**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.