Siegel Modular Forms and Black Hole Entropy

In the language of statistical physics, an extremal black hole is a zero temperature system with a huge amount of residual entropy. Understanding which class of counting formulas can account for a large degeneracy will undoubtedly unveil interesting properties of quantum gravity. In this talk I will discuss the application of Siegel modular forms to black hole entropy counting. The role of the Igusa cusp form in the D1D5P system is well-known in string theory, and its transformation properties are what allows precision microstate counting in this case. We implement this counting for other Siegel modular and paramodular forms, and we show that they could serve as candidates for other types of black holes.