Elliptic genera are ring morphisms from cobordism rings to rings of modular forms. After giving background on and motivation for these genera, I will describe both recent and older results about realizing elliptic genera by maps of ring spectra. It was originally an idea of Miller that equivariant elliptic cohomology can help in studying elliptic genera. In the second part, I will describe recent progress in the area of equivariant elliptic cohomology and outline how this might relate back to elliptic genera.

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