Abstract. All elliptic curves over Q are modular. This is the statement of the Modularity Theorem that relates arithmetic properties of the elliptic curve to a modular form for SL(2,Z). This modularity has been (and still is) the subject of much research in Number Theory.
At first, one might argue that this kind of modularity is irrelevant for physics. In this talk, however, I hope to present some recent work on (and examples of) "rank-2 attractors" which suggests that certain N=2 black holes that arise in String Theory are sensitive to the modularity of a Calabi-Yau manifold.
This is work produced in collaboration with Philip Candelas, Xenia de la Ossa and Duco van Straten.
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