On some problems in random discrete matrices
On some problems in random discrete matrices

Asaf Ferber, MIT
Fine Hall 110
In this talk we survey some interesting problems related to the singularity problem of random discrete matrices. In particular, we discuss the following problems:1. an extension of an old problem of Odlyzko about the probability for randomly chosen $\pm 1$ vectors to intersect the hypercube \{1,1\}^n in a nontrivial way, and
2. an approximate version of a problem of Vu about the probability that a random matrix can be made singular after changing `not too many' entries by an adversary.
This is based on joint works with Afonso Bandeira and Matthew Kwan, and on a recent work with Kyle Luh, Gweneth McKinley and Wojtek Samotij.