Fourier Analysis on Graphs

Although generally having no group structure, functions defined on the vertices of undirected graphs have a Fourier-like transform in which the complex exponentials/characters/representations are replaced by eigenfunctions of the graph Laplacian. After reviewing the basics of Fourier analysis on Euclidean space and locally compact abelian groups, we will explore several topics in spectral graph theory, especially those associated with applications in signal processing and analysis. In particular, the spectral properties of large graphs compare to those of its subgraphs.

Aditya Joshi

The University of Newcastle

Aditya Joshi is a 20-year-old in his second year at the University of Newcastle studying a Bachelor of Mathematics and Computer Science. He is currently majoring in pure mathematics and has a keen interest in topics such as Graph Theory, Complex Analysis and Analytic Number Theory. He has been studying graph theory under the supervision of a highly-qualified professor at Newcastle since 2017. Ensuing Aditya’s undergraduate studies he plans to commit himself to postgraduate studies and research in the area of pure mathematics.

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