Seminar on BV formalism Spring 2022

In the Spring 2022 I am running a PhD Seminar on the Batalin-Vilkovisky formalism.

The main reference we are following are the lecture notes by Pavel Mnev "Lectures on Batalin-Vilkovisky formalism and its applications in topological quantum field theory" available on the arXiv. They were also published by the AMS, see here .

Talks

  • Talk 1, February 8: Konstantin Wernli - Introduction to BV formalism

  • Talk 2, February 15: Zhongyu Zhang - Introduction to Super- and Z-graded manifolds (Sections 4.2.1, 4.2.2 in [1], see also [2],[3])

  • Talk 3, February 22 Santiago Rios - Integration and Vector fields on Supermanifolds (Sections 4.2.3 - 4.2.6 in [1], see also [2])

  • Talk 4, March 1: Chris Kuo - Odd symplectic geometry (Sections 4.4.1, 4.4.2 in [1], see also [4])

  • Talk 5, March 8: Chris Kuo - Odd symplectic geometry (Sections 4.4.3, 4.4.4 in [1], see also [4])

  • March 15: NO TALK due to illness

  • Talk 6, March 22: Konstantin Wernli - Fiber BV integrals, BV formalism (Sections 4.7, 4.8 in [1])

  • Talk 7, March 29: Tim Henke, BV algebras (Section 4.5 in [1])

  • April 5: External Speaker: Alberto Cattaneo

  • Talk 8, April 12: Ikshu Neithalath - BV formalism with half-densities (Section 4.6 in [1], see also [5],[6])

  • April 19: External Speaker: Pavel Mnev

  • April 26

  • May 3

  • May 10

  • May 17: External Speaker: Ivan Contreras

  • May 24

  • May 31

Notes

In these notes I am collecting the results of some discussions that I found interesting during the seminar.

References

[1] P. Mnev, "Lectures on Batalin-Vilkovisky formalism and its applications in topological quantum field theory", https://arxiv.org/abs/1707.08096

[2] S. Noja, "On the geometry of forms on supermanifolds", https://arxiv.org/abs/2111.12841

[3] J. Vysoky, "Global Theory of Graded Manifolds", https://arxiv.org/abs/2105.02534

[4] A. Schwarz, "Geometry of Batalin-Vilkovisky quantization", https://arxiv.org/abs/hep-th/9205088

[5] H. M. Khudaverdian, "Semidensities on odd symplectic supermanifolds", https://arxiv.org/abs/math/0012256

[6] P. Severa, "On the origin of the BV operator on odd symplectic supermanifolds", https://arxiv.org/abs/math/0506331