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.