On Well-rounded Ideal Lattices

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Mathematics (CMC)

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We will discuss a connection between two important classes of Euclidean lattices: well-rounded and ideal lattices. A lattice of full rank in a Euclidean space is called well-rounded if its set of minimal vectors spans the whole space. We consider lattices coming from rings of integers of number fields and their ideals, and address the question when such lattices are well-rounded? This question turns out to have an interesting answer. This is joint work with Kate Petersen. If time allows, we will also discuss the distribution of well-rounded sublattices of the hexagonal lattice in the plane, which includes the results of the Summer 2009 Claremont REU program.


This lecture is related to an article by Lenny Fukshansky and Kate Petersen: "On Well-Rounded Ideal Lattices" in the International Journal of Number Theory Volume 8, number 1, pages 189-206.

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© 2011 Lenny Fukshansky

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