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Lie群論・表現論セミナー
過去の記録 ～04/20｜次回の予定｜今後の予定 04/21～
| 開催情報 | 火曜日 16:30～18:00 数理科学研究科棟(駒場) 126号室 |
|---|---|
| 担当者 | 小林俊行 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html |
2026年04月28日(火)
16:00-17:00 数理科学研究科棟(駒場) 128号室
Khalid Koufany 氏 (University of Lorraine)
Geometric Means that preserve sparsity on homogeneous cones
(English)
Khalid Koufany 氏 (University of Lorraine)
Geometric Means that preserve sparsity on homogeneous cones
(English)
[ 講演概要 ]
This talk starts from a simple question: how can one define a geometric mean for sparse positive definite matrices without destroying their zero pattern?
For the arrowhead pattern, this leads naturally to the five-dimensional Vinberg cone, a basic non-symmetric homogeneous cone.
I will present two intrinsic means on this cone: a Cholesky-Vinberg mean built from triangular Cholesky factors, and a logarithmic Vinberg mean built from global clan (Vinberg algebra) coordinates.
The first is tied to a flat affine geometry with torsion, while the second belongs to a torsion-free flat geometry.
I will also explain why these means differ from the classical Riemannian midpoint and why this difference is a genuinely non-symmetric phenomenon.
If time permits, I will give an application to quantum information theory.
This talk starts from a simple question: how can one define a geometric mean for sparse positive definite matrices without destroying their zero pattern?
For the arrowhead pattern, this leads naturally to the five-dimensional Vinberg cone, a basic non-symmetric homogeneous cone.
I will present two intrinsic means on this cone: a Cholesky-Vinberg mean built from triangular Cholesky factors, and a logarithmic Vinberg mean built from global clan (Vinberg algebra) coordinates.
The first is tied to a flat affine geometry with torsion, while the second belongs to a torsion-free flat geometry.
I will also explain why these means differ from the classical Riemannian midpoint and why this difference is a genuinely non-symmetric phenomenon.
If time permits, I will give an application to quantum information theory.
