Mathematics
Seminar
Moonshine
SPEAKER | Michael Griffin
INSTITUTE | Princeton University
DATE | February 2(Tue), 2016
TIME | 15:00
PLACE | 1424
Keyword |
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ABSTRACT | In the 1970¡¯s, as mathematicians worked to classify the finite simple groups, Ogg, McKay and others observed several striking apparent coincidences connecting the then-conjectural Monster group (the largest of the sporadic simple groups) to the theory of modular functions. These ¡®coincidences¡¯ became known as ¡°Monstrous Moonshine¡± and were made into a precise conjecture by Conway and Norton. They conjectured the existence of a naturally occurring graded infinite dimensional Monster module whose graded traces at elements of the monster group give the Fourier coefficients of distinguished modular functions. Borcherds proved the conjecture in 1992, embedding Moonshine in a deeper theory of vertex operator algebras. For this work Borcherds was awarded a Fields Medal. Fifteen years after Borcherds¡¯ proof, Witten conjectured important connections between Monstrous Moonshine and pure quantum gravity in three dimensions. Under Witten¡¯s theory, the irreducible components of the Monster module represent black hole states. Witten asked how these states are distributed. In joint work with Ken Ono and John Duncan, we answer Witten¡¯s question giving exact formulas for these distributions.