Theta functions for positive definite and indefinite lattices are important examples of modular forms and mock-modular forms. Changing signs in the definition of theta functions breaks these modular symmetries and produces so-called false theta functions instead. By applying lessons from the study of indefinite theta functions, one can construct modular completions for these false theta functions, which I want to present in this talk.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/246