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Workshop

Identifiability of points and rigidity of graphs in applied algebraic geometry

Felix-Klein-Hörsaal Universität Leipzig (Leipzig)

Abstract

The identifiability problem arises naturally in various mathematical and computer science domains. Specific instances include local or global rigidity of graphs and the unique completability of partially-filled tensors with some rank conditions. The identifiability of points on secant varieties has also been studied in algebraic geometry, often formulated as the problem of identifying a set of points satisfying prescribed algebraic relations. A central question is then to establish conditions under which these relations guarantee the identifiability of points. I will explain a new framework designed to address the identifiability problem within the realm of algebraic relations with combinatorial structures. I will show how the underlying combinatorics influence the local or global identifiability of points. Our framework, rooted in the language of graph rigidity, where measurements are Euclidean distances between two points, is applicable in the generality of hypergraphs with arbitrary algebraic measurements. We establish necessary and sufficient (hyper)graph conditions for identifiability by exploiting techniques from graph rigidity theory and algebraic geometry of secant varieties.

This talk is based on multiple joint projects: (a) with James Cruickshank, Anthony Nixon, and Shin- ichi Tanigawa, and (b) with Sean Dewar, Georg Grasegger, Kaie Kubjas, and Anthony Nixon

Links

conference
29.07.24 02.08.24

MEGA 2024

MPI für Mathematik in den Naturwissenschaften Leipzig (Leipzig) E1 05 (Leibniz-Saal)
Universität Leipzig (Leipzig) Felix-Klein-Hörsaal

Mirke Olschewski

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Saskia Gutzschebauch

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Christian Lehn

Ruhr-Universität Bochum

Irem Portakal

Max Planck Institute for Mathematics in the Sciences

Rainer Sinn

Universität Leipzig

Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences

Simon Telen

Max Planck Institute for Mathematics in the Sciences