Problems, Algorithms, and Complexity in Algebraic Geometry

ACO Student Seminar
Friday, November 18, 2016 - 13:05
1 hour (actually 50 minutes)
Skiles 005
School of Mathematics, Georgia Tech
At the intersection of computability and algebraic geometry, the following question arises: does an integral polynomial system of equations have any integral solutions? Famously, the combined work of Robinson, Davis, Putnam, and Matiyasevich answers this in the negative. Nonetheless, algorithms have played in increasing role in the development of algebraic geometry and its many applications. I address some research related to this general theme and some outstanding questions.