## Seminar:

Fall 2011, Thursdays, Milner 216, 4:00-4:50 PM
__ Date:__ ** September 8 **

**" Solving Sudoku puzzles using Groebner bases "**

**Abraham Martin del Campo**

__Abstract__ Simply said, Algebraic Geometry is the study of solutions to polynomial equations. However, it was not until 1965 when Bruno Buchberger reveled a computational method to manipulate and solve general systems of polynomial equations. This method is what we call today Groebner bases and it can be thought as a generalization of three familiar techniques: Gaussian elimination for solving linear systems of equations, the Euclidean algorithm for computing the GCD of two univariate polynomials, and the Simplex algorithm for linear programming.

In this talk we will give a brief introduction to Groebner basis and we will show how to use them to solve Sudoku puzzles. Thus, the talk will be aimed at a general audience and will be as self-contained as possible; however, some familiarity with ideals of a polynomial ring in several variables is assumed.