ABHYANKAR 82nd BIRTHDAY CONFERENCE 

SPEAKER: Datta Kulkarni (General Motors)

TITLE: My Journey with Determinants: Theme of Discriminating and Counting

ABSTRACT: Abhyankar introduced discriminants (determinants of special resultants)
to me in my first meeting. 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
determinant 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.