Derived deformation quantization and perturbative skein theory

Short description

This proposal is about applying a modern “higher algebraic” perspective on topological field theories and deformation quantization to explicitly solve concrete problems in various areas of mathematics. It relies in particular on the PI’s recent result, built on the toolbox he developed with his coauthors, which solves the long standing problem of writing down explicit formulas for higher genus analogs of so-called Drinfeld associators. We will apply these techniques to: prove foundational results in derived deformation quantization, with application to the theory of Lie bialgebra and to string topology, simplify and extend the construction of a universal perturbative 3 dimensional TFT, and to develop a higher genus analog of Grothendieck-Teichmüller theory.

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