying certain constraints. In the first talk of these series, I'll cover some of the classical results and methods in extremal set theory. In particular, I'll cover the...

A (k,m)-Furstenberg set K in F^n, where F is a finite field, is a set such that any k-dimensional subspace of F^n can be shifted so that it intersects K in at least m points. Such sets generalize in a natural way finite field Kakeya sets (in which k...

Scaling problems, such as operator scaling and tensor scaling, have recently found several applications in diverse areas of math and CS. They have been used to give efficient algorithms for non-commutative rational identity testing, compute the...