## 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).