Matilde Marcolli Bücher

Focusing on the intersections of modern art, mathematics, and physics, the book delves into themes such as space, randomness, and the cosmos. Matilde Marcolli, a mathematical physicist, connects these concepts to the works of renowned artists like Paul Cezanne and Mark Rothko. Through her scientific inquiries, she highlights the shared puzzles of the universe, supported by over two hundred color images of modern and contemporary art, creating a rich dialogue between disciplines.

This volume features research and survey articles from the 2006 Istanbul conference on Arithmetic and Geometry around Quantization. It explores various topics in quantization, including symplectic geometry, representation theory, and quantum groups, showcasing contributions from leading mathematicians and highlighting potential new research directions.

This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differential-geometric approaches. It also covers recent developments in Noncommutative Geometry, which have close relations to quantization and quantum group symmetries. The volume collects surveys by experts which originate from an acitvity at the Max-Planck-Institute for Mathematics in Bonn.

The book explores the intricate relationship between Feynman integrals in quantum field theory and the theory of motives in algebraic geometry. It addresses the pivotal question of when the residues of these integrals correspond to periods of mixed Tate motives, stemming from earlier observations of multiple zeta values. Two distinct methodologies are examined: a "bottom-up" approach that constructs algebraic varieties from Feynman graphs, and a "top-down" approach that compares renormalization data with Tannakian categories of mixed Tate motives. The text also highlights ongoing research and connections to various mathematical fields.

Focusing on modified gravity models, this book introduces a unique approach utilizing noncommutative geometry, particularly the spectral action functional. It explores applications in early universe scenarios, slow-roll inflation, cosmic topology, and non-isotropic cosmologies such as mixmaster universes and Bianchi IX gravitational instantons. Additionally, it delves into the implications of multifractal structures in cosmology, offering a comprehensive examination of contemporary theoretical frameworks in the field.