Brigitte Stepanov, a mathematics student of Queen’s University, has put together a great event for the Fields Undergraduate Network.
She has invited three of Queen’s algebraic geometers, Mike Roth, Anthony Geramita, and Gregory Smith to give this set of specialized talks for undegraduates.
We hope to see you there and also that you would join us for dinner during the evening of the conference. If you choose to attend the dinner, please send an email to firstname.lastname@example.org
Please see below for the abstracts of the talks.
Algebraic Geometry as provider of insight
Mike Roth, Queen’s University
Abstract: One of the most appealing features of algebraic geometry is the way in which translating an algebraic problem to a geometric one can illuminate it, revealing aspects invisible from the point of view of equations. As a sample we will consider the problem of trying to find polynomial solutions to a single equation and see how the underlying geometry of the complex solutions completely resolves this algebraic question.
Sums of Squares: Evolution of an Idea
Anthony V. Geramita, Queen’s University and the University of Genoa
Abstract: Questions about sums of squares of integers were considered in Number Theory by Gauss, Lagrange, Fermat and others. I will show, in this talk, how these considerations in Number Theory evolved into a wonderful question in Geometry, particularly in Algebraic Geometry. Furthermore, that question still has aspects of it that are open problems which can be considered by undergraduates.
Polynomial Equations and Convex Polytopes
Gregory G. Smith, Queen’s University
Abstract: How many complex solutions should a system of n polynomial equations in n variables have? When n = 1, the Fundamental Theorem of Algebra bounds the number of solutions by the degree of the polynomial. In this talk, we will discuss generalizations for larger n. We will focus on some of especially attractive bounds which depend only on the combinatorial structure (i.e. the associated Newton polytopes) of the polynomials.