Computer Science/Discrete Mathematics Seminar I | |

Topic: | Diffuse Decompositions of Polynomials |

Speaker: | Daniel Kane |

Affiliation: | Stanford University |

Date: | Monday, April 22 |

Time/Room: | 11:15am - 12:15pm/S-101 |

Video Link: | https://video.ias.edu/csdm/1213/0422-DanielKane |

We study some problems relating to polynomials evaluated either at random Gaussian or random Bernoulli inputs. We present some new work on a structure theorem for degree-d polynomials with Gaussian inputs. In particular, if p is a given degree-d polynomial, then p can be written in terms of some bounded number of other polynomials q_1,...,q_m so that the joint probability density function of q_1(G),...,q_m(G) is close to being bounded. This says essentially that any abnormalities in the distribution of p(G) can be explained by the way in which p decomposes into the q_i . We then present some applications of this result.