Special Session 33

Spectral Graph Theory

Organizers: Francesco Belardo (University of Naples “Federico II”, Italy), Vilmar
Trevisan (Federal University of Rio Grande do Soul, Brazil)

MSC codes: 05C50

Description:

Spectral graph theory studies how eigenvalues, eigenvectors, and other linear-algebraic quantities associated with graphs can be used to extract meaningful structural and dynamical information. Spectral methods provide insights into fundamental graph properties such as connectivity and expansion, the quality of vertex partitions or colourings, and the mixing behaviour and convergence rates of random walks and diffusion processes. Beyond its deep theoretical foundations in algebraic combinatorics and graph theory, spectral techniques also play an important role in applications ranging from computer science and optimisation to data analysis and network science. Spectral graph theory is a well-established and actively developing research area within the mathematical community, with strong research groups in several universities in Italy and Brazil. These groups contribute to both the theoretical advancement of the field and the development of applications in related areas. This Special Session aims to bring together researchers working on spectral graph theory and its applications, including both established and early-career mathematicians, in order to exchange new ideas, techniques, and recent results. By fostering interactions between Italian and Brazilian researchers, the session seeks to stimulate discussion on current trends and open problems in spectral graph theory and related fields, encourage new collaborations, and strengthen long-term scientific cooperation. More broadly, the session aims to enhance academic ties and promote enduring scientific friendships between the Italian and Brazilian mathematical communities.