At the Hegel conference in London this May, Costas Douzinas made a great point about Badiou. Basically, in a moment where the left seems entirely dead, it seems appropriate that the major communist philosopher to rise to fame would be one whose emancipatory politics are based on hoping for a miracle of a historical change.
Badiou’s “Events” are unpredictable occurrences in a “Truth procedure,” in which the truth of an event comes about when an Idea enters “The Real.” This is influenced by both Louis Althusser and Jacques Lacan. The Althusserian influence happens specifically in the miraculous idea. Althusser was interested in aleatory materialism, a pre-socratic philosophy based on Epicures and Lucretius, who believe that the world is determined by the unexplainable accumulation of “atoms.” I recommend listening to, and reading Chris Cutrone’s responses to Badiou’s own “Communist Hypothesis” for a more in-depth examination of Badiou’s communism.