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DTSTART;TZID=America/Los_Angeles:20210914T123000
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CREATED:20210822T191624Z
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UID:2208-1631622600-1631625600@colleges.claremont.edu
SUMMARY:On Hermite's problem\, Jacobi-Perron type algorithms\, and Dirichlet groups (Oleg Karpenkov\, Liverpool)
DESCRIPTION:In this talk we introduce a new modification of the Jacobi-Perron algorithm in the three dimensional case. This algorithm is periodic for the case of totally-real conjugate cubic vectors. To the best of our knowledge this is the first Jacobi-Perron type algorithm for which the cubic periodicity is proven. This provides an answer in the totally-real case to the question of algebraic periodicity for cubic irrationalities posed in 1848 by Ch.Hermite. \nWe will briefly discuss a new approach which is based on geometry of numbers. In addition we point out one important application of Jacobi-Perron type algorithms to the computation of independent elements in the maximal groups of commuting matrices of algebraic irrationalities.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-pavel-guerzhoy-university-of-hawaii/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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