**Lecture notes** (updated frequently)

Aug 23 | Course Introduction. Examples of how volume changes with dimension. (K. Ball's intro to modern convex geometry.) |

Aug 25 | Learning via Sampling. Brunn-Minkowski inequality. (notes; R. Gardner's survey on B-M.) |

Aug 30 | Maxcut, Sparsest cut, min distortion embeddings. (Chaps 2, 3 from "The Random Projection Method"). |

Sep 1 | Grunbaum's inequality. Convex optimization via Sampling (notes). |

Sep 6 | Prekopa-Leindler inequality |

Sep 13, 15 | Rounding. Sandwiching. Isotropic position. |

Sep 20, 22 | Learning, Convex concepts. |

Sep 29 | Gaussian Isoperimetry. One-dim localization |

Oct 4,6 | Volume computation/Integration via Sampling. |

Oct 11, 13, 20 | Sampling, Isoperimetry |

Oct 25 | Student Presentation 1: Ying Xiao, sample complexity of covariance estimation. |

Oct 27 | SP2: Chris Berlind, Agnostic learning of halfspaces. |

Nov 1 | No class (Ravi Kannan's lecture at 4:30pm) |

Nov 3 | SP3: Anand Louis, Invariance principles |

Nov 8 | Near(est) neighbors, Random projection (RP book) |

Nov 10 | SP4: Liujia Hu, Locality-sensitive hashing |

Nov 17 | SP5: Arindam Khan, L1 embeddings revisited. |

Nov 22 | SP6: Tonghoon Suk, Central Limit Theorem for convex bodies. |

Nov 29 | Shortest Vector Problem, LLL algorithm. (survey on Algorithmic Geometry of Numbers) |

Dec 1 | Integer Programming (guest lecturer: Karthik). |

Dec 6 | Misc. topics, open problems. |