ABSTRACT: Elliptic cohomology has always been a natural big brother to ordinary cohomology and K-theory. However, in contrast to the plethora of geometric objects that provide representatives for cohomology and K-theory classes, we do not know any geometric objects that provide representatives for elliptic cohomology. I will explain in this talk a step forward for the case of equivariant elliptic cohomology over the complex numbers by using supersymmetric gauge-theoretic constructions as geometric models; this work is joint with D. Berwick-Evans. I will assume no prior knowledge of either elliptic cohomology or supersymmetric gauge theory.