| 講師 |
Remi Avohou (Okinawa Institute of Science and Technology) |
| タイトル |
Universality of the Tutte and Bollobás–Riordan Polynomials |
| 日時 |
2025年5月29日(木) 15時00分〜16時00分 |
| 場所 |
琉球大学理学部A408教室 |
| 世話人 |
木本 一史 |
The Bollobás–Riordan polynomial [Math. Ann. 323, 81 (2002)] extends the Tutte polynomial by generalizing its contraction/deletion rule from ordinary graphs to ribbon graphs, enriching combinatorial and topological insights. In this talk, I will provide a structured review of the Tutte polynomial, the fundamental concept of ribbon graphs, and the extension that leads to the Bollobás–Riordan polynomial. Additionally, I will discuss the Universality Theorem, highlighting its significance in this framework. If time permits, I will explore these polynomials in the context of a specialized family of combinatorial objects—rank-3 weakly colored stranded graphs [Combin. Probab. Comput. 31 (2022)]. Stranded graphs, which emerge in tensor models for quantum gravity in physics, serve as a natural extension of both graphs and ribbon graphs, offering new perspectives in combinatorial mathematics and theoretical physics.