# Colloquia/Fall18

## Contents

# Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, **unless otherwise indicated**.

## Spring 2018

date | speaker | title | host(s) | |
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January 29 (Monday) | Li Chao (Columbia) | Elliptic curves and Goldfeld's conjecture | Jordan Ellenberg | |

February 2 | Thomas Fai (Harvard) | TBA | Spagnolie, Smith | |

February 9 | Wes Pegden (CMU) | TBA | Roch | |

March 16 | Anne Gelb (Dartmouth) | TBA | WIMAW | |

April 4 (Wednesday) | John Baez (UC Riverside) | TBA | Craciun | |

April 6 | Reserved | TBA | Melanie | |

April 13 | Jill Pipher (Brown) | TBA | WIMAW | |

April 25 (Wednesday) | Hitoshi Ishii (Waseda University) Wasow lecture | TBA | Tran | |

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## Spring Abstracts

### Li Chao

January 29: Li Chao (Columbia)

Title: Elliptic curves and Goldfeld's conjecture

Abstract: An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.