Miranda Cheng

Thursday, 14th March 2019, 4.15pm

ETH Zürich, HG F 1

Miranda Cheng, University of Amsterdam

Mock Modular Forms are Everywhere

Modular forms are ubiquitous in mathematics and also play a significant role in theoretical physics. Mock modular forms arise from a more flexible notion of modularity. What exactly this notion should be has puzzled mathematicians since 1920, when at the end of his life Ramanujan wrote down 17 functions that he called "mock theta functions" without giving any further explanation. Nearly a century later, we have finally understood their three key properties: 'nice' Fourier coefficients, radial limits, and modularity. Since then, mock modular forms have found a wide range of applications in various fields in mathematics and theoretical physics. In this talk, I will briefly survey the history and the properties of mock modular forms, and explain how they appear in recent research in finite group representations (moonshine), string theory black holes, and three-dimensional topology.