Higher structures in topology, geometry, and physics / edited by Ralph M. Kaufmann, Martin Markl, and Alexander A. Voronov.

Includes bibliographical references.

Noncommutative differential forms -- Algebraic models for free loop spaces -- Colored coalgebras -- Frobenius objects -- Graph homology -- Moduli of bordered Riemann surfaces -- Segal conditions for generalized operads -- Topological Atiyah-Segal maps -- Bordism and field theories.

This volume contains research papers presented at the AMS Special Session on Higher Structures in Topology, Geometry, and Physics held virtually in March 2022. The collection explores contemporary developments in the mathematical formulation of field theories through the interaction of topology, geometry, algebra, and mathematical physics. Topics discussed include operads, string topology, conformal and open-closed field theories, Hochschild complexes, graph homology, Frobenius structures, bordism theory, BF/BV formalism, and generalized algebraic and geometric structures underlying modern theoretical physics. The contributions highlight the role of higher categorical and homotopical methods in understanding complex mathematical and physical systems. Intended for advanced students and researchers, the volume provides an overview of current trends and interdisciplinary research at the intersection of topology, geometry, algebra, and quantum field theory.