| Abstract: |
I will give an introduction to the subject of Moonshine, named by Conway after a seemingly crazy observation by McKay concerning the Monster finite group and modular forms. The original Moonshine conjectures, formulated by Conway and Norton, were proved by Borcherds and won him the Fields medal.
However, the geometry underlying the picture is still a bit of a mystery. A generalization of the original conjecture, known as "generalized Moonshine conjecture" (now also mostly proved) sheds some light on what this picture will be.
I will explain my interpretation of Norton's generalized Moonshine conjecture and explain why it is natural to use power operations in elliptic cohomology to rephrase some of the basic concepts of Moonshine.
Time permitting, I will conclude with some questions.
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