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String field theory, BV quantization, and moduli spaces: May 20 – 24, 2019

Organized by Kenji Fukaya, Owen Gwilliam, Stephan Stolz, Peter Teichner, and Mahmoud Zeinalian.

The main aim of this workshop is to strengthen the dialogue between string field theory and quantum field theory, via the shared language of the BV formalism. The BV formalism plays an increasingly important role in the mathematical treatment of QFT, as showcased by the recent work of Cattaneo-Mnev-Reshetikhin and Costello-Gwilliam. There is also an improved understanding of the natural homotopical algebra in topological string theory, as in the work of Cieliebak-Fukaya-Latschev, where BV algebras also play a prominent role.

This dialogue informs, and is informed by, several closely related activities. On the side of topological string theory, there is topological recursion and its recent refinement to geometric recursion. Moreover, Lurie’s proof of the Cobordism Hypothesis in two dimensions clarifies many mathematical aspects of topological string theory. On the side of field theory, recent work on BCOV theory provides a BV perspective on large N limits of gauge theories and its relationship with string field theory. It suggests that methods from higher category theory and higher algebra might apply to large N limits through the medium of factorization algebras. Finally, a new relationship between factorization algebras and functorial field theories offers a perspective on how these developments fit together.