Constantin Teleman: Quantization commutes with reduction: The quantum GIT conjecture #ICBS2024

“Quantization commutes with reduction” has been a recurring theme in the persistence of symmetries, in the mathematical transition from classical to quantum systems. The original results were obtained by Guillemin and Sternberg, for the geometric quantization of compact group actions on Kaehler manifolds, and by Kirwan for the topological study of the same. Categorical enhancements, from quantum mechanics to 2-dimensional QFT, were obtained for the $2$-dimensional B-model) by Halpern-Leistner and (independently) Ballard, Favero and Katzarkov. I will report on the latest results in this series, comparing the gauged and symplectic-reduced 2-dimensional A-models. The new results give complete agreement of quantum cohomologies in the monotone (Fano) case, and partial results, and intriguing conjectures more generally. This is joint work with Daniel Pomerleano.