Identifiability of Points and Rigidity of Hypergraphs under Algebraic Constraints

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• Fatemeh Mohammadi (KU Leuven)
• Tuesday 23 January 2024, 14:15-15:15
• Seminar Room 1, Newton Institute.

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I will present a new general framework aimed at addressing the identifiability problem arising from algebraic relations with a combinatorial structure. Additionally, I will introduce recent tools designed to analyze how the underlying combinatorial aspects impact the local or global identifiability of points. This framework is constructed within the context of graph rigidity, utilizing Euclidean distances as measurements between two points, and extends its applicability to hypergraphs with arbitrary algebraic measurements. I will illustrate necessary and sufficient conditions for identifiability by employing techniques derived from graph rigidity theory and the algebraic geometry of secant varieties. Furthermore, I will present a combinatorial analysis examining the effects of non-generic projections of secant varieties.This talk is based on recent work (https://arxiv.org/abs/2305.18990) joint with James Cruickshank (National University of Ireland Galway, Ireland), Anthony Nixon (Lancaster University, UK), and Shin-ichi Tanigawa (Tokyo University, Japan).

This talk is part of the Isaac Newton Institute Seminar Series series.

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