School Seminars and Colloquia

Fourier coefficients of modular forms and arithmetic embedding problems

School Seminar

by Michael Volpato

Institution: The University of Melbourne
Date: Mon 14th January 2008
Time: 2:00 PM
Location: Room 213, Richard Berry Building, The University of Melb

Abstract: We start by reviewing the history of some low rank algebraic structures and embeddings into certain non-associative structures, outlining how, from this, one could have predicted the existence of certain classes of exotic modular forms. We then illustrate how, through the optic of representation theory, one can construct such modular forms, whose associated Fourier coefficients count these arithmetic embeddings. If time permits, we will describe how these Fourier coefficients relate M. Bhargava's 'higher composition laws' to Euler product expansions of certain automorphic L-functions.

For More Information: Professor Peter Taylor