Algebra Seminar

Title: Diophantine geometry

Speaker: Amod Agashe

Abstract: Diophantine geometry concerns the study of rational solutions to polynomial equations with rational coefficients. We will focus on polynomials in two variables, whose solutions geometrically correspond to curves. We will see that when the degree of the polynomial is two, the local-to-global principle solves the problem completely. For higher degrees, it turns out that it is better to view the curves based on their genus, and we will mention what is known in this situation. This talk should be accessible to all graduate students (not just those in Algebra).