T-Minkowski Noncommutative Spacetimes

Explore a detailed lecture on T-Minkowski noncommutative spacetimes presented by Flavio Mercati at the Centre International de Rencontres Mathématiques. Discover a class of Hopf algebras called T-Poincaré, representing simple quantum group deformations of the Poincaré group at small scales and high energies. Learn how these models arise from classical r-matrices on the Poincaré group, leading to 16 multiparametric models. Understand how each T-Poincaré model admits a canonical 4-dimensional quantum homogeneous spacetime (T-Minkowski) that unifies established non-commutative spacetimes like Moyal, lightlike κ-Minkowski, and ρ-Minkowski. Examine the mathematical structures necessary for field theory on these spaces, including differential and integral calculus, noncommutative Fourier theory, and braided tensor products. Consider the challenges of describing Standard Model fields within this framework and developing quantum field theory while preserving Special Relativity principles with noncommutativity length scale. This 48-minute recording from the thematic meeting "Applications of NonCommutative Geometry to Gauge Theories, Field Theories, and Quantum Space-Time" (April 2025) is available with chapter markers, keywords, abstracts, and bibliographies on CIRM's Audiovisual Mathematics Library.