While I am not particularly "into" Badiou (I actually prefer Laruelle, as opaque as he is), my research this summer is drawing upon mathematics as ontology, and for mathematics as ontology Badiou is master.
This book - as far as I can tell from the review - offers an alternative to, and critique of, set theory. Set theory and predicate logic have long been staples in the analytic philosophical diet. Here a Continental figure has taken up mathematics in very different ways. The same is true with Badiou's Plato. There his interpretation is, well, like Badiou...but interesting nonetheless (I am referring to Badiou's rewriting of Plato's Republic. His choice for terms of translation says it all.)
Recently I heard the Badiou, as late as last summer, was working on category theory and the thought of C.S. Peirce. Now that's interesting.
NDPR review of Badiou's Mathematics of the Transcendental HERE.
