Is This Polynomial Solvable?

Dr. Anna Haensch

Assistant Professor

Department of Mathematics and Computer Science Duquesne University

Friday, December 1st, 4:30PM Kalkin – Room 002

Abstract: A rational polynomial f(x) is solvable if f(x)=0 has an integer solution. Hilbert’s 10th problem famously asks whether there is a general finite algorithm to determine whether a polynomial is solvable. From work completed in the 1960’s we know that the answer to Hilbert’s 10th problem is a definitive ``no.” However, if we restrict to certain types of polynomials the answer becomes ``yes.” In this talk we will explore linear, quadratic, and higher degree polynomials in the context of the solvability problem and we will look at some classical results in this area. We will discuss some familiar techniques like the Euclidean algorithm and the quadratic equation, and perhaps some less familiar techniques involving quadratic lattices and modular forms. Eventually we will land in the realm of cutting edge research problems in solvability for quadratic polynomials. This talk will be aimed at advanced undergraduate students, graduate students, and anyone with an inclination towards number theory.

ADA: Individuals requiring accommodations, please contact Doreen Taylor at (802) 656-3166

REFRESHMENTS WILL BE SERVED.