Lethbridge Number Theory and Combinatorics Seminar

Standard numerical methods focus on algorithms for matrices over the real and complex numbers: finding singular value decompositions, eigenvalues and eigenvectors, QR and LU decompositions.  Many of the same questions make sense for non-archimedian local fields, and some methods carry over.  Moreover, the ultrametric properties of p-adic arithmetic allow for much better tracking of precision than in the real and complex cases.  This is a report on early stages of joint work with Xavier Caruso, Tristan Vaccon, Jen Balakrishnan and Kiran Kedlaya.