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, which 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 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]].
M. Benini, P. Safronov and A. Schenkel, Classical BV formalism for group actions, Commun. Contemp. Math. 25, no. 01, 2150094 (2023) [arXiv:2104.14886 [math-ph]].
M. Benini, J. P. Pridham and A. Schenkel, Quantization of derived cotangent stacks and gauge theory on directed graphs, Adv. Theor. Math. Phys. 27, no. 5, 1275-1332 (2023) [arXiv:2201.10225 [math-ph]].
C. Kemp, R. Laugwitz and A. Schenkel, Infinitesimal 2-braidings from 2-shifted Poisson structures, arXiv:2408.00391 [math.QA].
M. Benini, T. Fernàndez and A. Schenkel, Derived algebraic geometry of 2d lattice Yang-Mills theory, arXiv:2409.06873 [math-ph].
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