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Friday, February 6, 2015

1:10 PM - 2:00 PM (ET)

ESC 638

Event Type

Lecture

Contact

Christopher Rasmussen,x2318

Department

Academic

Link

https://eaglet.wesleyan.edu/MasterCalendar/EventDetails.aspx?EventDetailId=48383

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.