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| 担当者 | 時弘哲治, ウィロックス ラルフ |
|---|
2017年02月09日(木)
17:30-18:30 数理科学研究科棟(駒場) 056号室
Dinh Tran 氏 (University of New South Wales, Sydney, Australia)
Growth of degrees of lattice equations and its signatures over finite fields (ENGLISH)
Dinh Tran 氏 (University of New South Wales, Sydney, Australia)
Growth of degrees of lattice equations and its signatures over finite fields (ENGLISH)
[ 講演概要 ]
We study growth of degrees of autonomous and non-autonomous lattice equations, some of which are known to be integrable. We present a conjecture that helps us to prove polynomial growth of a certain class of equations including $Q_V$ and its non-autonomous generalization. In addition, we also study growth of degrees of several non-integrable equations. Exponential growth of degrees of these equations is also proved subject to a conjecture. Our technique is to determine the ambient degree growth of the equations and a conjectured growth of their common factors at each vertex, allowing the true degree growth to be found. Moreover, our results can also be used for mappings obtained as periodic reductions of integrable lattice equations. We also study signatures of growth of degrees of lattice equations over finite fields.
We study growth of degrees of autonomous and non-autonomous lattice equations, some of which are known to be integrable. We present a conjecture that helps us to prove polynomial growth of a certain class of equations including $Q_V$ and its non-autonomous generalization. In addition, we also study growth of degrees of several non-integrable equations. Exponential growth of degrees of these equations is also proved subject to a conjecture. Our technique is to determine the ambient degree growth of the equations and a conjectured growth of their common factors at each vertex, allowing the true degree growth to be found. Moreover, our results can also be used for mappings obtained as periodic reductions of integrable lattice equations. We also study signatures of growth of degrees of lattice equations over finite fields.
