Date & Time: Monday, December 01, 2014, 16:00-17:00.
Venue: Ramanujan Hall
Title: The Dedekind determinant and generalizations
Speaker: M. Ram Murty, Queen's University
Abstract: In 1896, Dedekind proved a general result for the group determinant which initiated the development of representation theory. This group determinant has played a pivotal role in algebraic number theory, in particular, in the study of regulators. Around the same time, H.J.S. Smith discovered a number theoretic determinant which was later generalized to a combinatorial setting by Wilf in 1968. In 1977, Redheffer discovered a version of the Smith determinant related to the Riemann hypothesis. We will highlight a simple idea from linear algebra from which both determinants emerge as special cases. This generalization allows us to derive an analog of both the Dedekind and Smith determinants for modular forms. This is joint work with Kaneenika Sinha and the talk will be accessible to a wide audience.