Abstract

A number of problems in theoretical physics can be translated to problems in computational algebraic geometry. In this talk, I focus on one such problem: Describing the possible vacua of supersymmetric field theories. No prior knowledge of physics is required.

In one important case related to the standard model of particle physics, this problem boils down to a daunting computational algebra problem: understanding the image of a polynomial map froa 49 dimensional vector space to a 973 dimensional vector space, seemingly a hopeless task!

It turns out that we can solve a large part of this problem.

I will very briefly describe the physics, and how the problem is translated into a computational one, and then I will describe the algebraic geometric and computational methods and results which allow the structure to become apparent.

Joint work with:

Yang-Hui He (Oxford and London Institute of Mathematics, UK) Vishnu Jejjala (University of the Witwatersrand, Johannesburg, South Africa) Brent Nelson (Northeastern University, USA ) Hal Schenck (Auburn University, USA )