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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