**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.

____________________________________________________________________

**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.

____________________________________________________________________

**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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