Date & Time: Monday, August 12, 2013, 14:30-15:30.
Venue: Ramanujan Hall
Speaker: Devadatta Kulkarni, General Motors, USA
Title: My journey with determinants: discriminating and counting
Abstract: Abhyankar introduced discriminants ("determinants of special resultants") to me in 1977. With him, in the study of Young tableaux ("product of determinants"), I learned recurrence relations techniques to count special families of tableaux. The language of "binomial coefficients determinants" generalized formulas for enumerating non-intersecting paths.
In studying PDE numerical solutions, "multi-linearity of determinants" was used to establish that the characteristic polynomials of certain matrices are indeed combinations of Chebyshev polynomials. This result provided step wise stability of solutions to heat equations with special boundary constraints. In automotive engineering studies on large scale optimization and product development processes, structures and ranks of sub-matrices played pivotal roles.
Discriminating and counting capabilities of determinants have been a recurring theme in my professional journey -- in both academics and industry.