A Berkovich space is a type of analytic space over a non-Archimedean field. The Berkovich 1-dimensional line can be constructed as an inverse limit of finite rooted trees. In joint work with Masoud Khalkhali, we construct several spectral triples on the Berkovich line and investigate associated quantum mechanical systems. The KMS states allows us to recover the Patterson-Sullivan measure and the Canonical measure on the Berkovich projective line. One can then use these spectral triples to study the dynamics of rational maps with coefficients in non-Archimedean fields.

Bio: Damien Tageddine is a French and Canadian mathematician. Damien has recently (summer 2023) earned his Ph.D. from McGill University, under the supervision of Jean-Christophe Nave. His thesis titled 'Noncommutative Geometry on Infinitesimal Spaces' explores a possible bridge between the foundations of computational mathematics and noncommutative geometry.