Derived geometry and quantization

Bertrand Toën
Monday, July 22, 2013 - from 11:00 to 12:00
In this lecture I will report on recent progress on interactions between on the one hand derived algebraic geometry and on the other hand the quantum world (quantum group, deformation quantization ...). For this, I will start by presenting a theorem, stating that the derived moduli spaces of G-bundles on oriented manifolds have canonical quantization. An important part of the lecture will be devoted to explain this result in more details: to make precise the various notions and explain its relations with previously known results and concepts (quantum groups, quantum invariants of manifolds, hypersurface singularities ...). Finally, I will say few words about its proof and its possible future applications.