Modul: MAT752 Advanced Topics in Field Theory

• February 19, Giovanni Canepa
   Double BFV quantisation and application to 3d Gravity 
  
  In this talk I will extend the cohomological setting developed by Batalin, Fradkin and Vilkovisky (BFV), which produces a resolution of coisotropic reduction in terms of hamiltonian dg manifolds, to the case of nested coisotropic embeddings inside a symplectic manifold.  We will show that the data of a nested coisotropic embedding defines a natural graded coisotropic embedding, whose reduction can further be resolved using the BFV prescription. I will call this construction double BFV resolution, and I will use it to prove that "resolution commutes with reduction" for a general class of nested coisotropic embeddings. As an application, I will provide a well defined candidate space of (physical) quantum states of three-dimensional Einstein--Hilbert theory, which is thought of as a partial reduction of the Palatini--Cartan model for gravity.This talk is a based on arXiv:2410.23184,a joint work with Michele Schiavina.
  
  
  
  
• February 26, Orev Malatesta
  

  Gravity as a BV Pushforward of BF theory

  BV pushforward is a systematic way of integrating out degrees of freedom in a BV theory, yielding an effective field theory that retains a BV description. Motivated by the structural similarity between BF theory and Palatini-Cartan gravity, one can investigate whether Palatini-Cartan gravity can arise as an effective theory obtained from a suitable BF model.

  After presenting the BV pushforward construction in general terms, I will introduce a BF theory based on a Lie algebra given by a quadratic extension of so(3,1) by an orthogonal module, together with its BV extension. I will then perform the BV pushforward in this setting, which produces a (non-canonical) BV extension of Palatini-Cartan gravity, and discuss the problems that arise.
  
  
  

• March 19, Francesco Bonechi
  
  
  
• April 2, Marius Furter
  
  Sequential Monte Carlo in String Diagrams
  
  Sequential Monte Carlo (SMC) algorithms, also known as particle filters, iteratively infer hidden states in state-space models by maintaining a system of interacting weighted particles. In this talk, I demonstrate how abstractions from Category Theory can be used to derive, reason about, and generalize SMC. First, I introduce the category of s-finite kernels, which allows us to build and manipulate probability models using string diagrams. I then explain how this category is extended with weights via a monadic construction. Finally, I illustrate how the resulting structure facilitates intuitive reasoning about SMC algorithms.