FEYNMAN MOTIVES

Focusing on the intricate relationship between Feynman integrals in quantum field theory and algebraic varieties, this book explores whether residues of these integrals correspond to periods of mixed Tate motives. It presents two approaches: a "bottom-up" method that constructs algebraic varieties from Feynman graphs, and a "top-down" approach comparing renormalization data with mixed Tate motives. The text connects these perspectives and outlines ongoing research, serving as a resource for researchers and graduate students in mathematical physics, number theory, and algebraic geometry.