Umbral moonshine
In mathematics, umbral moonshine is the name for a mysterious connection between the Mathieu group M24 and K3 surfaces, observed by Tohru Eguchi, Hirosi Ooguri, and Yuji Tachikawa (2011).
Cheng, Duncan & Harvey (2012) also observed that some of the functions appearing in umbral moonshine are Ramanujan's Mock theta functions and it is conjectured that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay-Thompson series are certain distinguished mock modular forms. This conjecture is claimed to be proved in Duncan, Griffin & Ono (2015).
See also
References
- Cheng, Miranda C. N.; Duncan, John F. R.; Harvey, Jeffrey A. (2012), Umbral Moonshine
- Duncan, John F. R.; Griffin, Michael J.; Ono, Ken (2015), Proof of the Umbral Moonshine Conjecture
- Eguchi, Tohru; Hikami, Kazuhiro (2009), "Superconformal algebras and mock theta functions", Journal of Physics. A. Mathematical and Theoretical 42 (30): 304010, 23, doi:10.1088/1751-8113/42/30/304010, ISSN 1751-8113, MR 2521329
- Eguchi, Tohru; Hikami, Kazuhiro (2009), "Superconformal algebras and mock theta functions. II. Rademacher expansion for K3 surface", Communications in Number Theory and Physics 3 (3): 531–554, doi:10.4310/cntp.2009.v3.n3.a4, ISSN 1931-4523, MR 2591882
- Eguchi, Tohru; Ooguri, Hirosi; Tachikawa, Yuji (2011), "Notes on the K3 surface and the Mathieu group M₂₄", Experimental Mathematics 20 (1): 91–96, doi:10.1080/10586458.2011.544585, ISSN 1058-6458, MR 2802725