Title	K3 surfaces and elliptic fibrations in number theory
Creator	Elkies, Noam D.
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2018-01-23T14:02
Description	We outline several number-theoretical contexts where K3 surfaces and elliptic fibrations arise naturally: Diophantine equations, Euclidean and hyperbolic quadratic forms, elliptic and Shimura modular curves and higher-dimensional analogues, record ranks for elliptic curves and related tasks, and complex reflection groups and their invariants. Several of these contexts call for explicit formulas for surfaces are known to exist only by transcendental means (Torelli theorem for K3 surfaces). One of these formulas also yields a family of elliptically fibered Calabi-Yau threefolds with Mordell-Weil rank 10.
Extent	61 minutes
Subject	Mathematics; Algebraic geometry; Relativity and gravitational theory; Mathematical physics
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: Harvard University
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2018-07-23
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0369011
URI	http://hdl.handle.net/2429/66560
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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