Pure Maths Colloquium: Mock modular forms
27 October 2008 16:15 in CM221
The main motivation for the theory of mock modular forms comes from the study of Ramanujan's mock theta functions, which he defined in his last letter to Hardy, in 1920. Since then, many papers have been written (Watson, Selberg, Andrews, ...), studying Ramanujan's examples. However, no natural definition was known. In 2002, the missing intrinsic characterization of these mock theta functions was found, using results on indefinite theta functions, Appell-Lerch sums and Fourier coefficients of meromorphic Jacobi forms. This has led to a satisfactory general definition and seems to have sparked a flurry of recent activity involving these functions and generalizations thereof. In this talk we'll discuss some of these results, a general definition and a generalization to higher depth mock modular forms.