I hope to write a book on Alain Badiou some day. In the mean time, I have a new article just published on Badiou's digital philosophy. The title of the essay is "Mathification" and it aims to wrangle the central issue in Badiou, indeed the cause of some controversy: Badiou's relation to mathematics. Email me for the PDF if you're caught behind the paywall.
The essay is part of a special issue on "Economies of Existence" edited by Emily Apter and Martin Crowley, and containing texts by Arjun Appadurai, Gabriel Rockhill, and Peter Szendy, among others.
Also of potential interest: "21 Paragraphs on Badiou," a series of guesses and prognostications written in anticipation of Badiou's (then still forthcoming) Being and Event 3: The Immanence of Truths.