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