Miranda Cheng received an ERC starting grant for her project 'Moonshine and String Theory'. With the grant, dr Cheng will be able to further explore the mysterious 'moonshine relation' in the context of string theory. Cheng is affiliated to both the Institute of Physics and the Korteweg de Vries Institute for Mathematics at the University of Amsterdam.
The word moonshine, when used in mathematics, refers to an unexpected relation between two very different mathematical structures. The first is the structure of finite groups, often employed to describe symmetries of special objects such as lattices, codes and geometrical shapes. The second is the concept of modular forms, which are mathematical functions with special infinite symmetries that play a crucial role in a variety of scientific developments ranging from the proof of Fermat's last theorem in number theory to the study of transitions between different phases of matter. In 2013, a new and fascinating moonshine relation - named umbral moonshine - was discovered by Miranda C. N. Cheng (University of Amsterdam) together with her collaborators J. Duncan and J. Harvey.
String theory is a theory striving to a full understanding of the fundamental laws of nature and is the only theory known to have the power to unify Einstein gravity and quantum mechanics. Apart from its success in physics, it also enjoys a productive collaborative relation with mathematics. In the past two years, evidence has emerged suggesting that string theory holds the key to the understanding of the mysterious new umbral moonshine relation. Moreover, this moonshine relation points to exciting new symmetries of string geometry that will deepen our understanding of string theory and quantum gravity. With the ERC project Moonshine and String Theory, dr Cheng will lead a research group at the University of Amsterdam to study the moonshine relation in the context of string theory, with the two-fold goal of solving the puzzle of umbral moonshine and of shedding new light on the intricate structure of string theory using these novel symmetries.
http://arxiv.org/abs/1204.2779 (Umbral Moonshine, October 2013)
http://arxiv.org/abs/arXiv:1307.5793 (Umbral Moonshine and the Niemeier Lattices, Juli 2014)