In this talk, I will present a novel modular property of 4d N=1 supersymmetric partition functions of supersymmetric theories with R-symmetry. It is a generalization of the modular invariance of the supersymmetric partition function of two-dimensional supersymmetric theories on a torus i.e. of the elliptic genus. It comes from requiring consistency of partition functions under gluing and, among other things, can be used to rederive the supersymmetric Cardy formula for four-dimensional gauge theories that has played a key role in computing the entropy of supersymmetric black holes.
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Recordings of past talks can be found here: www.youtube.com/channel/UCw9LdPQ5t7Q7muD0qzn70TA