Colloquia/Fall18: Difference between revisions
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| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia) | | [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia) | ||
|[[# | |[[#Li Chao| Elliptic curves and Goldfeld's conjecture ]] | ||
| Jordan Ellenberg | | Jordan Ellenberg | ||
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== Spring Abstracts == | == Spring Abstracts == | ||
===Li Chao=== | |||
Title: | |||
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. | |||
== Past Colloquia == | == Past Colloquia == | ||
Revision as of 16:07, 24 January 2018
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) | |
|---|---|---|---|---|
| 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 | |
| date | person (institution) | TBA | hosting faculty | |
| date | person (institution) | TBA | hosting faculty | |
| date | person (institution) | TBA | hosting faculty | |
| date | person (institution) | TBA | hosting faculty | |
| date | person (institution) | TBA | hosting faculty | |
| date | person (institution) | TBA | hosting faculty | |
| date | person (institution) | TBA | hosting faculty | |
| date | person (institution) | TBA | hosting faculty | |
| date | person (institution) | TBA | hosting faculty |
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.