OUTREACH PROGRAMS

April 20, 2014

Fields Undergraduate Network:
Algebraic Geometry Conference
November 26, 2011

Queen's University

Jeffery Hall, 48 University Ave. Rm. 234

Organizers:
Brigitte Stepanov (Queen's University, Department of Mathematics, Math DSC Co-Chair)

Schedule:

Saturday November 26, 2011
11:00 - 12:00 Mike Roth (Queen's University)
Algebraic Geometry as provider of insight
12:00 - 1:30 Lunch
1:30 - 2:30 Anthony V. Geramita (Queen's University and the University of Genoa)
Sums of Squares: Evolution of an Idea
2:30 - 3:00 Snack/Coffee break
3:00 - 4:00 Gregory G. Smith (Queen's University)
Polynomial Equations and Convex Polytopes
4:00 - 4:30 Panel Discussion
7:00 Dinner (Windmills, 184 Princess St.)

We will be hosting the following talks:

Mike Roth (Queen's University)
Algebraic Geometry as provider of insight

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.
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Anthony V. Geramita (Queen's University and the University of Genoa)
Sums of Squares: Evolution of an Idea

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.
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Gregory G. Smith (Queen's University)
Polynomial Equations and Convex Polytopes

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.


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