In 2001 Balogh received his doctorate from the University of Memphis with advisor Béla Bollobás and thesis Graph properties and Bootstrap percolation.

As a postdoc Balogh was at AT&T Shannon Laboratories in Florham Park, New Jersey and for several months in 2002 at the Institute for Advanced Study.

It is based on a randomly chosen starting structure and Bollobás, Balogh, Hugo Duminil-Copin and Robert Morris proved an asymptotic (for large grids) formula for the threshold probability that the whole grid is infected, depending on d and r. He had previously treated the three-dimensional case with r = 3 with Bollobás and Morris.

He was named to the 2023 class of Fellows of the American Mathematical Society, "for contributions to extremal combinatorics, probability and additive number theory, and for graduate mentoring".

[4] In 2024 he was awarded the Leroy P. Steele Prize for Seminal Contribution to Research jointly with Robert Morris and Wojciech Samotij.