Seminar series
Date
Mon, 14 May 2012
Time
12:00 - 13:00
Location
L3
Speaker
Yang-Hui He
Organisation
City University London

We establish a correspondence between generalized quiver gauge theories in

four dimensions and congruence subgroups of the modular group, hinging upon

the trivalent graphs which arise in both. The gauge theories and the graphs

are enumerated and their numbers are compared. The correspondence is

particularly striking for genus zero torsion-free congruence subgroups as

exemplified by those which arise in Moonshine. We analyze in detail the

case of index 24, where modular elliptic K3 surfaces emerge: here, the

elliptic j-invariants can be recast as dessins d'enfant which dictate the

Seiberg-Witten curves.

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