Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, March 18, 2014, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Chandan Dubey

Peering through the local-to-global lense at Lattices

The study of quadratic forms i.e., homogeneous polynomials of uniform degree 2, leads to a beautiful local-to-global principle. Intuitively, the principle states that if a quadratic equation has solutions modulo p^k for each prime p and positive integer k, and it has a solution over reals then it has a rational solution. Lattices can be seen as positive definite quadratic forms. In this talk, I will apply the local-to-global principle on lattices and show how to generate interesting lattices using this application. In particular, we give a significantly better algorithm for lattice generation, compared to the one based on Minkowski's work. The talk will be introductory in nature and I will trade-off most of the machinery in favor of intuitive clarity.

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