Alternatively have a look at the program.

## Polyak section 1.1-2.3. Preliminaries on classical and quantum field theories, Feynman diagrams in finite dimension (n-point functions and Wick theorem)

## Polyak section 2.4-2.10. Adding a potential, cubic potential, general Feynman graphs, weights for graphs, free energy.

## Polyak sections 3.1-3.3. Gauge fixing, Faddeev-Popov ghost, Cattaneo section 12.2. BRST cohomology

## Chern-Simons theory for knots and matrix models

## BRST Cohomology

## Basics of the BV formalism

The Batalin-Vilkovisky (BV) formalism can be seen as a generalisation of the BRST cohomological methods to handle field theories with symmetries. In this talk I will give an introduction to the basics of this formalism, trying to recover what we already know and hinting at why this is a useful generalisation.

## An example of BV quantization in action

The purpose of this talk is to survey the machinery developed

by Costello, with an emphasis on the procedure by which one starts with

an action functional and ends up with higher algebraic structure at the

end. The running example will take as input the curved beta-gamma

system, a 2d sigma model of maps from a Riemann surface to a complex

manifold. I will sketch how to construct its BV quantization and how to

analyze its factorization algebra, which determines a sheaf of vertex

algebras known as "chiral differential operators." The talk aims to be

## Basics of the BV formalism - Part 2

If the Batalin-Vilkovisky formalism is a cohomological handle for field theories in the Lagrangian formalism, a similar construction can be set up for the associated Hamiltonian picture and goes under the name of Batalin, Fradkin and Vilkovisky (BFV).

The link between the two has been made explicit recently by Cattaneo, Mnev and Reshetikhin (CMR) as a tool to treat field theories on manifolds with boundary.

In this talk I will review the basics of the BFV and CMR constructions and show how they relate to what we have done so far.

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