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On Hermite’s problem, Jacobi-Perron type algorithms, and Dirichlet groups (Oleg Karpenkov, Liverpool)

September 14 @ 12:30 pm - 1:20 pm

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.

We 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.

Details

Date:
September 14
Time:
12:30 pm - 1:20 pm
Event Category:

Other

Speaker Name
Oleg Karpenkov (University of Liverpool)

Venue

On Zoom

Details

Date:
September 14
Time:
12:30 pm - 1:20 pm
Event Category:

Other

Speaker Name
Oleg Karpenkov (University of Liverpool)

Venue

On Zoom