March 7, 2024

SPEAKER:   Sarah Plosker, Associate Professor & Canada Research Chair, Brandon University

(Learn more about the speaker here)

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TITLE:   "Generalized Hadamard Matrices, Graphs Diagonalized by Such Matrices, and Quantum State Transfer"

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ABSTRACT:   A Hadamard matrix $H \in\mathcal{M}_n$ is a matrix whose entries are either 1 or -1 and satisfies $H^T H=n I$.  A recent generalization of this definition is the notion of a weak Hadamard matrix: a $\{-1,0, 1\}$-matrix $P$ such that $PP^T$ is tridiagonal. We further generalize to consider either $\{-1,0,1\}$- or $\{-1,1\}$-valued matrices, with various generalized orthogonality conditions so that $PP^T$ is banded. Combinatorial and algebraic properties of these matrices are considered. 

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Graphs whose Laplacian matrix is diagonalized by a Hadamard matrix have been of interest in recent years, and in particular have been studied for their quantum state transfer abilities. We therefore consider graphs whose Laplacian matrix is diagonalized by a weak Hadamard matrix, in relation to quantum state transfer. We provide a complete list of all simple, connected graphs on nine or fewer vertices that are $\{-1,0,1\}$- or $\{-1,1\}$-diagonalizable.

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TIME:  All in the Central Time Zone

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Meet and Greet:

• 2:00pm-2:30pm CST

​Talk:

• 2:30pm-3:20pm CST 

Questions:

• 3:20pm-3:30pm CST

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LOCATION:

The event will take place via Zoom.

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ZOOM LINK:   https://umanitoba.zoom.us/j/65198628181?pwd=S3M3eURZK21XT3psYU1nYWkvd1p5dz09

Meeting ID:   651 9862 8181

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Passcode:  443969