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Tuesday Seminar on Topology
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2019/12/10
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Takeyoshi Kogiso (Josai University)
q-Deformation of a continued fraction and its applications (JAPANESE)
Takeyoshi Kogiso (Josai University)
q-Deformation of a continued fraction and its applications (JAPANESE)
[ Abstract ]
A kind of q-Deformation of continued fractions was introduced by Morier-Genoud and Ovsienko. The most important application of this q-deformation of regular (or negative) continued fraction expansion of rational number r/s is to calculate the Jones polynomial of the rational link of r/s. Moreover we can apply the q-deformation of this continued fraction to quadratic irrational number theory and combinatorics.
On the other hand, there exist another recipes for determing the Jones polynomials by using Lee-Schiffler's snake graph and by using Kogiso-Wakui's Conway-Coxeter frieze method. Therefore, another approach of the result due to Morier-Genoud and Ovsienko can be considered from the viewpoint of a Conway-Coxeter frieze and a snake graph. Furthermore, we can consider a cluster-variable transformation of continued fractions as a further generalization by using ancestoral triangles used in the Kogiso-Wakui.
A kind of q-Deformation of continued fractions was introduced by Morier-Genoud and Ovsienko. The most important application of this q-deformation of regular (or negative) continued fraction expansion of rational number r/s is to calculate the Jones polynomial of the rational link of r/s. Moreover we can apply the q-deformation of this continued fraction to quadratic irrational number theory and combinatorics.
On the other hand, there exist another recipes for determing the Jones polynomials by using Lee-Schiffler's snake graph and by using Kogiso-Wakui's Conway-Coxeter frieze method. Therefore, another approach of the result due to Morier-Genoud and Ovsienko can be considered from the viewpoint of a Conway-Coxeter frieze and a snake graph. Furthermore, we can consider a cluster-variable transformation of continued fractions as a further generalization by using ancestoral triangles used in the Kogiso-Wakui.
