Algebra Seminar, Beth Malmskog (Villanova): 'Picard curves with good reduction away from 3, x+y=1, p=u2+v2, and other problems solved by the LLL algorithm

Friday, February 6, 2015
1:10 PM - 2:00 PM (ET)
ESC 638
Event Type
Christopher Rasmussen,x2318

Abstract: A lattice L is the set of integer linear combinations of an independent set of vectors. The set of generating vectors is called a basis for L. A particular lattice can have many bases some good (of shorter vectors which are closer to orthogonal), some bad (of longer vectors which are closer to parallel). In 1982, Henrik Lenstra, Arlen Lenstra, and Lovasz developed a fairly simple polynomial-time algorithm which, given any basis B for a lattice L, will produce a relatively good basis for L. This algorithm has found extensive application in surprising areas. This talk will discuss applications of LLL to recent work with Chris Rasmussen on Picard curves with certain reduction properties, number theoretic problems such as finding minimal polynomials for algebraic numbers, attacking lattice-based cryptosystems, and more.

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