What Perturbative Field Theory Teaches Us About Statistical Analysis

Explore a thought-provoking lecture on the intersection of particle physics, statistical mechanics, and functional analysis. Delve into the surprising applications of Feynman diagrams and integrals beyond their traditional domains. Discover how perturbative field theory techniques can be applied to the Optimal Transportation Problem, offering new insights and results. Examine the challenges of dealing with infinities and divergences across different fields, and learn why naive approaches fail while more sophisticated methods succeed in resolving apparent contradictions. Gain a deeper understanding of the connections between seemingly disparate areas of mathematics and physics through this 57-minute talk by Andrea Sportiello from Paris-North University, LIPN, presented at the Institut des Hautes Etudes Scientifiques (IHES).