This volume contains the proceedings of the AMS Special Session on Higher Structures in Topology, Geometry, and Physics, held virtually on March 26-27, 2022.
The articles give a snapshot survey of the current topics surrounding the mathematical formulation of field theories. There is an intricate interplay between geometry, topology, and algebra which captures these theories. The hallmark are higher structures, which one can consider as the secondary algebraic or geometric background on which the theories are formulated. The higher structures considered in the volume are generalizations of operads, models for conformal field theories, string topology, open/closed field theories, BF/BV formalism, actions on Hochschild complexes and related complexes, and their geometric and topological aspects.
Boris Tsygan, On noncommutative differential forms
Manuel Rivera, An algebraic model for the free loop space
Yang Mo, The structure of simply colored coalgebras
Ivan Contreras, Adele Long, Sophia Marx, and Rajan Amit Mehta, On examples
and classification of Frobenius objects in Rel
Benjamin C. Ward, Stirling decomposition of graph homology in genus 1
Ralph M. Kaufmann and Javier Zuniga, A combinatorial model for the moduli of
bordered Riemann surfaces and a compactification
Michael Monaco, Calculations for plus constructions
Philip Hackney, Segal conditions for generalized operads
Daniel A. Ramras, The topological Atiyah-Segal map
Arun Debray, Bordism for the 2-group symmetries of the heterotic and CHL
strings
Emil Hossjer, Philippe Mathieu, and Frank Thuillier, Generalized abelian
Turaev-Viro and U(1) BF theories
Ralph M. Kaufmann, Purdue University, West Lafayette, IN.
Martin Markl, Czech Academy of Sciences, Prague, Czech Republic.
Alexander A. Voronov, University of Minnesota, Minneapolis, MN.
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