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
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Spring Abstracts

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.