This U.S.-Czech mathematics project is a cooperative effort between Thomas Lada at North Carolina State University and James Stasheff of the University of North Carolina with their counterpart in Prague, Martin Markl at the Mathematical Institute of the Czech Academy of Sciences. Their goal is to clarify the homotopy invariance properties of various algebraic structures. To do so they intend to utilize operads to study the question of homotopy invariance in several algebraic settings. While homotopy invariant structures in the topological setting have been well studied, similar questions in algebraic settings still require attention. The problems to be investigated by this U.S.-Czech team deal with the category of strongly homotopy algebras and their homotopy theoretic properties. If successful, their investigation will integrate these ideas with several sophisticated algebraic structures that arise in mathematical physics. Results should improve the theoretical underpinning for cross-disciplinary advances in perturbation theory and deformation quantization.
This international project in topology fulfills the program objective of advancing scientific knowledge by enabling experts in the United States and Central Europe to combine complementary talents and share research resources in areas of strong mutual interest and competence.
