Quantization Commutes with Reduction: The Quantum GIT Conjecture - ICBS 2024

Explore the latest developments in the "Quantization commutes with reduction" theme, focusing on the persistence of symmetries in the transition from classical to quantum systems. Delve into the original results by Guillemin, Sternberg, and Kirwan for compact group actions on Kaehler manifolds. Examine categorical enhancements in quantum mechanics and 2-dimensional QFT, including the work of Halpern-Leistner, Ballard, Favero, and Katzarkov on the 2-dimensional B-model. Discover the most recent findings comparing gauged and symplectic-reduced 2-dimensional A-models, with complete agreement of quantum cohomologies in the monotone (Fano) case. Investigate partial results and intriguing conjectures in this field, based on joint work with Daniel Pomerleano. This one-hour and five-minute lecture, presented by Constantin Teleman at BIMSA, offers an in-depth look at the quantum GIT conjecture and its implications for mathematical physics.