# Study Group on Bianchi Modular Forms and Theta functions

This term's study group will be in two parts with a talk linking the two. First we will look at Bianchi modular forms, starting with an overview of the role they play in extending questions of modularity of elliptic curves from **Q** to imaginary quadratic fields, followed by a talk on topological aspects of Bianchi groups and one on Diophantine applications. The linking talk will be about theta functions associated to Bianchi Eisenstein series. In the second half of term we will have several talks about theta functions and their applications, including solving quintic equations (full details of topics, and speakers, to be decided).

All meetings will be at 1pm in D1.07 (Complexity Seminar Room).

Date |
Week |
Speaker |
Title |

Oct 6 | 1 | all | Planning session |

Oct 13 | 2 | John Cremona | Overview on Bianchi modular forms |

Oct 20 | 3 | Mattia Sanna | Topological aspects of Bianchi groups I |

Oct 27 | 4 | Topological aspects of Bianchi groups II | |

Nov 3 | 5 | George Turcas | Applications of Bainchi modular forms to Diophantine equations |

Nov 10 | 6 | No meeting | |

Nov 17 | 7 | David Lowry-Duda | Theta functions and Bianchi Eisenstein series |

Nov 24 | 8 | David Lowry-Duda | Solving polynomial equations using theta functions |

Dec 1 | 9 | John Cremona | Elliptic curves with prime conductor over imaginary quadratic fields |

Dec 8 | 10 | TBC | TBC |