- Date: 10 July. (Thu.)
- Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
- Time: 17:50-19:00
- Speaker 1: Shuhei Mano（The Institute of Statistical Mathematics）
- Time: 16:50-17:50
- Title: Symmetric quantum walks on Hamming graphs and their limit distributions
- Abstract:
We studied a class of symmetric quantum walks on Hamming graphs, where the distance between vertices specifies the transition probability. The simple quantum walk on the hypercube, which has been discussed in literature, is a special case. The zeros of certain self-reciprocal polynomials determine the dynamics of the quantum walks. We obtained a spectral representation of the wave function, where working with the coin space isomorphic to the state space and the commutative association scheme enables our systematic treatment. The limit distributions of several quantum walks are obtained. They are represented as the mixtures of a distribution that appears in random walks and another unknown distribution.
- Speaker 2: Hideo Mitsuhashi（Hosei University）
- Time: 18:00-19:00
- Title: 四元数重み付きグラフのゼータ関数とその一般化
- Abstract:
有向辺上に四元数重みをもつグラフのゼータ関数の、行列式表示やオイラー積表示に
ついて概観し、四元数環の元に重みをもつグラフへの一般化について、説明する。
四元数は非可換であるため、四元数行列の行列式は、通常の行列式の定義では
うまくいかないので、四元数行列の行列式についての概説も行って、初学者にも
わかるように解説したい。
日本語
English