| Speaker: | Yasuakib Gyoda (Nagoya University) |
|---|---|
| Title: | k-generalized Markov number and snake graph |
| Date (JST): | Thu, Jun 05, 2025, 13:30 - 15:00 |
| Place: | Seminar Room A |
| Abstract: |
A k-generalized Markov number refers to a positive integer that appears in a positive integer solution of the k-generalized Markov equation x2 + y2 + z2 + k(yz + zx + xy) = (3 + 3k)xyz. It is known that the set of positive integer solutions to this equation possesses a mutation structure in the context of (generalized) cluster algebras, and research in this area has been actively progressing in recent years. In this talk, we will introduce an algorithm for calculating k-generalized Markov numbers by snake graphs, which are combinatorial objects. This presentation is based on joint work with Shuhei Maruyama from Kanazawa University and Yusuke Sato from Osaka Institute of Technology. |
