FoCM 2014 conference

Workshop C1 - Computational Algebraic Geometry

December 18, 17:00 ~ 17:20 - Room B12

## Applications of computational algebraic geometry to vacuum moduli spaces of supersymmetric models in physics

### Michael Stillman

### Cornell University, USA - mike@math.cornell.edu

Given a supersymmetric potential function, such as one for the MSSM (minimal super-symmetric extension of the standard model of particle physics), there is a naturally associated affine algebraic variety, which is (essentially) the moduli space of possible vacua of the theory. In this talk we describe the structure of some of these moduli spaces, including the Electro-weak sector of the MSSM, which were obtained with the help of computational algebraic geometry and Macaulay2. We consider theories where one allows for more than 3 generations of particles. Since nature seems to have chosen 3 generations, theories for which this number of generations is forced would be ideal. Although it does not appear that 3 generations is forced here, we see how the geometry varies with different numbers of generations of particles.

We will assume no knowledge of physics during this talk. We will briefly describe the physics needed, and then we will describe the algebraic geometric and computational methods and results which allow the structure to become apparent.

This talk is based on the preprint arxiv.org/1408.6841

Joint work with Yang-Hui He (Oxford and City University London, UK), Vishnu Jejjala (University of the Witwatersrand, Johannesburg, South Africa), Cyril Matti (City University, London, UK) and Brent Nelson (Northeastern University, USA).