Nonlinear Waves Seminar: Masataka Kanki
Integrability of discrete equations over finite fields
Masataka Kanki
Graduate School of Mathematical Sciences,ÌýUniversity of Tokyo
Date and time:Ìý
Wednesday, July 31, 2013 - 3:00pm
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ECOT 226
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Discrete integrable systems defined over finite fields are studied. Dynamical systems over non-Archimedean fields are of great interest in the theory of arithmetic dynamics. Integrable equations over the field ofÌýp-adic numbers \(\mathbb{Q}_p\) are defined and then the evolutions are reduced to the finite field \(\mathbb{F}_p\). The integrable systems are shown to have a property that resembles a ‘good reduction’ modulo a prime. We observe that this generalization of the good reduction can be used to test integrability of equations over finite fields. We discuss the relation of our methods to other integrability tests, in particular, the famous ‘singularity confinement test.’ Applications of our approach to the two-dimensional lattice systems such as the discrete KdV equation are also studied.