Date:
Thu, 27/05/202114:30-15:30
Location:
מתמטיקה 2
Live broadcast: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=b6d4fc60-f971-4aac-a0fa-ad2d00fde42c
Title: Reducibility of polynomials under specializations
Abstract: Given an algebraic family of irreducible polynomials f(t,x) ∈ ℚ(t)[x] that depends on a parameter t, how large is the set of rational values t=t0 for which f(t0,x) ∈ ℚ[x] is reducible? When is it infinite?
We shall discuss this problem, its role in arithmetic geometry, applications to arithmetic dynamics, and, as time permits, its relation to the question: "can you hear the shape of the drum?"
Title: Reducibility of polynomials under specializations
Abstract: Given an algebraic family of irreducible polynomials f(t,x) ∈ ℚ(t)[x] that depends on a parameter t, how large is the set of rational values t=t0 for which f(t0,x) ∈ ℚ[x] is reducible? When is it infinite?
We shall discuss this problem, its role in arithmetic geometry, applications to arithmetic dynamics, and, as time permits, its relation to the question: "can you hear the shape of the drum?"