セミナー

2017年6月16日(金) 立命館大学幾何学セミナー

2017.06.13 Tue up
日時: 2017年6月16日(金) 15:00~17:15
場所: 立命館大学びわこ・くさつキャンパス(BKC) ウェストウィング6階 談話会室

講演①(15:00~16:00)
タイトル:Heidenberg 群上の(Sub-)Laplacian に対する熱核の展開公式とその応用

講演者:岩崎千里 (兵庫県立大学)

アブストラクト:
Heisenberg 群上のLaplacian およびSub-Laplacian に対する熱方程式の基本解をワイル表象を使って擬微分作用素として書き表すことにより,固有関数展開の手法が適用できることを示す.
この結果をHeisenberg 群上のform に作用するLaplacian の基本解の表示に応用する.

講演②(16:15~17:15)
タイトル:Band rearrangement against a control parameter through Dirac equations with boundary conditions

講演者:岩井敏洋 (京都大学)

アブストラクト:
An elementary band rearrangement or energy level redistribution takes place between two adjacent bands and any band rearrangement can be regarded as composed of elementary ones.
Band rearrangement can be viewed as a global topological change which is a collection of local contributions observed at critical points.
The local topological change can be detected by the linearization method applied at each critical point.
Dirac equations show up in this context as linear equations for the study of elementary band rearrangements.

The Dirac equations of space-dimension one, two, and three are studied under both the APS (Atiyah-Patodi-Singer) and the chiral bag boundary conditions, where bounded domains are an interval, a disk, and a ball, respectively, and where mass is treated as a parameter ranging over all real numbers.
Discrete symmetry of the boundary condition and the Hamiltonian are discussed to explain the symmetry observed in the pattern of change in eigenvalues against the parameter.
Related topics will be touched upon, including topological insulator in quantum physics.
This talk is based on joint works with B. Zhilinskii at Université du Littoral Côte d’Opale.

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