Derived algebraic geometry in mathematical physics
Project description
Derived algebraic geometry is a powerful geometric framework which plays an increasingly important role in both the foundations of algebraic geometry and in mathematical physics. It introduces a refined concept of "space", the so-called derived stacks, that is capable to describe correctly geometric situations that are problematic in traditional approaches, such as non-transversal intersections and quotients by non-free group actions.
This project is about applying the novel techniques of derived algebraic geometry to simple problems in mathematical physics, with a particular focus on shifted Poisson geometry and deformation quantization.
Project published references
- T. Pantev, B. Toën, M. Vaquié and G. Vezzosi, Shifted symplectic structures, Publ. Math. Inst. Hautes Études Sci. 117, 271-328 (2013) [arXiv:1111.3209 [math.AG]].
- D. Calaque, T. Pantev, B. Toën, M. Vaquié and G. Vezzosi, Shifted Poisson structures and deformation quantization, Journal of Topology 10(2), 483-584 (2017) [arXiv:1506.03699 [math.AG]].
- J. P. Pridham, Deformation quantisation for unshifted symplectic structures on derived Artin stacks, Sel. Math. New Ser. 24, 3027-3059 (2018) [arXiv:1604.04458 [math.AG]].
- M. Benini, P. Safronov and A. Schenkel, Classical BV formalism for group actions, Communications in Contemporary Mathematics [arXiv:2104.14886 [math-ph]].
- M. Benini, J. P. Pridham and A. Schenkel, Quantization of derived cotangent stacks and gauge theory on directed graphs, arXiv:2201.10225 [math-ph].
More information
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