Computer Science/Discrete Mathematics Seminar II | |

Topic: | Structural aspects of the null-cone problem in invariant theory |

Speaker: | Ankit Garg |

Affiliation: | Microsoft Research |

Date: | Tuesday, October 10 |

Time/Room: | 10:30am - 12:30pm/West Building Lecture Hall |

Video Link: | https://video.ias.edu/csdm/2017/1010-AnkitGarg |

Invariant theory studies the actions of groups on vector spaces and what polynomial functions remain invariant under these actions. An important object related to a group action is the null cone, which is the set of common zeroes of all homogeneous invariant polynomials. I will talk about the structural aspects of the null cone from a computational and optimization perspective. These will include the Hilbert-Mumford and Kempf-Ness theorems which imply that null cone membership is in NP intersect coNP (ignoring bit-size issues). I will explain how this should be thought of as a noncommutative generalization of linear programming duality, which arises when the group is commutative (group of invertible diagonal matrices aka algebraic tori).