Opening

Comments on selected aspects of the antifield formalism

• Marc Henneaux (International Solvay Institutes, Belgium)

Fedosov product on differential forms and flat connections on differential graded manifolds

• Ezra Getzler (Northwestern University, USA)

The Hochschild-Kostant-Rosenberg theorem relates negative cyclic homology of the functions on a differential graded manifold M to the de Rham complex of M. The natural A-infinity structure on negative cyclic homology corresponds to an A-infinity structure on the de Rham complex called the Fedosov product. (This product agrees with the usual one if either argument is closed, but it is not graded symmetric in general.) In this talk, we study the analogue of flat connections for this product: these are in bijection with flat connections for the usual product on the classical locus but appear to be different in general. The non-commutative analogue of the Gauss-Manin connection is our main example.

$L_\infty$ morphisms for higher BV operators

• Ted Voronov (Manchester University, UK)

I will introduce classical and quantum "thick morphisms" of supermanifolds. These are differential-geometric constructions that provide L-infinity morphisms for homotopy analogs of Poisson brackets; in particular, for homotopy brackets generated by higher-order Batalin-Vilkovisky type operators. They generalize ordinary smooth maps of supermanifolds with pullbacks on functions that are non-linear maps.

Generalized connections for Courant algebroid in sigma models and gravity

• Larisa Jonke (Rudjer Boskovic Institute, Zagreb)

Covariant phase space and $L_\infty$ algebras

• Ted Erler (Institute of Physics of the Czech Academy of Sciences)

Motivated by the problem of giving a Hamiltonian description of nonlocal field theories such as string field theory, we propose a formula for the phase space symplectic structure of a generic Lagrangian field theory expressed in BV form.

My interaction with Igor Batalin

• Klaus Bering (Masaryk University, Brno)

BV pushforward and applications

• Alberto Cattaneo (University of Zurich, Switzerland)

In the BV formalism the spaces of fields are presented as complexes whose cohomology returns the physical content. Different but equivalent complexes may be used, which turns out to be important conceptually and in practice. One useful operation is that of a partial integration (BV pushforward), which produces a chain map that, under some assumptions, is a quasiisomorphism. This has several applications: construction of observables (often as $L_\infty$ representations), renormalization à la Wilson, highly nontrivial equivalences of theories. I will discuss some examples.

BV quantization in topological/holomorphic QFT

• Si Li (Tsinghua University, China)

We discuss BV quantization that arises from topologically/holomorphically twisted quantum field theory. We illustrate some applications in topological/chiral algebraic index, topological B-model and mirror symmetry.

Complete sets of invariant fields in gauge theories and gravity from purely virtual particles

• Damiano Anselmi (University of Pisa, Italy)

Correlation functions and the homological perturbation lemma

• Richard Szabo (Heriot-Watt University, Edinburgh, UK)

Homotopy Algebra Perspective on Quantum Field Theory

• Martin Wolf (University of Surrey, UK)

I will review recent progress on understanding perturbative quantum field theory within the realm of homotopy algebras.

Poster session

Non-topological boundary conditions of perturbative Chern-Simons and AKSZ models

• Pavol Severa (University of Geneva, Switzerland)

In Witten's CS/WZW correspondence the chiral WZW model appears from the chiral boundary condition imposed on the CS theory. I will describe how similar boundary conditions (mixed chiral-antichiral) of the CS theory and of its AKSZ analogs produce many other interesting examples and how they explain, in particular, Poisson-Lie T-duality. Unlike the CS/WZW correspondence, this generalization is at the moment only perturbative; on the other hand, the perturbative renormalization leads quickly to the (generalized) Ricci tensor and hopefully still hides many interesting things. The calculation is done using the Batalin-Vilkovisky method and the main tool is a CS propagator compatible with the chiral boundary conditions. Based on joint works with J. Pulmann, F. Valach, and D. Youmans.

Gauge fixing in coset spaces and supergravities

• Antoine Van Proeyen (KU Leuven, Belgium)

BV actions for extended geometry

• Martin Cederwall (Chalmers University of Technology, Gothenburg, Sweden)

TBA

• Alexey Kotov (Hradec Králové University, Czech Republic)

TBA

Geometry of Dirac-BFV quantization and quantum cosmology

• Andrei Barvinsky (Lebedev Physics Institute, Moscow, Russia)

A BV field theory from super moduli space

• Ivo Sachs (Ludwig Maximilian University of Munich, Germany)

The BRST quantisation of the relativistic spinning particle pulls the path integral back to ist (super) moduli space and thereby interpolates between the space-time BV action and the BV-equation on super moduli space. This is perhaps the simplest toy model of super string field theory.

From Gauge Theories to the octonionic Lie groupoid.

• Thomas Strobl (Claude Bernard University Lyon, France)

We first review how one can turn the standard sigma model in to a gauge theory and under what conditions. This leads us to the notion of singular Riemannian foliations (SRFs) and equivalence of gauge theories leads to Morita equivalence of SRFs. This leads one looking at the octonionic singular foliation on R^16. In this talk we provide a Lie groupoid generating this foliation and show that it has the minimal possible dimension.

Monopoles, Dirac Strings and Generalised Symmetries

• Chris Hull (Imperial College London, UK)

Color-kinematics duality in BV formalism

• Maxim Zabzine (Uppsala University, Sweden)

On some applications of Igor’s work in String Theory

• Samson Shatashvili (Trinity College Dublin, Ireland)