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SUMMARY:Oleg Karpenkov (University of Liverpool)
DTSTART:20210907T123000Z
DTEND:20210907T133000Z
DTSTAMP:20260423T053131Z
UID:OWNS/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/53/">On
  Hermite's problem\, Jacobi-Perron type algorithms\, and Dirichlet groups<
 /a>\nby Oleg Karpenkov (University of Liverpool) as part of One World Nume
 ration seminar\n\n\nAbstract\nIn this talk we introduce a new modification
  of the Jacobi-Perron algorithm in the three dimensional case. This algori
 thm is periodic for the case of totally-real conjugate cubic vectors. To t
 he best of our knowledge this is the first Jacobi-Perron type algorithm fo
 r which the cubic periodicity is proven. This provides an answer in the to
 tally-real case to the question of algebraic periodicity for cubic irratio
 nalities posed in 1848 by Ch.Hermite.\n\nWe will briefly discuss a new app
 roach 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 alg
 ebraic irrationalities.\n
LOCATION:https://researchseminars.org/talk/OWNS/53/
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